Wikipedia tumwiki https://tum.wikipedia.org/wiki/Jani_likulu MediaWiki 1.47.0-wmf.18 first-letter Media Special Talk User User talk Wikipedia Wikipedia talk File File talk MediaWiki MediaWiki talk Template Template talk Help Help talk Category Category talk TimedText TimedText talk Module Module talk Event Event talk 0 6194 121863 46646 2026-09-09T08:33:14Z Anthonymunthali44 5642 121863 wikitext text/x-wiki {{Short description|Chigaŵa cha masamu}} {{About||the kind of algebraic structure|Algebra over a field|other uses}} {{pp-vandalism|small=yes}} {{Featured article}} {{Use mdy dates|date=August 2024 |cs1-dates=ly }} {{multiple image |perrow=1 / 1 |total_width=350 |image1=Polynomial2.svg |alt1=Polynomial equation: 2x^2 + 4x - 6 = 0 |link1=Polynomial equation |caption1=[[Elementary algebra|Algebra ya pulayimale]] yikusambira kuti ivyakuyaniska ivi vikuzirwa na vipimo vichi, ivyo vyakupangika mwakugwiliskira nchito za masamu. |image2=Ring of integers2.svg |alt2=Signature of the ring of integers |link2=Ring of integers |caption2=[[Abstract algebra|Algebra yakudumura]] yikusambira [[algebraic structure|magulu gha algebra]], nga umo mphete ya [[integer|vipendeko vyambura kugaŵika]] vikuchemeka <math>(\Z)</math> pamoza na [[Algebraic operation|nchito]] za [[addition|kusazga]] ({{tmath|1= + }}) na [[multiplication|kwandaniska]] ({{tmath|1= \times }}). }} '''Algebra''' ni chigaŵa cha [[mathematics|masamu]] icho chikukhwaskana na ndondomeko zambura kuwoneka, izo zikuchemeka [[algebraic structure|magulu gha algebra]], na kugwiriskira nchito mazgu mukati mwa ndondomeko izo (ivyo vikuchemeka [[Expression (mathematics)|viyelezgero]]). Ni kusazgirako kwa [[arithmetic|masamu ghakwamba]], icho chikwiza na [[Variable (mathematics)|vyambura-kumanyikwa]] na nchito zinyake padera pa nchito za masamu ghakwamba, nga [[addition|kusazga]] na [[multiplication|kwandaniska]]. [[Elementary algebra|Algebra ya pulayimale]] ndiyo nthowa yikuru ya algebra iyo yikusambizgika mu masukulu. Iwo ukusanda mazgu gha masamu mwakugwiliskira nchito vyakusintha vya vigaŵa vyambura kumanyikwa, na kukhumba kumanya kuti ni mikhaliro wuli iyo mazgu agha ghali ghaunenesko. Kuti ŵacite nthena, ŵakugwiriskira nchito nthowa zakupambana-pambana zakusinthira vyakuyaniska kuti ŵapature vinthu vyakusintha vya vigaŵa. [[Linear algebra|Algebra ya mzere]] ni chigaŵa chakukolerana chomene na algebra ya pulayimale, icho chikufufuza vyakuyaniska vya mzere na kunozgeka kwake, ivyo vikuchemeka ''[[system of linear equations|magulu gha vyakuyaniska vya mzere]]''. Chikupereka nthowa zakusanga vipimo ivyo vikwaniska vyakuyaniska vyose mu gulu pa nyengo yimoza, na kusambira gulu la vigaŵa ivi. <!-- paragraphs 1 and 2 are transcluded into [[Outline of algebra]] --> [[Abstract algebra|Algebra yakudumura]] yikusambira [[Algebraic structure|magulu gha algebra]], ivyo vikupangika na gulu la vinthu vya masamu pamoza na nchito yimoza panji zinandi izo zikulongosoreka pa gulu ilo. Ni kusazgirako kwa algebra ya pulayimale na ya mzere, chifukwa chikuzomerezga vinthu vinyake padera pa vipendeko na nchito zambura kuŵa za masamu ghakwamba. Chikupambaniska pakati pa mitundu yakupambana-pambana ya magulu gha algebra, nga [[Group (mathematics)|magulu]], [[Ring (mathematics)|mphete]], na [[Field (mathematics)|minda]], kuyana na unandi wa nchito izo zikugwiriskirika ntchito na madango agho ghakulondezgeka, ghakuchemeka [[axioms|madango ghakuzomerezgeka]]. [[Universal algebra|Algebra ya wonse]] na [[category theory|sambiro la mikhaliro]] vikupereka vipangiro vyakuwaneko kuti vifufuze vipimo vyambura kuwoneka ivyo vikulongosora magulu ghakupambana-pambana gha algebra. Nthowa za algebra zikasambika dankha mu [[ancient period|nyengo yakale]] kuti zithaske masuzgo ghapadera mu vigaŵa nga [[geometry]]. Ichi chikasintha mu vilimika vya m'ma 800 na [[Muḥammad ibn Mūsā al-Khwārizmī]], uyo wakanozga algebra kuŵa chigaŵa chakujipeleka cha masamu, chakupambana na geometry. Ŵasandi ŵakwamba ŵakalongosoranga vyakuyaniska na vyakuvitatuza mwakugwiliskira nchito mazgu na vifupikizgo, m'paka mu vilimika vya m'ma 1500 na 1600, apo nthowa yakukhwima ya viwimbo (symbols) yikapangika. Pakati pa vilimika vya m'ma 1800, uzelu wa algebra ukasazgirapo kuluska sambiro la vyakuyaniska pera na kusazgako mitundu yakupambana-pambana ya nchito na magulu gha algebra. Algebra yikukhwaskana na vigaŵa vinandi vya masamu, nga geometry, [[topology]], [[number theory|sambiro la vipendeko]], na [[calculus]], kweniso vigaŵa vinyake, nga [[logic]] na [[empirical sciences|kasandiro kakuzenga pa vyakuwonekera]]. == Ng'anamuro na Muko wa Lizgu == Algebra ni nthambi ya masamu iyo yikusambira magulu gha algebra na nchito izo ghakugwiliskira ntchito.<ref>{{multiref | {{harvnb|Merzlyakov|Shirshov|2020|loc=Lead section}} | {{harvnb|Gilbert|Nicholson|2004|p=[https://books.google.com/books?id=paINAXYHN8kC&pg=PA4 4]}} }}</ref> Gulu la algebra ni gulu la vinthu vya masamu ilo lilije kuŵa lambura kanthu, nga vipendeko vyambura kugaŵika, pamoza na nchito za algebra izo zikulongosoreka pa gulu ilo, nga kusazga na kwandaniska.<ref>{{multiref | {{harvnb|Fiche|Hebuterne|2013|p=[https://books.google.com/books?id=TqkckiuuXg8C&pg=PT326 326]}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ The Subject Matter of Algebra, Its Principal Branches and Its Connection with Other Branches of Mathematics.}} | {{harvnb|Gilbert|Nicholson|2004|p=[https://books.google.com/books?id=paINAXYHN8kC&pg=PA4 4]}} }}</ref>{{efn|When understood in the widest sense, an algebraic operation is a [[function (mathematics)|function]] from a [[Cartesian product#n-ary Cartesian power|Cartesian power of a set into that set]], expressed formally as {{tmath|1= \omega: A^n \to A }}. The addition of real numbers is an example of an algebraic operation: it takes two numbers as input and produces one number as output. It has the form {{nowrap|<math>+: \R^2 \to \R</math>.<ref>{{harvnb|Baranovich|2023|loc=Lead section}}</ref>}}}} Algebra yikufufuza malango, mikhaliro yose, na mitundu ya magulu gha algebra. Mu magulu ghanyake gha algebra, yikuwoneseska umo vinthu vyakusintha (vyambura-kumanyikwa) vikugwiriskirika ntchito mu vyakuyaniska na umo vingachitikira kuvisintha.<ref>{{multiref | {{harvnb|Pratt|2022|loc=Lead section, § 1. Elementary Algebra, § 2. Abstract Algebra, § 3. Universal Algebra}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ The Subject Matter of Algebra, Its Principal Branches and Its Connection with Other Branches of Mathematics.}} }}</ref>{{efn|Algebra is covered by division 512 in the [[Dewey Decimal Classification]]<ref>{{harvnb|Higham|2019|p=[https://books.google.com/books?id=ferEDwAAQBAJ&pg=PA296 296]}}</ref> and subclass QA 150{{hyphen}}272.5 in the [[Library of Congress Classification]].<ref>{{harvnb|Library of Congress|p=3}}</ref> It encompasses several areas in the [[Mathematics Subject Classification]].<ref>{{harvnb|zbMATH Open|2024}}</ref>}} Kanandi algebra yikupulikiskika kuŵa kusazgirako kwa [[arithmetic|masamu ghakwamba]].<ref>{{multiref | {{harvnb|Maddocks|2008|p=129}} | {{harvnb|Burgin|2022|p=[https://books.google.com/books?id=rWF2EAAAQBAJ&pg=PA45 45]}} }}</ref> Masamu ghakwamba ghakusambira nchito nga kusazga, [[subtraction|kuwuskapo]], kwandaniska, na [[Division (mathematics)|kugaŵa]], mu chigaŵa chinyake cha vipendeko, nga vipendeko vyaunenesko.<ref name="auto1">{{multiref | {{harvnb|Romanowski|2008|pp=302–303}} | {{harvnb|HC Staff|2022}} | {{harvnb|MW Staff|2023}} | {{harvnb|Bukhshtab|Pechaev|2020}} }}</ref> [[Elementary algebra|Algebra ya pulayimale]] njiyo mlingo wakwamba wa kudumuka. Nga umo masamu ghakwamba ghakucitira, yikujikanizga ku mitundu yinyake ya vipendeko na nchito. Yikusazgirapo nchito izi mwakuzomerezga unandi wambura kumanyikwa mu mtundu wa vyambura-kumanyikwa padera pa vipendeko.<ref>{{multiref | {{harvnb|Maddocks|2008|pp=129–130}} | {{harvnb|Pratt|2022|loc=Lead section, § 1. Elementary Algebra}} | {{harvnb|Wagner|Kieran|2018|p=[https://books.google.com/books?id=uW4ECwAAQBAJ&pg=PT225 225]}} }}</ref> Mlingo wapachanya wa kudumuka ukusangika mu [[abstract algebra|algebra yakudumura]], iyo yikumara yayi pa chigaŵa chinyake ndipo yikuwoneseska magulu gha algebra nga [[Group (mathematics)|magulu]] na [[Ring (mathematics)|mphete]]. Yikuluta kuluska nchito zamasamu ghakwamba mwakusazgaposo mitundu yinyake ya nchito.<ref>{{multiref | {{harvnb|Maddocks|2008|pp=131–132}} | {{harvnb|Pratt|2022|loc=§ 2. Abstract Algebra}} | {{harvnb|Wagner|Kieran|2018|p=[https://books.google.com/books?id=uW4ECwAAQBAJ&pg=PT225 225]}} }}</ref> [[Universal algebra|Algebra ya wonse]] njakudumura comenecomene chifukwa yikupulikira yayi magulu gha algebra ghapadera, kweni yikufufuza mikhaliro ya magulu gha algebra mwaunenesko.<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 3. Universal Algebra}} | {{harvnb|Grillet|2007|p=[https://link.springer.com/chapter/10.1007/978-0-387-71568-1_15 559]}} | {{harvnb|Denecke|Wismath|2018|p=[https://books.google.com/books?id=2UlZDwAAQBAJ&pg=PR5 v]}} | {{harvnb|Cohn|2012|p=[https://books.google.com/books?id=6tbuCAAAQBAJ&pg=PR13 xiii]}} }}</ref> [[File:Image-Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala.jpg|upright=.8|thumb|alt=Title page of The Compendious Book on Calculation by Completion and Balancing|Lizgu lakuti ''algebra'' likufuma ku mutu wa buku la [[al-Khwarizmi]] lakuti {{transliteration|ar|[[Al-Jabr]]}}.<ref>{{multiref | {{harvnb|Cresswell|2010|p=[https://books.google.com/books?id=J4i3zV4vnBAC&pg=PA11 11]}} | {{harvnb|OUP Staff}} | {{harvnb|Menini|Oystaeyen|2017|p=722}} }}</ref>]] Lizgu lakuti ''algebra'' nyengo zinyake likugwiriskirika ntchito mwakucepa kuti likung'anamurenge waka algebra ya pulayimale panji algebra yakudumura yekha.<ref>{{multiref | {{harvnb|Weisstein|2003|p=46}} | {{harvnb|Walz|2016|loc=[https://www.spektrum.de/lexikon/mathematik/algebra/12062 Algebra]}} }}</ref> Para likugwiriskirika ntchito nga zina lakuŵerengeka, algebra ni mtundu unyake wa gulu la algebra uwo ukukhwaskana na malo gha [[vector space|vector]] agho ghali na mtundu unyake wa nchito ya viŵiri viŵiri, iyo yikuchemeka [[bilinear map|nchito yakuŵiriska]].<ref>{{multiref | {{harvnb|Weisstein|2003|p=46}} | {{harvnb|Brešar|2014|p=[https://books.google.com/books?id=PkvPBAAAQBAJ&pg=PR33 xxxiii]}} | {{harvnb|Golan|1995|pp=[https://link.springer.com/chapter/10.1007/978-94-015-8502-6_18 219–227]}} }}</ref> Kulingana na umo vikuyowoyekera, algebra yingayowoyaso za vigaŵa vinyake vya algebra, nga [[Lie algebra]] panji [[associative algebra|algebra yakukolerana]].<ref>{{harvnb|EoM Staff|2017}}</ref> Lizgu lakuti ''algebra'' likufuma ku lizgu la Chiarabu lakuti {{lang|ar|الجبر}} ({{transliteration|ar|al-jabr}}), ilo pakwamba likang'anamuranga opareshoni yakuchizgira viwangwa. Mu vilimika vya m'ma 800 C.E., lizgu ili likaŵa na ng'anamuro la masamu apo [[Muhammad ibn Musa al-Khwarizmi]], uyo wakasambiranga masamu ku Persia, wakagwiriskira ntchito lizgu ili kuti wazunure nthowa yakusinthira vyakuyaniska. Wakagwiriskira ntchito lizgu ili pa mutu wa buku lake, ilo mutu wake ukung'anamulika kuti {{transliteration|ar|[[Al-Jabr|al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah]]}} [Buku Lakulongosora Kupenda mwa Kumalizga na Kulinganiza]. Mutu uwu ukang'anamulika mu Chilatini kuti {{lang|la|Liber Algebrae et Almucabola}}.{{efn|The exact meaning of the term {{transliteration|ar|al-jabr}} in al-Khwarizmi's work is disputed. In some passages, it expresses that a quantity diminished by subtraction is restored to its original value, similar to how a bonesetter restores broken bones by bringing them into proper alignment.<ref>{{multiref | {{harvnb|Oaks|Alkhateeb|2007|pp=45–46, 58}} | {{harvnb|Gandz|1926|p=437}} }}</ref>}} Lizgu ili likanjira mu Chingelezi mu vilimika vya m'ma 1500 kufuma ku Chiitaliya, Chisipanishi, na Chilatini cha mu nyengo ya Ŵamitundu.<ref>{{multiref | {{harvnb|Cresswell|2010|p=[https://books.google.com/books?id=J4i3zV4vnBAC&pg=PA11 11]}} | {{harvnb|OUP Staff}} | {{harvnb|Menini|Oystaeyen|2017|p=722}} | {{harvnb|Hoad|1993|p=10}} }}</ref> Pakwamba, ng'anamuro lake likaŵa waka pa fundo yakuti [[theory of equations|kufundizga vyakuyaniska]], ndikuti, uzeru wa kusintha [[polynomial equations|vyakuyaniska vyakuvinandi]] mwakukhumba kuvitatuza. Ichi chikasintha mu vilimika vya m'ma 1800{{efn|These changes were in part triggered by discoveries that solved many of the older problems of algebra. For example, the proof of the [[fundamental theorem of algebra]] demonstrated the existence of complex solutions of polynomials<ref name="auto7">{{multiref | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Kvasz|2006|p=308}} | {{harvnb|Corry|2024|loc=§ The Fundamental Theorem of Algebra}} }}</ref> and the introduction of [[Galois theory]] characterized the polynomials that have [[solution in radicals|general solutions]].<ref name="auto2">{{multiref | {{harvnb|Kvasz|2006|pp=314–345}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} | {{harvnb|Corry|2024|loc=§ Galois Theory, § Applications of Group Theory}} }}</ref>}} apo uzelu wa algebra ukasazgirapo kuti ukwatire kusambira mitundu yakupambana-pambana ya nchito na magulu gha algebra pamoza na [[axiom|madango ghakuzomerezgeka]] ghawo, malango agho ghakulondezgeka.<ref>{{multiref | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Corry|2024|loc=§ Structural Algebra}} | {{harvnb|Hazewinkel|1994|pp=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA73 73–74]}} }}</ref> == Vigaŵa Vikuru == === Algebra ya Pulayimale === {{main|Elementary algebra}} [[File:algebraic equation notation.svg|thumb|right|class=skin-invert-image|alt=Diagram of an algebraic expression|Umo mazgu gha algebra ghakulembeka:<br />&nbsp; 1 – chikwezgo (exponent)<br />&nbsp; 2 – muwandaniso (coefficient)<br />&nbsp; 3 – chigaŵa (term)<br />&nbsp; 4 – chiwimbo cha nchito (operator)<br />&nbsp; 5 – chigaŵa cambura-kusintha (constant term)<br />&nbsp; <math>c</math> – cambura-kusintha (constant)<br />&nbsp; <math>x</math> <math>y</math> – vyambura-kumanyikwa (variables)]] Algebra ya pulayimale, iyo yikuchemekaso algebra ya sukulu, ndiyo ni algebra yakale chomene ndiposo yakuzirwa chomene.<ref>{{multiref | {{harvnb|Arcavi|Drijvers|Stacey|2016|p=[https://books.google.com/books?id=N2R9DAAAQBAJ&pg=PA2 2]}} | {{harvnb|Benson|2003|pp=[https://books.google.com/books?id=nNbnCwAAQBAJ&pg=PA111 111–112]}} }}</ref> Ni generalization ya masamu ghakwamba iyo yikuthemba pa vyakusintha (vyambura-kumanyikwa) na kusanda umo mazgu gha masamu ghangasinthira.<ref name="auto4">{{multiref | {{harvnb|Maddocks|2008|p=129}} | {{harvnb|Berggren|2015|loc=Lead section}} | {{harvnb|Pratt|2022|loc=§ 1. Elementary Algebra}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ 1. Historical Survey}} }}</ref> Masamu ghakwamba ni kasandiro ka nchito za manambara. Ghakufufuza umo manambara ghakusazgikira na kusinthika mwakugwiliskira ntchito kusazga, [[subtraction|kuwuskapo]], [[multiplication|kwandaniska]], [[Division (mathematics)|kugaŵa]], kuwoneska (exponentiation), kufumiska misisi (roots), na [[logarithm|logarithimu]]. Mwachiyelezgero, nchito ya kusazga yikusazga manambara ghaŵiri, ghakuchemeka vyakusazgika, kuŵa nambara yachitatu, iyo yikuchemeka [[sum|muzgoro]], nga umo <math>2 + 5 = 7</math>.<ref name="auto1"/> Algebra ya pulayimale yikuthemba pa nchito zenezo waka kweni yikuzomerezga vyambura-kumanyikwa padera pa manambara ghaŵaka. Vyambura-kumanyikwa ni viwimbo vya vinthu ivyo vindamanyikwe panji ivyo vyambura kumanyikwa. Vikupangiska kuti wanthu ŵayowoye ukoli uwo munthu wandaumanye mwakukhwima, na kuyowoya malango ghakumanyikwa agho ghali ghaunenesko, kwambura kupwelelera manambara agho ghakugwiriskirika ntchito. Mwachiyelezgero, cakuyaniska <math>2 \times 3 = 3 \times 2</math> chikuŵa cha masamu ghakwamba ndipo chikulongora kuyana kwa manambara agha ghekha. Para tikapoka manambara na vyambura-kumanyikwa, tingayowoya dango likuru ilo likulongosoreka ku kunozgeka kose kwa manambara, nga dango la kusintha malo (commutative property) la kwandaniska, ilo likulongosoreka mu cakuyaniska {{nowrap|<math>a \times b = b \times a</math>.<ref name="auto4"/>}} [[Algebraic expression|Mazgu gha algebra]] ghakupangika mwakugwiliskira nchito za masamu ghakwamba kuti akole pamoza vyambura-kumanyikwa na manambara. Mwakuyana na umo vikuŵira, vilembo vichoko nga ni <math>x</math>, <math>y</math>, na <math>z</math> vikwimira vyambura-kumanyikwa. Mu vinthu vinyake, viwimbo vyapasi (subscripts) vikusazgikako kupambaniska vyambura-kumanyikwa, nga <math>x_1</math>, <math>x_2</math>, na <math>x_3</math>. Vilembo vichoko-choko nga ni <math>a</math>, <math>b</math>, na <math>c</math> kanandi ghakugwiriskirika ntchito pa vyambura-kusintha (constants) na vyakusazgirako pa kwandaniska (coefficients).{{efn|Constants represent fixed numbers that do not change during the study of a specific problem.<ref>{{harvnb|Sobolev|2015}}</ref>}} Mazgu ghakuti <math>5x + 3</math> ni mazgu gha algebra ghakupangika mwa kuchulukizga nambara 5 na cambura-kusintha <math>x</math> na kusazgako nambara 3 ku ivyo vikusangika. Vyakuwoneska vinyake vya mazgu gha algebra ni <math>32xyz</math> na {{nowrap|<math>64x_1{}^2 + 7x_2 - c</math>.<ref>{{multiref | {{harvnb|Maddocks|2008|pp=129–130}} | {{harvnb|Young|2010|p=[https://books.google.com/books?id=9HRLAn326zEC&pg=RA1-PA999 999]}} | {{harvnb|Majewski|2004|p=347}} | {{harvnb|Pratt|2022|loc=§ 1. Elementary Algebra}} | {{harvnb|Sorell|2000|p=[https://books.google.com/books?id=EksSDAAAQBAJ&pg=PA19 19]}} }}</ref>}} Mazgu ghanyake gha algebra ghakuŵa nga mazgu ghakukhwaskana na mazgu ghaŵiri pamoza. [[Equation|Cakuyaniska]] ni mazgu ghakupangika mwa kuyerezgera mazgu ghaŵiri, kuyowoya kuti ghakuyana waka. Ichi chingalongoreka mwakugwiliskira nchito chiwimbo cha kuyana ({{tmath|1= = }}), nga <math>5x^2 + 6x = 3y + 4</math>. [[Inequation|Vyambura-kuyana]] vikukhwaskana na mtundu wakupambana wa kuyerezgera, kuyowoya kuti vigaŵa viŵiri ivi ni vyakupambana. Ichi chingalongoreka mwakugwiliskira ntchito viwimbo nga chiwimbo cha kuchepa ({{tmath|1= < }}), chiwimbo cha kuluska ({{tmath|1= > }}), na chiwimbo cha kupambana ({{tmath|1= \neq }}). Kupambana na mazgu ghanyake, mazgu agha ghangaŵa ghaunenesko panji ghautesi, ndipo unenesko wawo ukuthemba pa mtengo wa vinthu ivyo vikusintha. Mwachiyelezgero, mazgu ghakuti <math>x^2 = 4</math> ni ghaunenesko usange <math>x</math> ni 2 panji −2, ndipo ghautesi mwakupambanako. Ma equation ghakukhala na vyambura-kumanyikwa vingagaŵika mu ma equation ghakumanyikwa (identity equations) na ma equation ghakukhazikika (conditional equations). Ma equation ghakumanyikwa ghali ghaunenesko pa vyose ivyo vingapelekeka ku vyambura-kumanyikwa, nga cakuyaniska {{tmath|1= 2x + 5x = 7x }}. Ma equation ghakukhazikika ghakuŵa ghaunenesko waka pa vinyake vyakusintha. Mwachiyelezgero, cakuyaniska <math>x + 4 = 9</math> ni chaunenesko waka usange <math>x</math> ni 5.<ref>{{multiref | {{harvnb|Musser|Peterson|Burger|2013|p=16}} | {{harvnb|Goodman|2001|p=[https://books.google.com/books?id=TvY7DQAAQBAJ&pg=PA5 5]}} | {{harvnb|Williams|2022}} }}</ref> Chakulinga chikuru cha algebra ya pulayimale nkhumanya mtengo uwo mazgu ghakuyowoyeka ghaunenesko. Ici cingacitika mwa kusintha na kugwiliskira nchito mazgu mwakuyana na malango ghanyake. Fundo yikuru njakuti nchito yiliyose iyo yikuchitika ku chigaŵa chimoza cha cakuyaniska yikweneraso kuchitika ku chigaŵa chinyake. Mwachiyelezgero, usange munthu wawuskako 5 ku chigaŵa cha kumaryero, wakwenerato kuwuskako 5 ku chigaŵa cha kumalyero kuti ŵalinganiske vigaŵa vyose viŵiri. Chilato cha ndondomeko izi nkhupatura chinthu icho munthu wakukhumba ku chigaŵa chimoza, ndondomeko iyo yikumanyikwa kuti nkhumazga cakuyaniska kwa chinthu icho chikusintha. Mwachiyelezgero, cakuyaniska <math>x - 7 = 4</math> chingamazgika kwa <math>x</math> mwa kusazgako 7 ku vigaŵa vyose viŵiri, ivyo vikupatura <math>x</math> ku chigaŵa cha kumaryero na kusanga cakuyaniska {{tmath|1= x = 11 }}.<ref>{{multiref | {{harvnb|Maddocks|2008|p=130}} | {{harvnb|McKeague|1986|pp=[https://books.google.com/books?id=sq7iBQAAQBAJ&pg=PA51 51–54]}} | {{harvnb|Pratt|2022|loc=§ 1. Elementary Algebra}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ 1. Historical Survey}} }}</ref> Pali nthowa zinyake zinandi izo zikugwiriskirika ntchito kumazga ma equation. [[Simplification (algebra)|Kupepuska]] kukugwiriskirika ntchito kuti chiŵike mazgu ghakusuzga na ghanyake ghakuyana kweni ghapusu. Mwachiyelezgero, mazgu ghakuti <math>7x - 3x</math> ghangaŵikika na mazgu ghakuti <math>4x</math> chifukwa <math>7x - 3x = (7-3)x = 4x</math> mwa dango la [[distributive property|kugaŵanya]].<ref>{{multiref | {{harvnb|Tan|Steeb|Hardy|2012|p=[https://books.google.com/books?id=UDb0BwAAQBAJ&pg=PA306 306]}} | {{harvnb|Lamagna|2019|p=[https://books.google.com/books?id=8PSDDwAAQBAJ&pg=PA150 150]}} }}</ref> Pa mazgu agho ghali na vyambura-kumanyikwa vinandi, kuŵikirapo m'malo mwake (substitution) ni nthowa yakumanyikwa yakusinthira chinthu chimoza na mazgu ghakuyana ghambura kusazgako cambura-kusintha ico. Mwachiyelezgero, usange munthu wamanya kuti <math>y = 3x</math>, wangapepuska mazgu ghakuti <math>7xy</math> na kusanga {{tmath|1= 21x^2 }}. Munthowa yakuyana, usange munthu wamanya mtengo wa cambura-kusintha chimoza, wangagwiriskira ntchito umo kumanya mtengo wa vinyake.<ref>{{multiref | {{harvnb|Berggren|2015|loc=§ Solving Systems of Algebraic Equations}} | {{harvnb|McKeague|2014|p=[https://books.google.com/books?id=nI7iBQAAQBAJ&pg=PA386 386]}} | {{harvnb|McKeague|1986|p=[https://books.google.com/books?id=sq7iBQAAQBAJ&pg=PA148 148]}} }}</ref> [[File:Graph (y = 0.5x - 1).svg|thumb|class=skin-invert-image|alt=Graph of equation "y = 0.5x − 1"|Ma equation gha algebra ghangagwiriskirika ntchito kulongosora vithuzi vya geometry. Mtengo wose wa <math>x</math> na <math>y</math> uwo ukumazga cakuyaniska ukupulikiskika kuŵa songo. Vikulembeka nga mzere wa cikuwundi, wakukwera, mu giraf yakucanya.]] Ma equation gha algebra ghangamasulika mu [[geometry]] kuti ghalongosore viŵelengero vya malo mu mtundu wa [[graph of a function|giraf]]. Vinthu vyakupambana-pambana ivyo vili mu equation vikupulikikwa nga ni [[Cartesian coordinate system|maryeruzgo]], ndipo vigaŵa ivyo vikumazga equation vikung'anamulika nga ni fundo za giraf. Mwachiyelezgero, usange <math>x</math> yikuŵikika pa zero mu equation {{tmath|1= y=0.5x - 1 }}, mbwenu <math>y</math> yikwenera kuŵa negative one kuti equation yiŵe yaunenesko. Ichi chikung'anamura kuti mafupa gha <math>(x, y)</math> ghakuti <math>(0, -1)</math> ni chigaŵa cha giraf ya equation. Mafupa gha <math>(x, y)</math> ghakuti {{tmath|1= (0, 7) }}, mwakupambanako, ghakumazga yayi equation ndipo ntheura ghali yayi chigaŵa cha giraf. Grafu yikukhwaska chiŵelengero chose cha x,y paŵiri awo ŵakumazga equation.<ref>{{multiref | {{harvnb|Maddocks|2008|pp=130–131}} | {{harvnb|Rohde|Jain|Poddar|Ghosh|2012|p=[https://books.google.com/books?id=vk2XbZpsBOwC&pg=PT89 89]}} | {{harvnb|Walz|2016|loc=[https://www.spektrum.de/lexikon/mathematik/algebra/12062 Algebra]}}}}</ref> ==== Ma Polynomial ==== {{main|Polynomial}} [[Polynomial|Polynomial]] ni mazgu ghakuchitika na chigaŵa chimoza panji vinandi ivyo vikusazgika panji kuwuskika pakati pawo, nga {{tmath|1= x^4+3xy^2+5x^3-1 }}. Chigaŵa chilichose ni cambura-kusintha, cambura-kumanyikwa, panji muzgoro wa cambura-kusintha na vyambura-kumanyikwa. Cambura-kumanyikwa chilichose chingakwezgeka ku chikwezgo cha cipendeko cambura kupambika (positive integer). Polynomial ya chigaŵa chimoza yikuchemeka [[monomial]], apo polynomial za vigaŵa viŵiri na vitatu zikuchemeka [[binomial]] na [[trinomial]]. [[Degree of a polynomial|Digiri ya polynomial]] ni mtengo wapachanya wa muzgoro wa vikwezgo vya vyambura-kumanyikwa (pakati pa vigaŵa vyake) (4 mu chiyelezgero ichi pacanya).<ref>{{multiref | {{harvnb|Bracken|Miller|2014|pp=386–387}} | {{harvnb|Kaufmann|Schwitters|2011|p=220}} | {{harvnb|Markushevich|2015}} }}</ref> Ma polynomial gha digiri yimoza ghakuchemeka ''ma polynomial gha mzere''. Algebra ya mzere yikusambira magulu gha ma polynomial gha mzere.<ref>{{multiref | {{harvnb|Sahai|Bist|2002|p=[https://books.google.com/books?id=yjkgNYfApj4C&pg=PA21 21]}} | {{harvnb|Maddocks|2008|p=131}} | {{harvnb|Barrera-Mora|2023|pp=[https://books.google.com/books?id=Xmu8EAAAQBAJ&pg=PR9 ix, 1–2]}} }}</ref> Polynomial yikuchemeka ''univariate'' panji ''multivariate'', kuyana na usange yikugwiriskira ntchito cambura-kumanyikwa chimoza panji vinandi.<ref>{{harvnb|Geddes|Czapor|Labahn|2007|p=[https://books.google.com/books?id=9fOUwkkRxT4C&pg=PA46 46]}}</ref> [[Factorization|Kugaŵaniska]] ni nthowa yakugwiriskira ntchito kupepuska ma polynomial, kupangiska kuti chiŵe chapusu kuvisanda na kumanya vigaŵa ivyo vikuŵa zero. Kugaŵaniska nkhulembaso polynomial kuŵa muzgoro wa vigaŵaniso vinandi. Mwachiyelezgero, polynomial <math>x^2 - 3x - 10</math> yingagaŵaniskika kuŵa {{tmath|1= (x + 2)(x - 5) }}. Polynomial yose njizero pekha usange chimoza mwa vigaŵaniso vyake ni zero, ndikuti, usange <math>x</math> ni −2 panji 5.<ref>{{multiref | {{harvnb|Lukas|2022|pp=[https://books.google.com/books?id=1-dvEAAAQBAJ&pg=PA47 47–49]}} | {{harvnb|Berggren|2015|loc=§ Algebraic Expressions, § Solving Algebraic Equations}} }}</ref> Pambere vilimika vya m'ma 1800 vindafike, vigaŵa vinandi vya algebra vikaŵanga vya equation ya polynomial, equation iyo yikasangika para munthu wakuyaniska polynomial na zero. Kuyezgayezga kwakwamba kwa kumazga ma equation gha polynomial kukaŵa kwakuti ŵalongore vyakumazga mu mazgu gha misisi ya nth. Muzgoro wa equation ya polynomial ya digiri yachiŵiri ukuperekeka na fomula ya quadratic<ref>{{multiref | {{harvnb|Berggren|2015|loc=§ Solving algebraic equations}} | {{harvnb|Corry|2024|loc=§ Classical algebra}} }}</ref> <math display="block">x = \frac{-b \pm \sqrt {b^2-4ac\ }}{2a}.</math> Mayankho gha madigiri ghatatu na ghanayi ghakupelekeka na mafomula gha [[cubic formula|cubic]] na [[quartic formula|quartic]]. Palije mayankho ghakumanyikwa ghakumazgira madigiri ghapachanya, nga umo vikawonekera mu vilimika vya m'ma 1800 na [[Abel–Ruffini theorem|fundo ya Abel-Ruffini]].<ref name="auto3"/> Nanga ni para mayankho ghakumanyikwa ghalipo yayi, mayankho ghakuyana waka ghangasangika mwakugwiliskira nchito vipangizo vya manambara nga [[Newton–Raphson method|nthowa ya Newton-Raphson]].<ref>{{harvnb|Igarashi|Altman|Funada|Kamiyama|2014|p=[https://books.google.com/books?id=58ySAwAAQBAJ&pg=PA103 103]}}</ref> [[Fundamental theorem of algebra|Fundo yikuru ya algebra]] yikuti equation yiliyose ya univariate polynomial ya digiri yiwemi iyo yili na coefficients yeneco panji yakusuzga yili na yankho limoza lakusuzga. Ntheura, polynomial yiliyose ya digiri yiwemi yingagaŵika mu ma [[polynomial factorization|polynomial gha mzere]]. Fundo yikuzirwa iyi yikakhozgeka kukwambilira kwa vilimika vya m'ma 1800, kweni yikupereka yayi nthowa yiliyose yakusangirapo vyakumazga.<ref>{{multiref | {{harvnb|Berggren|2015|loc=§ Solving algebraic equations}} | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Kvasz|2006|p=308}} | {{harvnb|Corry|2024|loc=§ The Fundamental Theorem of Algebra}} }}</ref> === Algebra ya Mzere === {{main|Linear algebra}} Algebra ya mzere yikwamba na kusambira [[System of linear equations|ndondomeko za ma equation gha mzere]].<ref>{{multiref | {{harvnb|Maddocks|2008|p=131}} | {{harvnb|Barrera-Mora|2023|pp=[https://books.google.com/books?id=Xmu8EAAAQBAJ&pg=PR9 ix, 1–2], }} }}</ref> [[Linear equation|Equation njakumzere]] usange yingalembeka mu njila ya {{tmath|1= a_1x_1 + a_2x_2 + ... + a_nx_n = b}}, apo {{tmath|1= a_1 }}, {{tmath|1= a_2 }}, ..., <math>a_n</math> na <math>b</math> ni vyambura-kusintha. Vyakuyelezgera ni <math>x_1 - 7x_2 + 3x_3 = 0</math> na {{tmath|1= \textstyle \frac{1}{4} x - y = 4 }}. ''Ndondomeko ya ma equation gha mzere'' ni gulu la ma equation gha mzere agho munthu wakukhumba kusanga vyakumazga vyakuyana pakati pawo.<ref>{{multiref | {{harvnb|Anton|Rorres|2013|pp=2–3}} | {{harvnb|Maddocks|2008|p=131}} | {{harvnb|Voitsekhovskii|2011}} }}</ref> [[Matrix (mathematics)|Ma matrix]] ni magulu ghakuŵungana gha manambara mwakachilato (rows na columns) agho ghakambiliranga kwiziliska nga chiwimbo chakufinya na chakuyana mwakukwana cha ndondomeko za ma equation gha mzere.<ref>{{multiref | {{harvnb|Saikia|2008|p=[https://books.google.com/books?id=KhM7BAAAQBAJ&pg=PA1 1]}} | {{harvnb|Lal|2017|p=[https://books.google.com/books?id=FwPNDgAAQBAJ&pg=PA31 31]}} | {{harvnb|Mirakhor|Krichene|2014|p=[https://books.google.com/books?id=G6XNAwAAQBAJ&pg=PT107 107]}} }}</ref> Mwachiyelezgero, ndondomeko ya ma equation <math display="block"> \begin{align} 9x_1 + 3x_2 - 13x_3 &= 0 \\ 2.3x_1 + 7x_3 &= 9 \\ -5x_1 - 17x_2 &= -3 \end{align} </math> yingalembeka nga <math display="block">AX=B,</math> apo {{tmath|1= A }}, <math>X</math> na <math>B</math> ni ma matrix <math display="block">A=\begin{bmatrix}9 & 3 & -13 \\ 2.3 & 0 & 7 \\ -5 & -17 & 0 \end{bmatrix}, \quad X= \begin{bmatrix}x_1 \\ x_2 \\ x_3 \end{bmatrix},\quad B = \begin{bmatrix}0 \\ 9 \\ -3 \end{bmatrix}.</math> Kuyana na vinjeru vya chiŵelengero cha mizere na mizati, ma matrix ghangasazgika, ghangandaniskika, ndipo nyengo zinyake ghangapiluskika (ghangawendeskeka mwakupiluka).{{efn|Kupiluskika (inversion) nkhung'anamura kusanga matrix yinyake iyo, para yandaniskika na matrix yakwamba, yikupeleka matrix ya "identity"—iyo njakuyana na cipendeko 1 pa nkhani ya kwandaniska manambara.}} Nthowa zose zakumazgira ndondomeko za mzere zingalongosoreka nga vyakuwendeska matrix mwakugwiliskira nchito izi. Mwachiyelezgero, kumazga ndondomeko yamucanya nkhupenja matrix yakupiluskika <math>A^{-1}</math> iyo <math>A^{-1}A = I,</math> apo <math>I</math> ni [[identity matrix|matrix ya identity]]. Penepapo, kwandaniska ku mkono wamazere mbali zose ziŵiri za equation ya matrix yamucanya na <math>A^{-1},</math> munthu wakusanga muzgoro wa ndondomeko ya ma equation gha mzere nga<ref>{{multiref | {{harvnb|Brown|2015|pp=[https://books.google.com/books?id=POlVBgAAQBAJ&pg=PA30 30–31]}} | {{harvnb|Waerden|2003|pp=70–72}} }}</ref> <math display="block">X=A^{-1}B.</math> Nthowa zakumazgira ndondomeko za ma equation gha mzere zikwambira ku izo zili zapafupi kumanya, nga kwiza-mu-malo-mwa (substitution)<ref>{{multiref | {{harvnb|Young|2010|pp=[https://books.google.com/books?id=9HRLAn326zEC&pg=PA697 697–698]}} | {{harvnb|Maddocks|2008|p=131}} | {{harvnb|Sullivan|2010|pp=[https://books.google.com/books?id=6NKaDwAAQBAJ&pg=PA53 53–54]}} }}</ref> na kuwuskapo (elimination),<ref>{{multiref | {{harvnb|Anton|Rorres|2013|pp=7–8}} | {{harvnb|Sullivan|2010|pp=[https://books.google.com/books?id=6NKaDwAAQBAJ&pg=PA55 55–56]}} | {{harvnb|Atanasiu|Mikusinski|2019|p=[https://books.google.com/books?id=VbySDwAAQBAJ&pg=PA75 75]}}}}</ref> kufika ku vipangizo vyapachanya ivyo vikugwiliskira ntchito ma matrix, nga [[Cramer's rule|dango la Cramer]], [[Gaussian elimination|kuwuskapo kwa Gauss]], na [[LU decomposition|kugaŵaniska kwa LU]].<ref>{{multiref | {{harvnb|Maddocks|2008|p=131}} | {{harvnb|Anton|Rorres|2013|pp=7–8, 11, 491}} }}</ref> Ndondomeko zinyake za ma equation nizambura-kuyana (inconsistent),<ref name="auto10">{{multiref | {{harvnb|Anton|Rorres|2013|pp=3–7}} | {{harvnb|Mortensen|2013|pp=[https://books.google.com/books?id=KYDrCAAAQBAJ&pg=PA73 73–74]}} | {{harvnb|Young|2023|pp=[https://books.google.com/books?id=pMSZEAAAQBAJ&pg=PA714 714–715]}} }}</ref> ndikuti, vyakumazga vilipo yayi chifukwa ma equation ghakususkana wene.{{efn|Mwachiyelezgero, ma equation <math>x_1 - 3x_2 = 0</math> na <math>x_1 - 3x_2 = 7</math> ghakususkana wene chifukwa palije mtengo wa <math>x_1</math> na <math>x_2</math> uwo ungamazga ma equation ghaŵiri ghara pa nyengo yimoza.<ref name="auto10"/>}} Ndondomeko zakuyana zili na yankho limoza lakupambanapambana panji viŵelengero vyambura kumazgika vya vyakumazga.<ref name="auto11">{{multiref | {{harvnb|Maddocks|2008|p=131}} | {{harvnb|Harrison|Waldron|2011|p=[https://books.google.com/books?id=_sisAgAAQBAJ&pg=PT464 464]}} | {{harvnb|Anton|2013|p=[https://books.google.com/books?id=neYGCwAAQBAJ&pg=PA255 255]}} }}</ref>{{efn|Usange ndondomeko yakuyana ya ma equation yili na yankho limoza pera, ivi vikukhozga pa chiŵelengero cha vyambura-kumanyikwa na ma [[independent equation|equation ghakujipima paŵiri]]. Ma equation ghakuti ghakujipima paŵiri usange ghakupeleka yayi mzimu umoza ndipo ghangafuma yayi kuchimoza na chinyake. Yankho limoza likuŵako usange chiŵelengero cha vyambura-kumanyikwa nchakuyana na chiŵelengero cha ma equation ghakujipima paŵiri. [[Underdetermined system|Ndondomeko zambura kumazgikirathu]], kusambazgana na izi, zili na vyambura-kumanyikwa vinandi kuluska ma equation ghakujipima paŵiri ndipo zili na viŵelengero vyambura kumazgika vya vyakumazga usange nizakuyana.<ref name="auto11"/>}} Kusambira [[vector space|malo gha vector]] na [[linear map|mapu gha mzere]] nkhukuru mu algebra ya mzere. Malo gha vector ni gulu la algebra ilo likupangika na gulu (set) lino lili na kusazga uko kukupangiska kuŵa [[abelian group|gulu la abelian]] na kwandaniska na cipendeko (scalar multiplication) uko kukuyanapo na kusazga (wonani [[vector space|malo gha vector]] kuti mumanye vinandi). Mapu gha mzere ni nchito (function) pakati pa malo gha vector iyo yikuyanapo na kusazga na kwandaniska na cipendeko. Pa nkhani ya [[finite-dimensional vector space|malo gha vector ghakumalira]], ma vector na mapu gha mzere ghangayimilirika na ma matrix. Ichi chikung'anamura kuti masambiro gha ma matrix na malo gha vector ghakumalira ghakuyana waka. Comenecomene, malo gha vector ghakupereka nthowa yachitatu yakulongosolera na kugwiliskira ntchito ndondomeko za ma equation gha mzere.<ref>{{multiref | {{harvnb|Valenza|2012|p=[https://books.google.com/books?id=7x8MCAAAQBAJ&pg=PR7 vii]}} | {{harvnb|Chahal|2018|loc=[https://books.google.com/books?id=BGR8DwAAQBAJ&pg=PT10 § 1.1 What is Linear Algebra?]}} | {{harvnb|Solomon|2014|pp=[https://books.google.com/books?id=BpvSBQAAQBAJ&pg=PA57 57–58, 61–62]}} | {{harvnb|Ricardo|2009|p=[https://books.google.com/books?id=s7bMBQAAQBAJ&pg=PA389 389]}} }}</ref> Kwiza pa mkhalidwe uwu, matrix ni chithunzithunzi cha mapu gha mzere: usange munthu wakusankha [[Basis (linear algebra)|msingi]] wanyake wakulongosolera ma vector agho ghakusinthika, mbwenu ivyo vikulembeka mu matrix vikupereka vyakufumapo vya kugwiliskira ntchito mapu gha mzere ku ma vector gha msingi.<ref>{{multiref | {{harvnb|Solomon|2014|p=[https://books.google.com/books?id=BpvSBQAAQBAJ&pg=PA57 57]}} | {{harvnb|Ricardo|2009|pp=[https://books.google.com/books?id=s7bMBQAAQBAJ&pg=PA395 395–396]}} }}</ref> [[File:Linear Function Graph.svg|thumb|alt=Graph of two linear equations|Ma equation gha mzere agho ghali na vyambura-kumanyikwa viŵiri ghangang'anamulika nga [[Line (geometry)|mizere]]. Yankho la ndondomeko ya ma equation gha mzere ni apo mizere yikukhwaskana.]] Ndondomeko za ma equation zingang'anamulika nga vithunzithunzi vya geometry. Ku ndondomeko zakuŵa na vyambura-kumanyikwa viŵiri, equation yiliyose yikwimira [[Line (geometry)|mzere]] mu [[two-dimensional space|malo gha mibaru yiŵiri]]. Apo mizere yiŵiri yikukhwaskana ndipo ni yankho la ndondomeko yose chifukwa apa ndipapera apo pakumazga equation yakwamba na yachiŵiri pamoza. Ku ndondomeko zambura-kuyana, mizere yiŵiri yikwenda mwakuyana kwambura kukhwaskana, ndikuti, palije yankho chifukwa yikukhwaskana yayi nakale. Usange ma equation ghaŵiri ngambura kujipima paŵiri, ghakulongosora mzere umoza wene, ndikuti, yankho la equation yimoza njakumazgaso equation yinyake. Vyakuyanapo ivi vikupangiska kuti munthu wasange vyakumazga mwakuwona pa giraf, kulemba ma equation na kumanya apo ghakukhwaskana.<ref>{{multiref | {{harvnb|Anton|Rorres|2013|pp=3–5}} | {{harvnb|Young|2010|pp=[https://books.google.com/books?id=9HRLAn326zEC&pg=PA696 696–697]}} | {{harvnb|Sneyd|Fewster|McGillivray|2022|p=[https://books.google.com/books?id=zqd3EAAAQBAJ&pg=PA211 211]}} }}</ref> Fundo zenezi zikugwira ntchito so ku ndondomeko za ma equation zakuŵa na vyambura-kumanyikwa vinandi, kweni kupambana nkhwakuti ma equation agha ghakulongosora yayi mizere kweni vithunzithunzi vyapachanya kuluska. Mwachiyelezgero, ma equation gha vyambura-kumanyikwa vitatu ghakuyana na [[Plane (mathematics)|mabwalo]] mu [[three-dimensional space|malo gha mibaru yitatu]], ndipo apo mabwalo ghose ghakukhwaskana ndipo pakumazga ndondomeko ya ma equation.<ref>{{multiref | {{harvnb|Anton|Rorres|2013|pp=3–5}} | {{harvnb|Young|2010|p=[https://books.google.com/books?id=9HRLAn326zEC&pg=PA713 713]}} | {{harvnb|Sneyd|Fewster|McGillivray|2022|p=[https://books.google.com/books?id=zqd3EAAAQBAJ&pg=PA211 211]}} }}</ref> === Algebra Yakudumura === {{main|Abstract algebra}} Algebra yakudumura, iyo yikuchemekaso algebra ya sono,<ref>{{multiref | {{harvnb|Gilbert|Nicholson|2004|p=[https://books.google.com/books?id=paINAXYHN8kC&pg=PA1 1]}} | {{harvnb|Dominich|2008|p=[https://books.google.com/books?id=uEedNKV3nlUC&pg=PA19 19]}} }}</ref> njakusambira [[algebraic structures|magulu gha algebra]]. Gulu la algebra ni chiwongo cha kupulikiska [[Operation (mathematics)|nchito]] pa [[mathematical object|vinthu vya masamu]], nga kusazga kwa vipendeko. Apo algebra ya pulayimale na algebra ya mzere zikugwira ntchito pakati pa vipimo vya magulu gha algebra ghakupambanapambana, algebra yakudumura yikutora nthowa yikuru kuluska, yakuyaniska umo magulu gha algebra ghakupambanirana na mitundu yose ya magulu gha algebra iyo yiliko, nga [[Group (mathematics)|magulu]], [[Ring (mathematics)|mphete]], na [[Field (mathematics)|minda]].<ref>{{multiref | {{harvnb|Maddocks|2008|pp=131–132}} | {{harvnb|Pratt|2022|loc=Lead section, § 2. Abstract Algebra}} | {{harvnb|Gilbert|Nicholson|2004|pp=[https://books.google.com/books?id=paINAXYHN8kC&pg=PA1 1–3]}} | {{harvnb|Dominich|2008|p=[https://books.google.com/books?id=uEedNKV3nlUC&pg=PA19 19]}} }}</ref> Kupambana kukuru pakati pa mitundu iyi ya magulu gha algebra nkhu chiŵelengero cha nchito izo zikugwiliskira ntchito na madango agho ghakuzomerezgeka.<ref name="auto9"/> Mu [[mathematics education|masambizgo gha masamu]], algebra yakudumura yikwimira kalasi yapachanya ya ku yunivesite iyo ŵakusambira masamu ŵakusambira pamanyuma pakumazga makalasi gha algebra ya mzere.<ref>{{harvnb|Hausberger|2020|loc=Abstract Algebra Teaching and Learning}}</ref> [[File:Binary operations as black box.svg|thumb|class=skin-invert-image|alt=Diagram of binary operation|Magulu ghanandi gha algebra ghakuzirwa pa nchito zaŵiri (binary operations), izo zikutora vinthu viŵiri kuŵa vyakwiza-mu nchito ndipo vikuvikoleranga kuŵa chinthu chimoza kuŵa vyakufumamo, nga umo kusazga na kwandaniska vikuchitira.]] Pa mkhalidwe wakuzomerezgeka, gulu la algebra ni [[Set (mathematics)|gulu la vinthu]]{{efn|Gulu la vinthu ni chiŵungano cha vinthu vyakupambanapambana ivyo vilije njila yakukhwaskana, nga vipendeko, ma vector, panji magulu ghanyake. [[Set theory|Sambiro la magulu]] likulongosora madango na mikhaliro ya magulu.<ref>{{multiref | {{harvnb|Tanton|2005|p=460}} | {{harvnb|Murthy|2012|p=[https://books.google.com/books?id=CBc8BAAAQBAJ&pg=PA3 1.3]}} }}</ref>}} lakuzikapo, pamoza na nchito yimoza panji zinandi.{{efn|Kuyana na malongosoro ghanyake, magulu gha algebra ghakusazgapo chinthu chakupambana nga chigaŵa chinyake chakusazgikapo, nga chinthu cha identity pa nkhani ya kwandaniska.<ref name="auto5">{{harvnb|Ovchinnikov|2015|p=[https://books.google.com/books?id=UMbXBgAAQBAJ&pg=PA27 27]}}</ref>}} Algebra yakudumura yikukhumbisiska comenecomene [[binary operation|nchito zaŵiri]],{{efn|Magulu ghanyake gha algebra agho ghakusambirika na algebra yakudumura ghali na [[unary operation|nchito yimoza]] kusazgikapo pa nchito zaŵiri. Mwachiyelezgero, [[normed vector space|malo gha vector ghakuŵa na muyeso]] ghali na [[Norm (mathematics)|muyeso]] (norm), uwo ni nchito yimoza iyo yikugwiliskikira comenecomene kukhwaskanya vector na utali wake.<ref>{{harvnb|Grillet|2007|p=[https://books.google.com/books?id=LJtyhu8-xYwC&pg=PA247 247]}}</ref>}} izo zikutora vinthu viŵiri vilivyose mu gulu lakuzikapo kuŵa vyakwiza-mu, ndipo zikuvipeleka ku chinthu chinyake mu gulu ili kuŵa chakufumamo.<ref>{{multiref | {{harvnb|Whitelaw|1995|p=[https://books.google.com/books?id=f2hyf0QoB_0C&pg=PA61 61]}} | {{harvnb|Nicholson|2012|p=[https://books.google.com/books?id=w-GaLpapRcEC&pg=PA70 70]}} | {{harvnb|Fiche|Hebuterne|2013|p=[https://books.google.com/books?id=TqkckiuuXg8C&pg=PT326 326]}} | {{harvnb|Pratt|2022|loc=Lead section, § 2. Abstract Algebra}} }}</ref> Mwachiyelezgero, gulu la algebra <math>\langle \N, + \rangle</math> lili na [[natural numbers|vipendeko vyakuŵelenjera]] ({{tmath|1= \N }}) kuŵa gulu lakuzikapo na kusazga ({{tmath|1= + }}) kuŵa nchito yake yaŵiri.<ref name="auto5"/> Gulu lakuzikapo lingaŵa na vinthu vinyake kupambuka vipendeko, ndipo nchito zake nizakukakikizgika yayi ku nchito zaumaliro za masamu pera.<ref>{{multiref | {{harvnb|Maddocks|2008|pp=131–132}} | {{harvnb|Pratt|2022|loc=Lead section, § 2. Abstract Algebra}} }}</ref> Mwachiyelezgero, gulu lakuzikapo la [[symmetry group|gulu la symmetry]] la chinthu cha geometry likupangika na [[geometric transformation|kusintha kwa geometry]], nga [[rotation|kuzingilizga]], apo munsi mwake chinthu chikukhalilira [[Invariant (mathematics)|chambura-kusintha]]. Nchito yake yaŵiri ni [[function composition|kukolerana kwa mapu]], iyo yikutora vyakusintha viŵiri kuŵa vyakwiza-mu ndipo yili na chakusintha icho chikufuma pa kugwiliskira ntchito chakusintha chakwamba kulondezgeka na chachiŵiri kuŵa chakufumamo.<ref>{{multiref | {{harvnb|Olver|1999|pp=[https://books.google.com/books?id=1GlHYhNRAqEC&pg=PA55 55–56]}} | {{harvnb|Abas|Salman|1994|pp=[https://books.google.com/books?id=5snsCgAAQBAJ&pg=PA58 58–59]}} | {{harvnb|Häberle|2009|p=[https://books.google.com/books?id=McvSa-cFZCMC&pg=PA640 640]}} }}</ref> ==== Sambiro la Magulu ==== {{main|Group theory}} Algebra yakudumura yikupatuliska magulu gha algebra kuyana na madango panji [[axiom|maxiom]] agho nchito zake zikuzomerezga na chiŵelengero cha nchito izo zikugwiliskira ntchito. Mtundu wa chiyambipo comenecomene ni gulu (group), ilo lili na nchito yimoza ndipo likukhumba kuti nchito iyi njakukolerana ([[Associative property|associative]]) ndiposo yili na [[identity element|chinthu cha identity]] na [[inverse element|vinthu vyakupiluska]]. Nchito njakukolerana usange kalongozgero ka kugwiliskira ntchito kanandi kalije mphampha, ndikuti, usange {{nowrap|<math>(a \circ b) \circ c</math>{{efn|Viwimbo <math>\circ</math> na <math>\star</math> vikugwiliskika mu nkhani iyi kwimira nchito yiliyose iyo yingayana panji yambakuyana na nchito za masamu.<ref>{{harvnb|Gilbert|Nicholson|2004|p=[https://books.google.com/books?id=paINAXYHN8kC&pg=PA4 4]}}</ref>}}}} nchakuyana na <math>a \circ (b \circ c)</math> ku vinthu vyose. Nchito yili na chinthu cha identity panji chinthu chambura-kusintha usange chinthu chimoza ''e'' chilipo icho chikusintha yayi mtengo wa chinthu chilichose chinyake, ndikuti, usange {{tmath|1= a \circ e = e \circ a = a }}. Nchito yili na vinthu vyakupiluska usange ku chinthu chilichose <math>a</math> pali chinthu chakuwelengana <math>a^{-1}</math> icho chikuwuskapo vya {{tmath|1= a }}. Usange chinthu chikugwira ntchito pa icho chakupiluska chake mbwenu muzgoro ni chinthu chambura-kusintha ''e'', chakulongosoreka mwakuzomerezgeka nga {{tmath|1= a \circ a^{-1} = a^{-1} \circ a = e }}. Gulu la algebra lililose ilo likukwaniska vikhumbikwa ivi ni gulu.<ref>{{multiref | {{harvnb|Kargapolov|Merzlyakov|2016|loc=§ Definition}} | {{harvnb|Khattar|Agrawal|2023|pp=[https://books.google.com/books?id=7-nIEAAAQBAJ&pg=PA4 4–6]}} | {{harvnb|Maddocks|2008|pp=131–132}} | {{harvnb|Pratt|2022|loc=Lead section, § 2. Abstract Algebra}} | {{harvnb|Neri|2019|p=[https://books.google.com/books?id=NMOlDwAAQBAJ&pg=PA258 258]}} }}</ref> Mwachiyelezgero, <math>\langle \Z, + \rangle</math> ni gulu ilo lapangika na gulu la [[integers|vipendeko vyambura kugaŵika]] pamoza na nchito ya kusazga. Chinthu chambura-kusintha ni 0 ndipo chinthu chakupiluska cha cipendeko chilichose <math>a</math> ni {{nowrap|<math>-a</math>.<ref>{{multiref | {{harvnb|Khattar|Agrawal|2023|pp=[https://books.google.com/books?id=7-nIEAAAQBAJ&pg=PA6 6–7]}} | {{harvnb|Maddocks|2008|pp=131–132}} | {{harvnb|Adhikari|Adhikari|2013|p=[https://books.google.com/books?id=lBO7BAAAQBAJ&pg=PA72 72]}}}}</ref>}} Vipendeko vyakuŵelenjera pamoza na kusazga, kususkana na ivi, vikupanga yayi gulu chifukwa vili pera na vipendeko vyakuzomerezgeka ndipo ntheura vikusoŵa vinthu vyakupiluska.<ref>{{multiref | {{harvnb|McWeeny|2002|p=[https://books.google.com/books?id=x3fjIXY93TsC&pg=PA6 6]}} | {{harvnb|Kramer|Pippich|2017|p=[https://books.google.com/books?id=nvM-DwAAQBAJ&pg=PA49 49]}} }}</ref> [[Group theory|Sambiro la magulu]] likusanda umo magulu ghaliri, pamoza na fundo za musingi nga [[fundamental theorem of finite abelian groups|fundo yikuru ya magulu gha abelian ghakumalira]] na [[Feit–Thompson theorem|fundo ya Feit-Thompson]].<ref>{{multiref | {{harvnb|Tanton|2005|p=242}} | {{harvnb|Bhattacharya|Jain|Nagpaul|1994|p=[https://books.google.com/books?id=hiQ8e0b48swC&pg=PA141 141]}} | {{harvnb|Weisstein|2003|p=[https://books.google.com/books?id=D_XKBQAAQBAJ&pg=PA1020 1020]}} }}</ref> Iyi yachiŵiri yikaŵa njira yikuru yakwambilira mu chimoza mwa vinthu vikuru comenecomene mu masamu vya vilimika vya m'ma 1900: nchito yakugwirira pamoza, iyo yikatora mapeji ghakuluska 10,000 mu majenali ndipo yikafuma comenecomene pakati pa 1960 na 2004, iyo yikafiskira ku [[classification of finite simple groups|kupatuliska magulu ghapusu ghakumalira]] kwakukwana.<ref>{{multiref | {{harvnb|Elwes|2006}} | {{harvnb|Wilson|2009|p=2}} }}</ref> ==== Sambiro la Mphete na Sambiro la Munda ==== {{main|Ring theory|Field (mathematics)}} Mphete ni gulu la algebra lino lili na nchito ziŵiri izo zikugwira ntchito mwakuyana na kusazga na kwandaniska kwa vipendeko ndipo zikuchemeka na kulembeka mwakuyana. Mphete ni [[commutative group|gulu lakusinthana]] pasi pa kusazga: kusazga kwa mphete nkhwakukolerana, kwakusinthana, ndipo kuli na chinthu cha identity na vinthu vyakupiluska. Kwandaniska nkhwakukolerana ndiposo [[distributivity|kwakugaŵira]] ku kusazga; ndikuti, <math>a (b + c) = a b + a c</math> na <math>(b + c) a = b a + c a.</math> Kweniso, kwandaniska nkhwakukolerana ndipo kuli na [[identity element|chinthu cha identity]] icho chikuchemeka comenecomene {{math|1}}.<ref>{{multiref | {{harvnb|Weisstein|2003|p=2579}} | {{harvnb|Maxwell|2009|pp=[https://books.google.com/books?id=yD0irRUE_u4C&pg=PA73 73–74]}} | {{harvnb|Pratt|2022|loc=§ 2.3 Rings}} }}</ref>{{efn|Ŵalembi ŵanyake ŵakukhumba yayi kuŵako kwa chinthu cha identity mu kwandaniska. Mphete iyo yilije chinthu cha identity mu kwandaniska nyengo zinyake yikuchemeka {{not a typo|[[rng (algebra)|rng]].}}<ref>{{harvnb|Silverman|2022|p=[https://books.google.com/books?id=PKFnEAAAQBAJ&pg=PA64 64]}}</ref>}} Kwandaniska nkhukhumbikwa yayi kuŵa kwakusinthana; usange nkhwakusinthana, munthu wali na [[commutative ring|mphete yakusinthana]].<ref>{{harvnb|Geddes|Czapor|Labahn|2007|p=[https://books.google.com/books?id=9fOUwkkRxT4C&pg=PA24 24]}}</ref> [[ring of integers|Mphete ya vipendeko vyambura kugaŵika]] ({{tmath|1= \Z }}) ni yimoza mwa mphete zapusu comenecomene izo zili zakusinthana.<ref>{{harvnb|Smith|2015|p=[https://books.google.com/books?id=MXu9CgAAQBAJ&pg=PA161 161]}}</ref> ''[[field (mathematics)|Munda]]'' ni mphete yakusinthana iyo {{tmath|1\ne 0}}{{efn|Ichi chikung'anamura kuti kwandaniska na kusazga vikugwiliskira ntchito vinthu vyakupambanapambana vya identity.<ref>{{harvnb|Moh|1992|pp=[https://books.google.com/books?id=maK3sbTVhsoC&pg=PA102 102–103]}}</ref>}} ndipo chinthu chilichose ichi mbura kuŵa zero chili na [[multiplicative inverse|chakupiluska cha kwandaniska]].<ref>{{multiref | {{harvnb|Geddes|Czapor|Labahn|2007|p=[https://books.google.com/books?id=9fOUwkkRxT4C&pg=PA24 24]}} | {{harvnb|Weisstein|2003|pp=1047, 2579}} | {{harvnb|Pratt|2022|loc=§ 2.4 Fields}} }}</ref> Mphete ya vipendeko vyambura kugaŵika njambura kupanga munda chifukwa yikusoŵa vyakupiluska vya kwandaniska. Mwachiyelezgero, chakupiluska cha kwandaniska cha <math>7</math> ni {{tmath|1= \tfrac{1}{7} }}, icho ndi cipendeko cambura kugaŵika yayi. [[rational numbers|Vipendeko vyakugaŵikika]], [[real numbers|vipendeko vyeneco]], na [[complex numbers|vipendeko vyakusuzga]] vilivyose vikupanga munda na nchito za kusazga na kwandaniska.<ref>{{multiref | {{harvnb|Irving|2004|pp=77, 236}} | {{harvnb|Weisstein|2003|pp=1047, 2579}} | {{harvnb|Hohn|2013|pp=[https://books.google.com/books?id=9XlFu4XQ6nUC&pg=PA83 83–84]}} }}</ref> [[Ring theory|Sambiro la mphete]] ni kusambira mphete, kupenja vinthu nga [[subring|mphete zamunsi]], [[quotient ring|mphete za mgaŵano]], [[polynomial ring|mphete za polynomial]], na [[Ideal (ring theory)|ma ideal]] pamoza na fundo nga [[Hilbert's basis theorem|fundo ya msingi ya Hilbert]].<ref>{{multiref | {{harvnb|Serovajsky|2020|loc=§ Room 4B.5 Rings}} | {{harvnb|Kleiner|2007|p=[https://books.google.com/books?id=udj-1UuaOiIC&pg=PA63 63]}} | {{harvnb|Kline|1990|p=[https://books.google.com/books?id=8YaBuGcmLb0C&pg=PA1153 1153]}} }}</ref> Sambiro la munda likukhwaskana na minda, kupenja [[field extension|kutandarizga kwa munda]], [[algebraic closure|kujara kwa algebra]], na [[finite fields|minda yakumalira]].<ref>{{multiref | {{harvnb|Waerden|2003|pp=110–114, 231, 246}} | {{harvnb|Karpilovsky|1989|p=[https://books.google.com/books?id=-2WR0fw9gLMC&pg=PA45 45]}} | {{harvnb|Kleiner|2007|p=[https://books.google.com/books?id=udj-1UuaOiIC&pg=PA63 63]}} }}</ref> [[Galois theory|Sambiro la Galois]] likupenja uzeru pakati pa sambiro la munda na sambiro la magulu, likujizika pa [[fundamental theorem of Galois theory|fundo yikuru ya sambiro la Galois]].<ref>{{multiref | {{harvnb|Lang|2005|pp=[https://books.google.com/books?id=Fge-BwqhqIYC&pg=PA261 261–262]}} | {{harvnb|Cox|2012|pp=[https://books.google.com/books?id=vBKrOch1AkYC&pg=PA161 161–162]}} }}</ref> ==== Sambiro la Kukhwaskana Pakati pa Magulu gha Algebra ==== [[File:Magma to group2.svg|thumb|class=skin-invert-image|alt=Diagram of relations between some algebraic structures|Chithunzithunzi cha ukhwaskano pakati pa magulu ghanyake gha algebra. Mwachiyelezgero, mbali yake yapachanya kumalyo yikulongora kuti [[Magma (algebra)|magma]] yikuŵa [[semigroup|semigroup]] usange nchito yake njakukolerana.]] Kupambuka magulu, mphete, na minda, kuli magulu ghanandi ghanyake gha algebra agho ghakusambirika na algebra. Ghakusazgamo [[Magma (algebra)|ma magma]], [[semigroup|ma semigroup]], [[monoid|ma monoid]], [[abelian group|magulu gha abelian]], [[commutative ring|mphete zakusinthana]], [[Module (mathematics)|ma module]], [[Lattice (order)|ma lattice]], [[vector space|malo gha vector]], [[Algebra over a field|algebra pa munda]], na magulu [[associative|ghakukolerana]] na [[non-associative algebras|ghambura kukolerana]]. Ghakupambana pakati pawo pa mtundu wa vinthu ivyo ghakulongosora na vikhumbikwa ivyo nchito zawo zikufiska. Ghanandi ghakukhwaskana wene pakati pawo mu ntchito yakuti gulu la musingi lingasinthika kuŵa gulu lakuzikirapo comenecomene mwakusazgirapo vikakiro.<ref name="auto9">{{multiref | {{harvnb|Pratt|2022|loc=Lead section, § 2. Abstract Algebra}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=The Subject Matter of Algebra, Its Principal Branches and Its Connection with Other Branches of Mathematics.}} | {{harvnb|Bourbaki|1998|pp=[https://books.google.com/books?id=STS9aZ6F204C&pg=PA428 428–430, 446]}} }}</ref> Mwachiyelezgero, magma yikuŵa semigroup usange nchito yake njakukolerana.<ref>{{harvnb|Cooper|2011|p=[https://books.google.com/books?id=Fybzl6QB62gC&pg=PA60 60]}}</ref> [[Homomorphism|Ma homomorphism]] ni vipangizo vyakupenjera vinjeru vya mzimu mwakuyaniska magulu ghaŵiri gha algebra.<ref>{{multiref | {{harvnb|Rowen|2006|p=[https://books.google.com/books?id=AhEPCgAAQBAJ&pg=PA12 12]}} | {{harvnb|Pratt|2022|loc=§ 3.3 Birkhoff's Theorem}} | {{harvnb|Grätzer|2008|p=34}} }}</ref> Homomorphism ni mapu ghakufuma ku gulu lakuzikapo la gulu limoza la algebra kuya ku gulu lakuzikapo la gulu linyake la algebra, ghakusunga mikhaliro yinyake ya mzimu. Usange magulu ghaŵiri gha algebra ghakugwiliskira ntchito nchito zaŵiri ndipo ghali mu mtundu <math>\langle A, \circ \rangle</math> na <math>\langle B, \star \rangle</math> mbwenu mapu <math>h: A \to B</math> ni homomorphism usange ghakukwaniska ivi: {{tmath|1= h(x \circ y) = h(x) \star h(y) }}. Kuŵako kwa homomorphism kukulongora kuti nchito <math>\star</math> mu gulu lachiŵiri la algebra yikugwira ntchito yakuyana na iyo nchito <math>\circ</math> yikugwira mu gulu lakwamba la algebra.<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 3.3 Birkhoff's Theorem}} | {{harvnb|Rowen|2006|p=[https://books.google.com/books?id=AhEPCgAAQBAJ&pg=PA12 12]}} | {{harvnb|Gowers|Barrow-Green|Leader|2010|pp=[https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA27 27–28]}} | {{harvnb|Adhikari|2016|pp=[https://books.google.com/books?id=MIAXDQAAQBAJ&pg=PA5 5–6]}} }}</ref> [[Isomorphisms|Ma isomorphism]] ni mtundu wapadera wa homomorphism uwo ukulongora kuyanako kukuru pakati pa magulu ghaŵiri gha algebra. Isomorphism ni homomorphism [[bijective|yakwenerana pa chimoza-na-chimoza]], ndikuti, yikupanga ukhwaskano wa chimoza-na-chimoza pakati pa vinthu vya magulu ghaŵiri gha algebra. Ichi chikung'anamura kuti chinthu chilichose cha gulu lakwamba la algebra chikuya ku chinthu chimoza chapadera mu gulu lachiŵiri, kwambura vinthu vyakusoŵa mapu mu gulu lachiŵiri.<ref>{{multiref | {{harvnb|Neri|2019|pp=[https://books.google.com/books?id=NMOlDwAAQBAJ&pg=PA278 278–279]}} | {{harvnb|Ivanova|Smirnov|2012}} | {{harvnb|Deo|2018|p=[https://books.google.com/books?id=HjtRDwAAQBAJ&pg=PA295 295]}} | {{harvnb|Ono|2019|p=[https://books.google.com/books?id=SR2nDwAAQBAJ&pg=PA84 84]}}}}</ref> [[File:Venn A subset B.svg|thumb|alt=Venn diagram of a set and its subset|[[Subalgebra|Vigulu vyamunsi vya algebra]] vikufinyikizga nchito zake ku chigaŵa cha gulu lakuzikapo la gulu la algebra lakwamba.]] Chipangizo chinyake cha kuyaniska nkhukhwaskana pakati pa gulu la algebra na [[Subalgebra#Subalgebras in universal algebra|chigulu chamunsi cha algebra]] chake.<ref name="auto8">{{multiref | {{harvnb|Indurkhya|2013|pp=[https://books.google.com/books?id=foTrCAAAQBAJ&pg=PA217 217–218]}} | {{harvnb|Pratt|2022|loc=§ 3.3 Birkhoff's Theorem}} | {{harvnb|Grätzer|2008|p=34}} }}</ref> Gulu la algebra na chigulu chamunsi chake vikugwiliskira ntchito nchito zakuyana,{{efn|Kuyana na malongosoro ghanyake, chigulu chamunsi chingaŵaso na nchito zichoko.<ref name="auto6">{{harvnb|Indurkhya|2013|pp=[https://books.google.com/books?id=foTrCAAAQBAJ&pg=PA217 217–218]}}</ref>}} izo zikulondezga maxiom ghakuyana. Kupambana kwapera nkhwakuti gulu lakuzikapo la chigulu chamunsi ni chigaŵa cha gulu lakuzikapo la gulu la algebra.{{efn|Ichi chikung'anamura kuti vinthu vyose vya gulu lakwamba nivyaso vinthu vya gulu lachiŵiri kweni gulu lachiŵiri lingaŵa na vinthu ivyo vilipo yayi mu gulu lakwamba.<ref>{{harvnb|Efimov|2014}}</ref>}} Nchito zose mu chigulu chamunsi zikukhumbikwa kuŵa [[Closure (mathematics)|zakujara]] mu gulu lake lakuzikapo, ndikuti, zikufumiska pera vinthu ivyo vili mu gulu ili.<ref name="auto8"/> Mwachiyelezgero, gulu la [[Parity (mathematics)|vipendeko vyakwenerana]] pamoza na kusazga ni chigulu chamunsi cha gulu lose la vipendeko vyambura kugaŵika pamoza na kusazga. Ichi nchakuti chifukwa muzgoro wa vipendeko viŵiri vyakwenerana ni cipendeko cakwenerana kavili. Kweni gulu la vipendeko vyambura kwenerana pamoza na kusazga nichigulu chamunsi yayi chifukwa nichambura kujara: kusazga vipendeko viŵiri vyambura kwenerana vikufumiska cipendeko chakwenerana, icho ndi chigaŵa yayi cha gulu ilo lasankhika.<ref name="auto6"/> [[Universal algebra|Algebra ya wonse]] ni sambiro la magulu gha algebra mwaŵukuru. Nga chigaŵa cha vinjeru vyake vyakuwonera vinthu vyakuzomerezgeka, yikupwelelera yayi vinthu vyeneco ivyo vikupanga magulu ghakuzikapo ndipo yikuwona nchito izo zili na vyakwiza-mu vinandi kuluska viŵiri, nga [[ternary operation|nchito zitatu]]. Yikupereka chiwongo cha kupenja vinjeru vya mzimu ivyo magulu ghakupambanapambana gha algebra ghali navyo pamoza.<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 3. Universal Algebra}} | {{harvnb|Cohn|2012|p=[https://books.google.com/books?id=6tbuCAAAQBAJ&pg=PR13 xiii]}} }}</ref>{{efn|Nthowa yakupambanako pachoko yikupulikiska algebra ya wonse kuŵa sambiro la mtundu umoza wa magulu gha algebra ghakumanyikwa nga ma algebra ghawonse. Ma algebra ghawonse ghakulongosoreka mwakuzirwa kuti ghasazgemo magulu ghanyake ghanandi gha algebra. Mwachiyelezgero, magulu na mphete ni mitundu yapadera ya algebra ya wonse.<ref>{{multiref | {{harvnb|Smirnov|2020}} | {{harvnb|Grätzer|2008|pp=7–8}} | {{harvnb|Bahturin|2013|p=[https://books.google.com/books?id=8RbvCAAAQBAJ&pg=PA346 346]}} }}</ref>}} Chimoza mwa vinjeru vya mzimu ivi vikukhwaskana na [[Identity (mathematics)#Logic and universal algebra|vinthu vyakuyana]] (identities) ivyo nivyanadi mu magulu ghakupambanapambana gha algebra. Mu mkhalidwe uwu, chinthu chakuyana ni equation [[Universal quantification|yawonse]] panji equation iyo nyanadi ku vinthu vyose vya gulu lakuzikapo. Mwachiyelezgero, kusinthana (commutativity) ni equation yawonse iyo yikuti <math>a \circ b</math> nichakuyana na <math>b \circ a</math> ku vinthu vyose.<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 3.2 Equational Logic}} | {{harvnb|Mal’cev|1973|pp=210–211}} }}</ref> [[Variety (universal algebra)|Mtundu wakuyana]] (variety) ni gulu la magulu ghose gha algebra agho ghakukwaniska vinthu vinyake vyakuyana. Mwachiyelezgero, usange magulu ghaŵiri gha algebra ghakukwaniska kusinthana mbwenu ghose ghaŵiri ni chigaŵa cha mtundu wakuyana uwo ukuyana nawo.<ref>{{multiref | {{harvnb|Mal’cev|1973|pp=210–211}} | {{harvnb|Cohn|2012|p=[https://books.google.com/books?id=6tbuCAAAQBAJ&pg=PA162 162]}} | {{harvnb|Rosen|2012|p=[https://books.google.com/books?id=-oVvEAAAQBAJ&pg=PA779 779]}} | {{harvnb|Hazewinkel|1994|p=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA406 406]}} }}</ref>{{efn|Mtundu uliwose wa gulu la algebra ukupanga yayi mtundu wakuyana. Mwachiyelezgero, magulu na mphete vyose vikupanga mtundu wakuyana kweni minda njambura kupanga.<ref>{{harvnb|Cohn|1995|p=[https://books.google.com/books?id=u-4ADgUgpSMC&pg=PA8 8]}}</ref>}}{{efn|Kupambuka vinthu vyakuyana, algebra ya wonse yikukhumbikwaso na vinjeru vya mzimu ivyo vikukhwaskana na [[quasi-identity|vinthu vyakuyana pachoko]] (quasi-identities). Chinthu chakuyana pachoko ni chinthu chakuyana icho chikukhumbikwa pera pasi pa vikhumbikwa vinyake (ivyo vikuŵa mu mtundu wa [[Horn clause|chigaŵa cha Horn]]<ref>{{harvnb|Mal’cev|1973|p=211}}</ref>). Ni kutandarizga kwa chinthu chakuyana mu mzimu wakuti chinthu chilichose chakuyana ni chinthu chakuyana pachoko kweni chinthu chilichose chakuyana pachoko ni yayi chinthu chakuyana. [[Quasivariety|Mtundu wakuyana pachoko]] ni gulu la magulu ghose gha algebra agho ghakukwaniska vinthu vinyake vyakuyana pachoko.<ref>{{multiref | {{harvnb|Mal’cev|1973|pp=210–211}} | {{harvnb|Pratt|2022|loc=§ 3. Universal Algebra}} | {{harvnb|Artamonov|2003|p=[https://books.google.com/books?id=sLDGY4Hk8V0C&pg=PA873 873]}} }}</ref>}} [[Category theory|Sambiro la mikhaliro]] likupenja umo vinthu vya masamu vikukhwaskirana na chinyake mwakugwiliskira ntchito mzimu wa [[Category (mathematics)|mikhaliro]] (categories). Mkhaliro ni chiŵungano cha vinthu pamoza na chiŵungano cha [[morphisms|vilongozgi]] panji "mivi" pakati pa vinthu ivi. Viŵungano ivi viŵiri vikwenera kukwaniska vikhumbikwa vinyake. Mwachiyelezgero, vilongozgi vingakolerana, panji ku ''kolerana'': usange muvi ukuŵako kufuma ku chinthu <math>a</math> kuya ku chinthu {{tmath|1= b }}, ndipo muvi unyake kufuma ku chinthu <math>b</math> kuya ku chinthu {{tmath|1= c }}, mbwenu pakwenera kuŵakoso muvi kufuma ku chinthu <math>a</math> kuya ku chinthu {{tmath|1= c }}. Kukolerana kwa vilongozgi kukukhumbikwa kuŵa kwakukolerana, ndipo pakwenera kuŵako "muvi wa identity" ku chinthu chilichose.<ref>{{multiref | {{harvnb|Weisstein|2003|pp=347–348}} | {{harvnb|Gowers|Barrow-Green|Leader|2010|pp=[https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA6 6, 165]}} | {{harvnb|Cheng|2023|p=102}} }}</ref> Mikhaliro yikugwiliskika comenecomene mu masamu gha sono chifukwa yikupereka chiwongo chakukoleranya kuti chilongosore na kupenja vinjeru vinandi vya musingi vya masamu. Mwachiyelezgero, magulu ya vinthu ghangalongosoreka na [[category of sets|mkhaliro wa magulu]], ndipo gulu lililose lingawoneka kuŵa vilongozgi vya mkhaliro uwo uli na chinthu chimoza pera.<ref>{{multiref | {{harvnb|Gowers|Barrow-Green|Leader|2010|pp=[https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA6 6, 165]}} | {{harvnb|Borceux|1994|p=[https://books.google.com/books?id=YfzImoopB-IC&pg=PA20 20]}} | {{harvnb|Laos|1998|p=[https://books.google.com/books?id=1r7dSn4ZqogC&pg=PA100 100]}} | {{harvnb|Cheng|2023|pp=128–131}} }}</ref> == Mbiri == {{main|History of algebra|Timeline of algebra}} [[File:Rhind Mathematical Papyrus.jpg|thumb|alt=Rhind Papyrus|[[Rhind Mathematical Papyrus|Papyrus ya Rhind Mathematical]] kufuma ku [[ancient Egypt|Egypt yakale]], iyo yikuŵa ya {{circa|1650 BCE}}, ni chimoza cha vyolálemba vyakale comenecomene ivyo vikudumbiskana masuzgo gha algebra.]] Chiyambi cha algebra chili mu kuyezgayezga kwakumazga masuzgo gha masamu agho ghakukhwaskana na kuŵelenga na viŵelengero vyambura kumanyikwa. Vyakukula ivi vikachitika mu nyengo yakale mu [[Babylonia]], [[Ancient Egypt|Egypt]], [[Ancient Greece|Greece]], [[Ancient China|China]], na [[Ancient India|India]]. Chimoza mwa vyolálemba vyakale comenecomene pa masuzgo gha algebra ni [[Rhind Mathematical Papyrus|Papyrus ya Rhind Mathematical]] kufuma ku Egypt yakale, iyo yikalembeka pafupifupi mu 1650&nbsp;BCE.{{efn|Zuŵa lenelene nkhwakususkana, ndipo ŵalongozgi ŵanyake ŵa mbiri ŵakuti liŵe pafupifupi mu 1550&nbsp;BCE.<ref>{{multiref | {{harvnb|Corry|2024|loc=§ Problem-Solving in Egypt and Babylon}} | {{harvnb|Brezinski|Meurant|Redivo-Zaglia|2022|p=[https://books.google.com/books?id=4IGhEAAAQBAJ&pg=PA34 34]}} }}</ref>}} Yikudumbiskana vyakumazga vya [[linear equations|ma equation gha mzere]], nga umo vikulongosoreka mu masuzgo nga "Chinthu; chigaŵa chake chachinayi chikusazgikapo pa icho. Chikuŵa 15. Kasi chinthu ni chiwuli?" Mabuwe gha dongo gha ku Babylon kufuma pa nyengo yeneyiyo ghakulongosora nthowa zakumazga ma equation gha mzere na [[Quadratic equation|polynomial gha digiri yachiŵiri]], nga nthowa ya [[completing the square|kukwaniska cikwezgo]].<ref>{{multiref | {{harvnb|Tanton|2005|p=9}} | {{harvnb|Kvasz|2006|p=290}} | {{harvnb|Corry|2024|loc=§ Problem Solving in Egypt and Babylon}} }}</ref> Vinandi mwa vinjeru ivi vikafika ku Ŵagiriki ŵakale. Kwambira mu vilimika vya 6 BCE, chikhumbo chawo chikuru chikaŵa geometry m'malo mwa algebra, kweni ŵakagwiliskira ntchito nthowa za algebra kumazga masuzgo gha geometry. Mwachiyelezgero, ŵakasandanga vithunzithunzi vya geometry apo utali na malo ghake vikatoleka kuŵa viŵelengero vyambura kumanyikwa ivyo vikwenera kusangika, nga umo vikawonekera mu nthowa ya [[Pythagoras]] ya [[difference of two squares|mphambano wa vikwezgo viŵiri]] na munyuma mu buku la [[Euclid's Elements|Euclid's Elements]].<ref>{{multiref | {{harvnb|Tanton|2005|p=9}} | {{harvnb|Kvasz|2006|p=290}} | {{harvnb|Corry|2024|loc=§ The Pythagoreans and Euclid}} }}</ref> Mu vilimika vya 3 CE, [[Diophantus]] wakapeleka malongosoro ghakuzura gha umo wangamazgira ma equation gha algebra mu magazini ghakuchemeka ''[[Arithmetica]]''. Ndiyo wakaŵa wakwamba kuyezgayezga kugwiliskira ntchito viwimbo (symbolic notation) kulongosora ma polynomial.<ref>{{multiref | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} | {{harvnb|Sialaros|2018|p=[https://books.google.com/books?id=2PZYDwAAQBAJ&pg=PT55 55]}} | {{harvnb|Corry|2024|loc=§ Diophantus}} }}</ref> Ntchito ya Diophantus yikakhwaskira kukula kwa algebra ku Ŵaarabu, apo nthowa zake zinandi zikawonekera mu vinjeru na vipangizo ivyo vikagwiliskika mu algebra ya Chiarabu ya nyengo za pakati.<ref>{{multiref | {{harvnb|Hettle|2015|pp=139–141, 160–161}} | {{harvnb|Christianidis|Megremi|2019|pp=16–17}} }}</ref> Ku China wakale, ''[[The Nine Chapters on the Mathematical Art]]'', buku ilo likalembeka pa nyengo yakufuma ku vilimika vya 10 BCE kufika ku vilimika vya 2 CE,<ref>{{harvnb|Burgin|2022|p=[https://books.google.com/books?id=rWF2EAAAQBAJ&pg=PA10 10]}}</ref> likasandaso nthowa zakupambanapambana zakumazgira ma equation gha algebra, kusazgamo kugwiliskira ntchito vinthu vyakuyana na matrix.<ref>{{harvnb|Higgins|2015|p=[https://books.google.com/books?id=QANiCgAAQBAJ&pg=PA89 89]}}</ref> [[File:Al-Khwarizmi portrait.jpg|thumb|upright=0.6|left|Chithunzi cha kuyezgayezga cha [[Al-Khwarizmi]], chakufuma pa sitembu ya Soviet]] Nkhwakususkana usange vyakukula ivi vyakale ni chigaŵa cha algebra panji ni vyakwambiliranji pera. Vikapeleka vyakumazga vya masuzgo gha algebra kweni vikaghanaghanira yayi mwamzimu wakudumura na wawonse, m'malo mwake vikakhalilira pa mkhalidwe pakuyowoya na kugwiliskika padera pera.<ref>{{multiref | {{harvnb|Kvasz|2006|pp=290–291}} | {{harvnb|Sialaros|2018|p=[https://books.google.com/books?id=2PZYDwAAQBAJ&pg=PT55 55]}} | {{harvnb|Boyer|Merzbach|2011|p=[https://books.google.com/books?id=bR9HAAAAQBAJ&pg=PA161 161]}} | {{harvnb|Derbyshire|2006|p=[https://books.google.com/books?id=mLqaAgAAQBAJ&pg=PT39 31]}} }}</ref> Ichi chikasintha na msandi wa masamu wa ku Persia, [[Al-Khwarizmi]],{{efn|Ŵalongozgi ŵanyake ŵa mbiri ŵakumuwona kuŵa "wiske wa algebra" apo ŵanyake ŵakupeleka zina ili ku Diophantus.<ref>{{multiref | {{harvnb|Boyer|Merzbach|2011|p=[https://books.google.com/books?id=bR9HAAAAQBAJ&pg=PA161 161]}} | {{harvnb|Derbyshire|2006|p=[https://books.google.com/books?id=mLqaAgAAQBAJ&pg=PA31 31]}} }}</ref> }} uyo wakafumiska buku lake ''[[The Compendious Book on Calculation by Completion and Balancing]]'' mu 825 CE. Al-Khwarizmi wakapeleka malongosoro ghakwamba ghakuzomerezgeka ghakumazgira ma equation mwakughaŵika mu mitundu 6 yakuzomerezgeka{{Efn|Mitundu iyi ni <math> bx = c </math>, <math> ax^2 = bx </math>, <math> ax^2 = c </math>, <math> ax^2 + bx = c </math>, <math> ax^2 + c = bx </math>, na <math> ax^2 = bx + c </math>.{{sfn|Bradley|2006|p=[http://books.google.com/books?id=EIdtVPeD7GcC&pg=PA95 95]}}}} ndiposo kupereka ndondomeko zakuzomerezgeka, mwakuyila-kuyila, za vyakuvimazga. Mwakuwuskapo nthowa izi ku vithunzithunzi vyapadera vya geometry na kuwona viŵelengero vyambura kumanyikwa kuŵa vinthu vyawonse vya algebra, wakakhozga chiwongo cha kugwira ntchito chakuzomerezgeka. Kusintha uku, kufuma ku kumazga masuzgo ghapadera kuya ku kukhozga nthowa yawonse, nkhwakasintha algebra kuŵa sambiro lakujimira paokha.<ref>{{multiref | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Kvasz|2006|pp=291–293}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} }}</ref> Vyakukhwaskira vinyake vyakuzirwa ku algebra vikafuma ku msandi wa masamu wa Chiarabu [[Thābit ibn Qurra]] naye so mu vilimika vya 9 CE na msandi wa masamu wa ku Persia [[Omar Khayyam]] mu vilimika vya 11 na 12.<ref>{{multiref | {{harvnb|Waerden|2013|pp=3, 15–16, 24–25}} | {{harvnb|Jenkins|2010|p=[https://books.google.com/books?id=giEkCQAAQBAJ&pg=PA82 82]}} | {{harvnb|Pickover|2009|p=[https://books.google.com/books?id=JrslMKTgSZwC&pg=PA90 90]}} }}</ref> Ku India, [[Brahmagupta]] wakasanda umo wangamazgira ma equation gha digiri yachiŵiri na ndondomeko za ma equation gha vyambura-kumanyikwa vinandi mu vilimika vya 7 CE. Pakati pa vyakukula vyake vikaŵako kugwiliskira ntchito zero na vipendeko vyakusuzga (negative numbers) mu ma equation gha algebra.<ref>{{multiref | {{harvnb|Tanton|2005|pp=9–10}} | {{harvnb|Corry|2024|loc=§ The Equation in India and China}} }}</ref> Ŵasandi ŵa masamu ŵa ku India [[Mahāvīra (mathematician)|Mahāvīra]] mu vilimika vya 9 na [[Bhāskara II]] mu vilimika vya 12 ŵakakhozgaso nthowa na vinjeru vya Brahmagupta.<ref>{{multiref | {{harvnb|Seshadri|2010|p=[https://books.google.com/books?id=w_JdDwAAQBAJ&pg=PA156 156]}} | {{harvnb|Emch|Sridharan|Srinivas|2005|p=[https://books.google.com/books?id=qfJdDwAAQBAJ&pg=PA20 20]}} }}</ref> Mu 1247, msandi wa masamu wa ku China [[Qin Jiushao]] wakalemba buku la ''[[Mathematical Treatise in Nine Sections]]'', ilo likusazgamo [[Horner's method|nthowa yakuŵelenga]] ya [[Polynomial evaluation|kuŵelenga mtengo wa ma polynomial]], kusazgamo ma polynomial gha madigiri ghapachanya.<ref>{{multiref | {{harvnb|Smorynski|2007|p=[https://books.google.com/books?id=qY657eFq7UgC&pg=PA137 137]}} | {{harvnb|Zwillinger|2002|p=[https://books.google.com/books?id=gE_MBQAAQBAJ&pg=PA812 812]}} }}</ref> {{multiple image | perrow = 2 | total_width = 350 | image1 = Francois Viete.jpeg | alt1 = Drawing of François Viète | image2 = Frans Hals - Portret van René Descartes (cropped).jpg | alt2 = Painting of René Descartes | footer = [[François Viète]] (kumalyo) na [[René Descartes]] ŵakasanga viwimbo vyakwenerana kulongosora ma equation mwamzimu wakudumura na wachidango. }} Msandi wa masamu wa ku Italy [[Fibonacci]] wakiza na vinjeru na nthowa za Al-Khwarizmi ku Ulaya mu mabuku ghake, kusazgamo ''[[Liber Abaci]]''.<ref>{{multiref | {{harvnb|Waerden|2013|pp=32–35}} | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Kvasz|2006|p=293}} }}</ref> Mu 1545, msandi wa masamu wa mitundu yinandi wa ku Italy [[Gerolamo Cardano]] wakafumiska buku lake ''[[Ars Magna (Cardano book)|Ars Magna]]'', ilo likakhwaskira vinthu vinandi mu algebra, likadumbiskana [[imaginary numbers|vipendeko vya mung'anamuro]], ndipo likaŵa lakwamba kupeleka nthowa zawonse zakumazgira ma equation gha [[Cubic equation|digiri yitatu]] na [[quartic equation|digiri yinayi]].<ref>{{multiref | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Kvasz|2006|p=293}} | {{harvnb|Corry|2024|loc=§ Cardano and the Solving of Cubic and Quartic Equations}} | {{harvnb|Miyake|2002|p=[https://books.google.com/books?id=G0P2BwAAQBAJ&pg=PA268 268]}} }}</ref> Mu vilimika vya 16 na 17, ŵasandi ŵa masamu ŵa ku France [[François Viète]] na [[René Descartes]] ŵakiza na malembelo na viwimbo kwimira vyambura-kumanyikwa na nchito, kupangiska kuti ma equation ghalembeke mwamzimu wachidango na wakudumura. Awo ŵakaŵako panthazi pawo ŵakajighemezga pa malongosoro ghakuyowoya gha masuzgo na vyakumazga.<ref>{{multiref | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Kvasz|2006|pp=291–292, 297–298, 302}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} | {{harvnb|Corry|2024|loc=§ Viète and the Formal Equation, § Analytic Geometry}} }}</ref> Ŵalongozgi ŵanyake ŵa mbiri ŵakuwona kukula uku kuŵa mzuŵa wakuzirwa mu mbiri ya algebra ndipo ŵakuwona ivyo vikaŵako pambere kuŵa mbiri-ntchakwamba ya algebra chifukwa vikasoŵanga mzimu wakudumura uwo ukujimira pa kugwiliskira ntchito viwimbo.<ref>{{multiref | {{harvnb|Hazewinkel|1994|p=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA73 73]}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} }}</ref> Mu vilimika vya 17 na 18, kuyezgayezga kwakuluska kukachitika kupenja vyakumazga vyawonse ku ma polynomial gha digiri yankonde na yapachanya. Vyose ivi vikafiliskika.<ref name="auto3">{{multiref | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} | {{harvnb|Corry|2024|loc=§ Impasse with Radical Methods}} }}</ref> Kumapeleko gha vilimika vya 18, msandi wa masamu wa ku Germany [[Carl Friedrich Gauss]] wakalongosora fundo yikuru ya algebra, iyo yikulongosora kuŵako kwa [[Zero of a function|vizero]] vya ma polynomial gha digiri yiliyose kwambura kupeleka yankho lawonse.<ref name="auto7"/> Kwambilira kwa vilimika vya 19, msandi wa masamu wa ku Italy [[Paolo Ruffini]] na msandi wa masamu wa ku Norway [[Niels Henrik Abel]] [[Abel–Ruffini theorem|ŵakakhozga]] kuti palije yankho lawonse ilo lilipo ku ma polynomial gha digiri yankonde na yapachanya.<ref name="auto3"/> Kwiza pa na pamanyuma pachoko pa vyakusanga vyawo, msandi wa masamu wa ku France [[Évariste Galois]] wakakhozga icho pamanyuma chikachemeka [[Galois theory|sambiro la Galois]], ilo likapeleka kupenja kwakukuzura kwa vyakumazga vya ma polynomial apo so likakhozga msingi wa [[group theory|sambiro la magulu]].<ref name="auto2"/> Ŵasandi ŵa masamu paukhwakuŵa ŵakamanya kuzirwa kwa sambiro la magulu ku magulu ghanyake gha masamu ndipo ŵakaligwiliskira ntchito ku vipangizo nga geometry na sambiro la vipendeko.<ref>{{multiref | {{harvnb|Corry|2024|loc=§ Applications of Group Theory}} | {{harvnb|Bueno|French|2018|pp=[https://books.google.com/books?id=kmZaDwAAQBAJ&pg=PA73 73–75]}} }}</ref> [[File:Garrett Birkhoff.jpeg|thumb|alt=Photo of Garrett Birkhoff|[[Garrett Birkhoff]] wakakhozga vinjeru vinandi vya msingi vya algebra ya wonse.|left|upright=0.8]] Kwambira pakati pa vilimika vya 19, chikhumbo mu algebra chikasintha kufuma ku kusambira ma polynomial ivyo vikakhwaskana na algebra ya pulayimale kuya ku kupenja kwakukuru kwa magulu gha algebra, ndipo ichi chikawoneka pakufuma kwa [[abstract algebra|algebra yakudumura]]. Nthowa iyi yikapenja msingi wa maxiom wa nchito za algebra zakupambanapambana.<ref>{{multiref | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Corry|2024|loc=§ Structural Algebra}} | {{harvnb|Hazewinkel|1994|pp=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA73 73–74]}} }}</ref> Kusangika kwa ndondomeko nyifya za algebra izo zikuzirwa pa nchito na vinthu vyakupambanapambana vikalondezga kukula uku, nga [[Boolean algebra]], [[Vector space|algebra ya vector]], na [[matrix algebra|algebra ya matrix]].<ref>{{multiref | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Corry|2024|loc=§ Matrices, § Quaternions and Vectors}} }}</ref> Vyakukula vyakuzirwa vyakwamba mu algebra yakudumura vikapangika na ŵasandi ŵa masamu ŵa ku Germany [[David Hilbert]], [[Ernst Steinitz]], na [[Emmy Noether]] pamoza na msandi wa masamu wa ku Austria [[Emil Artin]]. Ŵakasanda mitundu yakupambanapambana ya magulu gha algebra ndipo ŵakaghapatuliska kuyana na maxiom ghawo ghakuzikapo kuŵa mitundu, nga magulu, mphete, na minda.<ref>{{multiref | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} | {{harvnb|Corry|2024|loc=§ Hilbert and Steinitz, § Noether and Artin}} | {{harvnb|Hazewinkel|1994|pp=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA73 73–74]}} }}</ref> Mzimu wa nthowa yikuru comenecomene iyo yikukhwaskana na algebra ya wonse ukaghanaghanika na msandi wa masamu wa ku England [[Alfred North Whitehead]] mu buku lake la 1898 ''A Treatise on Universal Algebra''. Kwambira mu vya 1930, msandi wa masamu wa ku America [[Garrett Birkhoff]] wakatandarizga vinjeru ivi ndipo wakakhozga vinjeru vinandi vya msingi vya gulu ili la sambiro.<ref>{{multiref | {{harvnb|Grätzer|2008|p=[https://books.google.com/books?id=8lNkXPJas4wC&pg=PR7 vii]}} | {{harvnb|Chang|Keisler|1990|p=[https://books.google.com/books?id=uiHq0EmaFp0C&pg=PA603 603]}} | {{harvnb|Knoebel|2011|p=[https://books.google.com/books?id=VWS_sgO2uvgC&pg=PA5 5]}} | {{harvnb|Hazewinkel|1994|pp=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA74 74–75]}} }}</ref> Kusangika kwa algebra ya wonse kukalongozgera ku kufuma kwa vipimo vinyake vinyifya ivyo vikang'anamuka pa kupanga algebra ya masamu ghanyake{{em dash}}ndikuti, kugwiliskira ntchito nthowa za algebra ku magulu ghanyake gha masamu. Algebra ya topology yikafuma mu vilimika vyakwamba vya 20, kusambira magulu gha algebra nga [[topological groups|magulu gha topology]] na [[Lie groups|magulu gha Lie]].<ref>{{multiref | {{harvnb|Hazewinkel|1994|pp=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA74 74–75]}} | {{harvnb|Kleiner|2007|p=[https://books.google.com/books?id=udj-1UuaOiIC&pg=PA100 100]}} | {{harvnb|Carlson|2024|loc=§ History of topology}} }}</ref> Mu vya 1940 na 50, [[homological algebra|algebra ya homology]] yikafuma, kugwiliskira ntchito nthowa za algebra kusambira [[Homology (mathematics)|homology]].<ref>{{multiref | {{harvnb|Hazewinkel|1994|pp=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA74 74–75]}} | {{harvnb|Weibel|1995|p=[https://books.google.com/books?id=UtIhAwAAQBAJ&pg=PR11 xi, 4]}} }}</ref> Pafupifupi nyengo yeneyiyo, [[category theory|sambiro la mikhaliro]] likafuma ndipo lyakhala likugwira ntchito yikuru mu [[foundations of mathematics|msingi wa masamu]].<ref>{{multiref | {{harvnb|Krömer|2007|p=[https://books.google.com/books?id=41bHxtHxjUAC&pg=PA61 61]}} | {{harvnb|Laos|1998|p=[https://books.google.com/books?id=1r7dSn4ZqogC&pg=PA100 100]}} }}</ref> Vyakukula vinyake vikaŵa kupangika kwa [[model theory|sambiro la vimodel]] na kusambira [[free algebra|algebra zamahara]].<ref>{{multiref | {{harvnb|Hazewinkel|1994|pp=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA74 74–75]}} | {{harvnb|Pratt|2022|loc=§ 6. Free Algebras}} }}</ref> {{clear}} == Kugwiliskika Ntchito == {{see also|Applied mathematics}} Chikoliro cha algebra nkhutandarika comenecomene, mu masamu mwene na mu kugwiliskika kwake ku magulu ghanyake gha masamu.<ref>{{multiref | {{harvnb|Houston|2004|p=[https://books.google.com/books?id=jsWL_XJt-dMC&pg=PA319 319]}} | {{harvnb|Neri|2019|p=[https://books.google.com/books?id=NMOlDwAAQBAJ&pg=PR12 xii]}} | {{harvnb|Lidl|Pilz|1997|pp=[https://books.google.com/books?id=_49AmSWo4_AC&pg=PR7 vii–viii]}} }}</ref> Kupanga masamu ghanyake kuŵa gha algebra nkhu ndondomeko ya kugwiliskira ntchito nthowa na vinjeru vya algebra ku [[branches of mathematics|magulu ghanyake gha masamu]], nga [[geometry]], [[topology]], [[number theory|sambiro la vipendeko]], na [[calculus]]. Ichi chikuchitika mwakugwiliskira ntchito viwimbo mu mtundu wa vyambura-kumanyikwa kulongosora vinjeru vya masamu pa vipimo vikuru, kupangiska kuti ŵasandi ŵa masamu ŵapange vimodel vyakuzomerezgeka ivyo vikulongosora umo vinthu vikukhwaskirana na kukolerana wene.<ref>{{multiref | {{harvnb|Kleiner|2007|p=[https://books.google.com/books?id=udj-1UuaOiIC&pg=PA100 100]}} | {{harvnb|Pratt|2022|loc=§ 5. Algebraization of Mathematics}} | {{harvnb|Maddocks|2008|p=130}} | {{harvnb|Pratt|2022|loc=§ 5. Algebraization of Mathematics}} | {{harvnb|Mancosu|1999|pp=[https://books.google.com/books?id=60qaEePdqcoC&pg=PA84 84–85]}} }}</ref> [[File:Sphere Quadric.png|thumb|alt=Rendered image of a sphere|Equation ya algebra <math>x^2 + y^2 + z^2 = 1</math> yikulongosora [[sphere|sphere]] ku [[Origin (mathematics)|malo ghakwambira]] ghali na radius ya 1.]] Nchito yimoza, iyo yikusangika mu geometry, ni kugwiliskira ntchito mazgu gha algebra kulongosora vithunzithunzi vya geometry. Mwachiyelezgero, equation <math>y = 3x - 7</math> yikulongosora mzere mu malo gha mibaru yiŵiri apo equation <math>x^2 + y^2 + z^2 = 1</math> yikuyana na [[sphere|sphere]] mu malo gha mibaru yitatu. Vyakuzirwa comenecomene ku [[algebraic geometry|geometry ya algebra]] ni [[algebraic varieties|mitundu yakuyana ya algebra]],{{efn|Mitundu yakuyana ya algebra iyo yikusambirika mu geometry njakupambana na mitundu yakuyana yikuru iyo yikusambirika mu algebra ya wonse.<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 1.4 Cartesian geometry, § 3. Universal Algebra}} | {{harvnb|Danilov|2006|p=[https://books.google.com/books?id=-QMWR-x66XUC&pg=PA174 174]}} }}</ref>}} izo ni vyakumazga vya [[systems of polynomial equations|ndondomeko za ma equation gha polynomial]] ivyo vingagwiliskika kulongosora vithunzithunzi vyapasuzgika vya geometry.<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 5.1 Algebraic Geometry}} | {{harvnb|Danilov|2006|pp=[https://books.google.com/books?id=-QMWR-x66XUC&pg=PA172 172, 174]}} }}</ref> Kughanaghanira mwa algebra kungamazgaso masuzgo gha geometry. Mwachiyelezgero, munthu wangamanya usange na apo mzere wakulongosoreka na <math>y = x + 1</math> ukukhwaskana na dindi (circle) ilo likulongosoreka na <math>x^2 + y^2 = 25</math> mwakumazga ndondomeko ya ma equation ghakupangika na ma equation ghaŵiri agha.<ref>{{harvnb|Vince|2007|p=[https://books.google.com/books?id=B574tQbP6WcC&pg=PA133 133]}}</ref> Topology yikusambira vinjeru vya vithunzithunzi vya geometry panji [[topological space|malo gha topology]] ivyo vikukhalilira mwambura kusintha para vichitikirwa [[continuous deformation|kusintha kwakulutilira]]. [[Algebraic topology|Topology ya algebra]] yikuzirwa pa vinjeru vya algebra nga sambiro la magulu kupatuliska malo gha topology. Mwachiyelezgero, [[homotopy groups|magulu gha homotopy]] ghakupatuliska malo gha topology kuyana na kuŵako kwa [[Loop (topology)|majoro]] panji [[Hole#In mathematics|maenja]] mwa iwo.<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 5.3 Algebraic Topology}} | {{harvnb|Rabadan|Blumberg|2019|pp=[https://books.google.com/books?id=2967DwAAQBAJ&pg=PA49 49–50]}} | {{harvnb|Nakahara|2018|p=[https://books.google.com/books?id=p2C1DwAAQBAJ&pg=PA121 121]}} | {{harvnb|Weisstein|2003|pp=52–53}} }}</ref> Sambiro la vipendeko likukhwaskana na vinjeru na ukhwaskano pakati pa vipendeko vyambura kugaŵika. [[Algebraic number theory|Sambiro la vipendeko la algebra]] likugwiliskira ntchito nthowa na vinjeru vya algebra ku chipangizo ichi cha kupenja. Vyakuyelezgera ni kugwiliskira ntchito mazgu gha algebra kulongosora madango ghawonse, nga [[Fermat's Last Theorem|fundo yaumaliro ya Fermat]], na kugwiliskira ntchito magulu gha algebra kusanda mkhalidwe wa vipendeko, nga [[ring of integers|mphete ya vipendeko vyambura kugaŵika]].<ref>{{multiref | {{harvnb|Pratt|2022|loc=§ 5.2 Algebraic Number Theory}} | {{harvnb|Jarvis|2014|p=[https://books.google.com/books?id=0j0qBAAAQBAJ&pg=PA1 1]}} | {{harvnb|Viterbo|Hong|2011|p=[https://books.google.com/books?id=d89QRR24jbMC&pg=PA127 127]}} }}</ref> Chipangizo chakukhwaskana ichi cha [[combinatorics|combinatorics]] chikugwiliskira ntchito nthowa za algebra kumazga masuzgo ghakukhwaskana na kuŵelenga, kunozga, na kukoleranya vinthu vyakupambanapambana. Chiyelezgero mu [[algebraic combinatorics|combinatorics ya algebra]] ni kugwiliskira ntchito sambiro la magulu kusanda [[Graph (discrete mathematics)|ma graph]] na symmetries.<ref>{{multiref | {{harvnb|Gowers|Barrow-Green|Leader|2010|pp=[https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA550 550, 561]}} | {{harvnb|Godsil|2017|p=[https://books.google.com/books?id=hLs6DwAAQBAJ&pg=PR8 viii]}} | {{harvnb|Betten|Kohnert|Laue|Wassermann|2013|p=[https://books.google.com/books?id=G1TmCAAAQBAJ&pg=PP9 ix]}} }}</ref> Vinjeru vya algebra vikuzirwaso ku calculus, iyo yikugwiliskira ntchito mazgu gha masamu kupenja [[rates of change|liŵiro la kusintha]] na [[Integral|kuwungana]]. Yikuzirwa pa algebra, mwachiyelezgero, kupulikiska umo mazgu agha ghangasinthika na mzimu uwo vyambura-kumanyikwa vikugwira mwa iwo.<ref>{{multiref | {{harvnb|Kilty|McAllister|2018|pp=x, 347, 589}} | {{harvnb|Bressoud|2021|p=[https://books.google.com/books?id=GkgHEAAAQBAJ&pg=PA64 64]}} }}</ref> [[Algebraic logic|Logic ya algebra]] yikugwiliskira ntchito nthowa za algebra kulongosora na kusanda magulu na vinjeru ivyo vili musingi wa [[logical reasoning|kughanaghanira kwa logic]],<ref>{{multiref | {{harvnb|Halmos|1956|p=363}} | {{harvnb|Burris|Legris|2021|loc=§ 1. Introduction}} }}</ref> kupenja vyose viŵiri, magulu ghenegho gha masamu na kugwiliskika kwawo ku masuzgo ghakuwoneka gha logic.<ref>{{harvnb|Andréka|Németi|Sain|2001|pp=[https://link.springer.com/chapter/10.1007/978-94-017-0452-6_3 133–134]}}</ref> Yikusazgamo kusambira [[Boolean algebra]] kulongosora [[propositional logic]]<ref>{{multiref | {{harvnb|Andréka|Madarász|Németi|2020|loc=§ Concrete Algebraic Logic}} | {{harvnb|Pratt|2022|loc=§ 5.4 Algebraic Logic}} | {{harvnb|Plotkin|2012|pp=[https://books.google.com/books?id=-v3xCAAAQBAJ&pg=PA155 155–156]}} | {{harvnb|Jansana|2022|loc=Lead section}} }}</ref> pamoza na kupanga na kusanda magulu gha algebra ghakuyana na [[Logic#Systems_of_logic|ndondomeko za logic]] zapasuzgika kuluska.<ref>{{multiref | {{harvnb|Andréka|Madarász|Németi|2020|loc=§ Abstract Algebraic Logic}} | {{harvnb|Jansana|2022|loc=§ 4. Algebras}} }}</ref> [[File:Rubik's cube.svg|thumb|upright=0.8|alt=Picture of Rubik's cube|Mbali za [[Rubik's Cube]] zingazingilizgika kusintha kunozgeka kwa vipande vyakupambanapambana mitundu (colored patches). Vipimo ivyo vikufuma pamanyuma (permutations) vikupanga gulu ilo likuchemeka [[Rubik's Cube group|gulu la Rubik's Cube]].<ref>{{harvnb|Joyner|2008|p=92}}</ref>]] Nthowa za algebra zikugwiliskikaso comenecomene mu magulu ghanyake, nga sayansi za chilengechilenge. Mwachiyelezgero, zikugwiliskika kulongosora [[scientific laws|madango gha kasandiro]] na kumazga ma equation mu [[physics]], [[chemistry]], na [[biology]].<ref>{{multiref | {{harvnb|Houston|2004|p=[https://books.google.com/books?id=jsWL_XJt-dMC&pg=PA319 319]}} | {{harvnb|Neri|2019|p=[https://books.google.com/books?id=NMOlDwAAQBAJ&pg=PR12 xii]}} | {{harvnb|Anton|Rorres|2010|p=[https://books.google.com/books?id=1PJ-WHepeBsC&pg=PA327 327]}} }}</ref> Kugwiliskika kwakuyana kukusangikaso mu magulu nga [[economics]], [[geography]], [[engineering]] (kusazgamo [[electronics]] na [[robotics]]), na [[computer science]] kulongosora ukhwaskano, kumazga masuzgo, na kupanga vimodel vya ndondomeko.<ref>{{multiref | {{harvnb|Neri|2019|p=[https://books.google.com/books?id=NMOlDwAAQBAJ&pg=PR12 xii]}} | {{harvnb|Aleskerov|Ersel|Piontkovski|2011|pp=[https://books.google.com/books?id=ipcSD8ZGB8cC&pg=PA1 1–9]}} | {{harvnb|Straffin|1980|p=[https://www.jstor.org/stable/2689388 269]}} | {{harvnb|Menini|Oystaeyen|2017|p=[https://books.google.com/books?id=3mlQDwAAQBAJ&pg=PR5 v]}} | {{harvnb|Lovett|2015|p=[https://books.google.com/books?id=jRUqCgAAQBAJ&pg=PR9 ix]}} | {{harvnb|Lidl|Pilz|1997|pp=[https://books.google.com/books?id=_49AmSWo4_AC&pg=PR7 vii–viii]}} }}</ref> Algebra ya mzere yikugwira ntchito yikuru mu [[artificial intelligence]] na [[machine learning]], mwachiyelezgero, mwakukhozgera kuwendeska na kusanda [[dataset|masetu gha data]] ghakuru mwakuzomerezgeka.<ref>{{multiref | {{harvnb|Wheeler|2023|p=[https://books.google.com/books?id=IqQIEQAAQBAJ&pg=PA29 29, 36–37]}} | {{harvnb|Gallier|Quaintance|2020|pp=[https://books.google.com/books?id=jWLcDwAAQBAJ&pg=PA1 1–2]}} }}</ref> Magulu ghakupambanapambana ghakuzirwa pa magulu gha algebra ghakusambirika na algebra yakudumura. Mwachiyelezgero, sayansi za vinthu nga [[crystallography]] na [[quantum mechanics]] zikugwiliskira ntchito comenecomene sambiro la magulu,<ref>{{multiref | {{harvnb|Klimov|2014|p=[https://books.google.com/books?id=DZK3DwAAQBAJ&pg=PR9 ix]}} | {{harvnb|Bengtsson|Życzkowski|2017|pp=313–353}} }}</ref> ilo likugwiliskikaso kusambira ma puzzle nga [[Sudoku]] na [[Rubik's Cube]],<ref>{{harvnb|Terras|2019|pp=63–64, 142}}</ref> na [[Mathematics of paper folding|origami]].<ref>{{harvnb|Hull|2021|p=[https://books.google.com/books?id=LdX7DwAAQBAJ&pg=PA180 180]}}</ref> Vyose viŵiri [[coding theory|sambiro la ma code]] na [[cryptology]] zikuzirwa pa algebra yakudumura kumazga masuzgo ghakukhwaskana na [[data transmission|kutuma data]], nga kujiwezga na vikwaskiro (noise) na kukhozgera [[data security|chitetezo cha data]].<ref>{{multiref | {{harvnb|Lidl|Pilz|1997|pp=183–184, 239–240}} | {{harvnb|Carstensen|Fine|Rosenberger|2011|pp=[https://books.google.com/books?id=Xo6iSxRfXz0C&pg=PA326 326–327]}} }}</ref> == Masambizgo == {{See also|Mathematics education}} [[File:Balance scale.svg|thumb|upright=1.3|class=skin-invert-image|alt=Diagram of a balance scale|[[Balance scales|Vipimiro vyakulinganya]] vikugwiliskika mu masambizgo gha algebra kovwira ŵasambiri kupulikiska umo ma equation ghangasinthika kuti ghamanye viŵelengero vyambura kumanyikwa.<ref>{{multiref | {{harvnb|Kieran|2006|p=[https://books.google.com/books?id=OTCsKu0BZ0kC&pg=PA15 15]}} | {{harvnb|Kaput|2018|p=[https://books.google.com/books?id=1GUPEAAAQBAJ&pg=PA186 186]}} |{{harvnb|Gardella|DeLucia|2020|pp=[https://books.google.com/books?id=HBXFDwAAQBAJ&pg=PA19 19–22]}} }}</ref>]] Masambizgo gha algebra ghakuzirwa comenecomene pa algebra ya pulayimale, chimoza mwa vifukwa ivyo algebra ya pulayimale yikuchemekaso "algebra ya sukulu". Comenecomene, yikwambiskika yayi kwambira mu [[secondary education|masambizgo ghapachanya]] chifukwa yikukhumba kumanya makora masamu ghakwamba apo yikwizaso na vyakusuzga vinyake vipya ivyo vikukhwaskana na kughanaghanira kwakudumura na kwawonse.<ref>{{multiref | {{harvnb|Arcavi|Drijvers|Stacey|2016|p=xiii}} | {{harvnb|Dekker|Dolk|2011|p=[https://books.google.com/books?id=7sVFaMhwackC&pg=PA69 69]}} }}</ref> Yikukhumba kuzgoŵeska ŵasambiri na mbali yakuzomerezgeka ya masamu mwakuŵawovwira kupulikiska viwimbo vya masamu, mwachiyelezgero, umo vyambura-kumanyikwa vingagwiliskika kwimira viŵelengero vyambura kumanyikwa. Kususka kwinyake ku ŵasambiri nkhwakuti, kupambana na kuŵelenga kwaumaliro, mazgu gha algebra ghakusuzga comenecomene kumazgika mwakwenderana. M'malo mwake, ŵasambiri ŵakukhumbikwa kusambira umo ŵangaghasinthira kuyana na madango ghanyake, kanandi kuti ŵamanye chiŵelengero chambura kumanyikwa.<ref>{{multiref | {{harvnb|Arcavi|Drijvers|Stacey|2016|pp=2–5}} | {{harvnb|Drijvers|Goddijn|Kindt|2011|pp=[https://books.google.com/books?id=7sVFaMhwackC&pg=PA8 8–10, 16–18]}} }}</ref> Vipangizo vinyake vyakwiziska ŵasambiri ku mbali yakudumura ya algebra vikuzirwa pa vimodel vyakuwoneka na kulongora ma equation, kusazgamo vyakuyelezgera vya geometry, vipangizo vyakugwira nawo nchito nga vikoli panji makapu, na "makina gha nchito" (function machines) ivyo vikulongora ma equation kuŵa [[flow diagram|maonekero gha kuluta patsogolo]]. Nthowa yimoza yikugwiliskira ntchito [[balance scales|vipimiro vyakulinganya]] kuŵa nthowa yakuwoneka yakovwira ŵasambiri kupulikiska masuzgo ghakwamba gha algebra. Uzito wa vinthu vinyake pa chipimiro nchambura kumanyikwa ndipo ukwimira vyambura-kumanyikwa. Kumazga equation kukuyana na kusazga na kuwuskapo vinthu ku mbali zose ziŵiri mwakuti mbali zikhalilire mu ulinganyi mpaka chinthu chimoza pera icho chikhala pa mbali yimoza ni chinthu chambura kumanyikwa uzito wake.<ref>{{multiref | {{harvnb|Kieran|2006|p=[https://books.google.com/books?id=OTCsKu0BZ0kC&pg=PA15 15]}} | {{harvnb|Kaput|2018|p=[https://books.google.com/books?id=1GUPEAAAQBAJ&pg=PA186 186]}} |{{harvnb|Gardella|DeLucia|2020|pp=[https://books.google.com/books?id=HBXFDwAAQBAJ&pg=PA19 19–22]}} | {{harvnb|Star|Foegen|Larson|McCallum|2015|pp=16–17}} }}</ref> [[Word problem (mathematics education)|Masuzgo gha mazgu]] ni chipangizo chinyake chakulongora umo algebra yikugwiliskika ku vinthu vyaunenesko vya moyo. Mwachiyelezgero, ŵasambiri ŵangapika mu mkhalidwe uwo mbale wa Naomi wali na machiyembe ghakuŵirapo kuŵiri kuluska Naomi. Pakuti ŵaŵiri wose pamoza ŵali na machiyembe 12, ŵasambiri ŵakupikika kuti ŵasange equation ya algebra iyo yikulongosora mkhalidwe uwu ({{tmath|1= 2x + x = 12 }}) na kumanya machiyembe ghaŵi agho Naomi wali nagho {{nowrap|({{tmath|1= x = 4 }}).<ref>{{multiref | {{harvnb|Arcavi|Drijvers|Stacey|2016|pp=58–59}} | {{harvnb|Drijvers|Goddijn|Kindt|2011|p=[https://books.google.com/books?id=7sVFaMhwackC&pg=PA13 13]}} }}</ref>}} Pa vipimo vya yunivesite, ŵasambiri ŵa masamu ŵakukhwaskana na mitu yapachanya ya algebra kufuma ku algebra ya mzere na algebra yakudumura. Makalasi ghakwamba gha [[undergraduate|digiri yakwamba]] mu algebra ya mzere ghakuzirwa pa ma matrix, malo gha vector, na mapu gha mzere. Para ŵamalizga, ŵasambiri comenecomene ŵakwiziskika ku algebra yakudumura, uko ŵakusambira magulu gha algebra nga magulu, mphete, na minda, pamoza na ukhwaskano pakati pawo. Masambiro (curriculum) ghakuzirwa comenecomene ghakukhwaskaso vithuzi vyapadera vya magulu gha algebra, nga ndondomeko za vipendeko vyakugaŵikika, vipendeko vyeneco, na ma polynomial.<ref>{{harvnb|Hausberger|Zandieh|Fleischmann|2021|pp=147–148}}</ref> == Vinyake Vyakukhwaskana == {{div col|colwidth=30em}} * {{annotated link|Commutative algebra}} * {{annotated link|Computer algebra}} * {{annotated link|Exterior algebra}} * {{annotated link|F-algebra}} * {{annotated link|Geometric algebra}} * {{annotated link|Non-associative algebra}} * {{annotated link|Outline of algebra}} * {{annotated link|Representation theory}} * {{annotated link|Tensor}} {{div col end}} == References == === Notes === {{notelist}} === Citations === {{reflist}} === Sources === {{refbegin|30em}} * {{cite book |last1=Abas |first1=Syed Jan |last2=Salman |first2=Amer Shaker |title=Symmetries Of Islamic Geometrical Patterns |date=1994 |publisher=World Scientific |isbn=978-981-4502-21-4 |url=https://books.google.com/books?id=5snsCgAAQBAJ |language=en |access-date=March 12, 2024}}{{cbignore}} * {{cite book |last1=Adhikari |first1=Mahima Ranjan |title=Basic Algebraic Topology and its Applications |publisher=Springer |isbn=978-81-322-2843-1 |url=https://books.google.com/books?id=MIAXDQAAQBAJ&pg=PA5 |language=en |date=2016 |access-date=August 5, 2024}}{{cbignore}} * {{cite book |last1=Adhikari |first1=Mahima Ranjan |last2=Adhikari |first2=Avishek |title=Basic Modern Algebra with Applications |publisher=Springer |isbn=978-81-322-1599-8 |url=https://books.google.com/books?id=lBO7BAAAQBAJ&pg=PA72 |language=en |date=2013 |access-date=August 5, 2024}}{{cbignore}} * {{cite book |last1=Aleskerov |first1=Fuad |last2=Ersel |first2=Hasan |last3=Piontkovski |first3=Dmitri |title=Linear Algebra for Economists |date=2011 |publisher=Springer |isbn=978-3-642-20570-5 |url=https://books.google.com/books?id=ipcSD8ZGB8cC&pg=PA1 |language=en |access-date=March 11, 2024}}{{cbignore}} * {{cite web |last1=Andréka |first1=H. |last2=Madarász |first2=J. 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I. |title=Linear Equation |url=https://encyclopediaofmath.org/wiki/Linear_equation |website=Encyclopedia of Mathematics |publisher=Springer |access-date=January 10, 2024 |date=2011 |archive-date=November 23, 2023 |archive-url=https://web.archive.org/web/20231123235759/https://encyclopediaofmath.org/wiki/Linear_equation |url-status=live}} * {{cite book |last1=Waerden |first1=Bartel L. van der |author-link=Bartel Leendert van der Waerden |title=Algebra |publisher=Springer |isbn=0-387-40624-7 |volume=1 |date=2003}} * {{cite book |last1=Waerden |first1=Bartel L. van der |title=A History of Algebra: From al-Khwārizmī to Emmy Noether |date=2013 |publisher=Springer |isbn=978-3-642-51599-6 |url=https://books.google.com/books?id=W6DwCAAAQBAJ |language=en |access-date=January 27, 2024}}{{cbignore}} * {{cite book |last1=Wagner |first1=Sigrid |last2=Kieran |first2=Carolyn |title=Research Issues in the Learning and Teaching of Algebra: The Research Agenda for Mathematics Education |volume=4 |date=2018 |publisher=Routledge |isbn=978-1-135-43421-2 |url=https://books.google.com/books?id=uW4ECwAAQBAJ&pg=PT225 |language=en |access-date=January 13, 2024}}{{cbignore}} * {{cite book |last1=Walz |first1=Guido |title=Lexikon der Mathematik: Band 1: A bis Eif |date=2016 |publisher=Springer |isbn=978-3-662-53498-4 |url=https://www.spektrum.de/lexikon/mathematik/algebra/12062 |language=de |chapter=Algebra |access-date=January 13, 2024 |archive-date=January 12, 2024 |archive-url=https://web.archive.org/web/20240112171819/https://www.spektrum.de/lexikon/mathematik/algebra/12062 |url-status=live |trans-title=Encyclopedia of Mathematics: Volume 1: A to Eif}} * {{cite book |last1=Weibel |first1=Charles A. |author-link=Charles Weibel |title=An Introduction to Homological Algebra |publisher=Cambridge University Press |isbn=978-1-139-64307-8 |url=https://books.google.com/books?id=UtIhAwAAQBAJ&pg=PR11 |language=en |date=1995}} * {{cite book |last1=Weisstein |first1=Eric W. |title=CRC Concise Encyclopedia of Mathematics |date=2003 |publisher=Chapman & Hall/CRC |isbn=978-1-58488-347-0 |edition=2nd}} * {{cite book |last1=Wheeler |first1=Jeffrey Paul |title=An Introduction to Optimization with Applications in Machine Learning and Data Analytics |publisher=CRC Press |isbn=978-1-003-80359-1 |url=https://books.google.com/books?id=IqQIEQAAQBAJ&pg=PA29 |language=en |date=2023}} * {{cite book |last1=Whitelaw |first1=T. A. |title=Introduction to Abstract Algebra, Third Edition |publisher=CRC Press |isbn=978-0-7514-0147-9 |url=https://books.google.com/books?id=f2hyf0QoB_0C&pg=PA61 |language=en |date=1995}}{{cbignore}} * {{cite book |last1=Williams |first1=G. Arnell |title=Algebra the Beautiful: An Ode to Math's Least-Loved Subject |date=2022 |publisher=Basic Books |isbn=978-1-5416-0070-6 |url=https://books.google.com/books?id=581CEAAAQBAJ&pg=PT62 |language=en |access-date=March 11, 2024}}{{cbignore}} * {{cite book |last=Wilson |first=Robert A. |author-link=Robert Arnott Wilson |title=The Finite Simple Groups |publisher=[[Springer-Verlag]] |series=[[Graduate Texts in Mathematics]] |isbn=978-1-84800-987-5 |doi=10.1007/978-1-84800-988-2 |year=2009 |zbl=1203.20012 |volume=251}} * {{cite book |last1=Young |first1=Cynthia Y. |title=Precalculus |date=2010 |publisher=John Wiley & Sons |isbn=978-0-471-75684-2 |url=https://books.google.com/books?id=9HRLAn326zEC&pg=RA1-PA999 |language=en |access-date=January 16, 2024}}{{cbignore}} * {{cite book |last1=Young |first1=Cynthia Y. |title=Precalculus |date=2023 |publisher=John Wiley & Sons |isbn=978-1-119-86940-5 |url=https://books.google.com/books?id=pMSZEAAAQBAJ&pg=PA714 |language=en |access-date=January 18, 2024}}{{cbignore}} * {{cite web |author1=zbMATH Open |title=Classification |url=https://zbmath.org/classification/ |website=zbMATH Open |publisher=Mathematical Reviews and zbMATH Open |access-date=March 17, 2024 |language=en |date=2024 |archive-date=July 19, 2020 |archive-url=https://web.archive.org/web/20200719184539/https://zbmath.org/classification/ |url-status=live}} * {{cite book |last1=Zwillinger |first1=Daniel |title=CRC Standard Mathematical Tables and Formulae |date=2002 |publisher=CRC Press |isbn=978-1-4200-3534-6 |url=https://books.google.com/books?id=gE_MBQAAQBAJ&pg=PA812 |language=en |access-date=January 27, 2024}}{{cbignore}} {{Refend}} == External links == {{Wikiquote}} {{Wiktionary|algebra}} {{Wikibooks|Algebra}} {{EB1911 poster|Algebra}} {{Algebra}} {{Polynomials}} {{Areas of mathematics}} {{Authority control}} [[Category:Algebra| ]] tt2r9qa98urj7ynrf5arg10n5efnw9i 2 6886 121843 121784 2026-09-08T21:11:34Z Tumbuka Arch 6863 121843 wikitext text/x-wiki <!-- ========================================================= TUMBUKA ARCH — USER PAGE Short multicolour design — no red ========================================================= --> {| style="width:100%; background:transparent; padding:0.3em; margin:auto;" |- ! style="background:#6A5ACD; color:white; padding:0.5em; text-align:center; border-radius:8px;" | <big>{{CURRENTDAYNAME}}, {{CURRENTDAY}} {{CURRENTMONTHNAME}} {{CURRENTYEAR}}; {{CURRENTTIME}} (UTC)</big> [[File:Clock.gif|40px]] |- | style="background:#E6E6FA; padding:0.5em; text-align:center; border-radius:8px;" | {{user date}} |} <!-- ===================== USERNAME NOTE ===================== --> {| style="width:100%; border:2px solid #6A5ACD; background:#F3F0FF; padding:0.5em; margin-bottom:0.7em; border-radius:8px;" |- ! style="background:#6A5ACD; color:white; padding:0.4em; font-size:115%;" | A small confession about my username |- | style="padding:0.7em;" | <small>I sometimes regret choosing '''“Tumbuka Arch”.''' 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Boma ili likaŵapo pakati pa 1953 na 1963. Wupu uwu ukapangika pa 1 Ogasiti 1953,<ref>Rhodesia and Nyasaland Federation Act, 1953 of the [[United Kingdom]] (1 and 2 EI, 2, c. 30)</ref><ref>Federation of Rhodesia and Nyasaland (Constitution) Order in Council, 1953 of the United Kingdom, S.I. 1953 No. 1199, p. 1804</ref>na kazembe uyo ni mwimiliri wa fumukazi. Malo ghatatu agha ghakaŵa ghambura kukhwaskika, nangauli malango ghanyake ghakaŵa ghakuyana waka na gha ufumu wa Britain.<ref name="CnC">{{cite book|last=Roberts-Wray|first=Kenneth|author-link=Kenneth Roberts-Wray|date=1966|title=Commonwealth and Colonial Law|url=https://archive.org/details/commonwealthcolo0000sirk|location=London|publisher=Stevens|page=[https://archive.org/details/commonwealthcolo0000sirk/page/745 745]|isbn=}}</ref> Chinthu chinyake icho chikaŵa chiphya ni African Affairs Board, iyo yikakhazikiskika kuti yovwire ŵanthu ŵa mu Africa ndipo yikaŵa na mazaza ghakwendeskera fundo izo zikapelekeka. Apo caru cose cikafumako ku vyaru ivyo vikalamuliranga ŵanthu mu vyaka vya m'ma 1950 na m'ma 1960, caru ca United Kingdom cikakhwaskika na wupu wa United Nations na Organization of African Unity (OAU). Magulu agha ghakakolerana na ivyo ŵanthu ŵa ku Africa ŵakakhumbanga, ndipo ŵakakolerana nawo. Wupu uwu ukamara pa Disembala 31, 1963. Mu 1964, pakati pajumpha nyengo yichoko waka kufuma apo charu ichi chikamazgikira, Northern Rhodesia na Nyasaland ŵakajiyimira ŵekha. Mu Novembala 1965, charu cha Southern Rhodesia chikapharazga kuti ntchakujiyimira pawekha kufuma ku United Kingdom. == Mbili == === Wupu wa Central African Council === Mu 1929, Komiti ya Hilton Young yikati "mu nyengo iyo vinthu viliri nthena, vyakusanguluska vya ku Nyasaland na Northern Rhodesia, vya vyachuma na vya ndyali, vikukolerana yayi na vyaru vya ku East Africa, kweni vikukolerana na vyaru vinyake na vyaru vya Southern Rhodesia". Mu 1938, Komiti ya Bledisloe yikati vigaŵa vyose viŵenge vyakukolerana, kweni yikaleka kupempha kuti viŵe mu wupu wa federal. M'malo mwake, wupu uwu ukayowoya kuti paŵe wupu wa pakati pa vigaŵa kuti uwovwire boma na kuwona ivyo vikukhumbikwa mu cigaŵa ici. Nkhondo Yachiŵiri ya Caru Cose yikapangiska kuti wupu uwu uleke kukhazikiskika mu 1945, apo wupu wa Central African Council ukapangika kuti ukhozge ndondomeko na vyakucita pakati pa vigaŵa ivi. Kazembe wa ku Southern Rhodesia ndiyo wakaŵa na mazaza pa ungano uwu. Wupu uwu ukaŵa waka na mazaza gha kucezga, kweni ghakakanizganga yayi.<ref name=":0">{{Cite book|title=Handbook to the Federation of Rhodesia and Nyasaland|url=https://archive.org/details/handbooktofedera0000wvbr_t5q1|publisher=Cassell and Company, Ltd.|year=1960|editor-last=Brelsford|location=London}}</ref>{{Rp|591}} === Madumbizgilano === Mu Novembala 1950, Jim Griffiths, Secretary of State for the Colonies, wakaphalira House of Commons kuti boma laghanaghana kuti liwoneso umo vyaru vya ku Central Africa vingaŵira pamoza, ndipo kuti ungano wa maboma na wa Central African Council uŵengeko mu Malichi 1951. Ungano uwu ukati pakukhumbikwa kukolerana comene, ndipo ukayowoya za umo vyaru vitatu ivi vikukolerana. Ŵakati vigaŵa ivi vikaŵa vyambura kuvikilirika ndipo vingaŵa makora usange vingaŵa na chuma chikuru. Kweniso ŵakayowoya kuti usange maofesi ghanyake gha boma ghaŵa ghamoza, ghangapangiska kuti vinthu viŵe makora. Ŵakapeleka ulongozgi wakuti boma likhazikiske wupu wa wupu wakulongozga, ndipo boma likwenera kuŵa na mazaza ghanyake. Ungano unyake ukachitika mu Seputembala 1951 ku Victoria Falls, ndipo Griffiths na Patrick Gordon Walker nawo ŵakiza. Maungano ghanyake ghaŵiri ghakacitikira ku London mu 1952 na 1953, ndipo pa ungano uwu, ŵakanozgekera umo boma la Britain liŵirenge.<ref name=":0" />{{Rp|592}} Nangauli pa maungano agho ghakacitika pamanyuma pake pakaŵa fundo zinandi zakususkana, kweni zinandi zikaŵa zakusuzga kuzipulikiska, ndipo zinyake zikawonekanga zambura kumazga. Maungano agha ghakaŵa ghakusuzga. Southern Rhodesia na Northern Territories vikaŵa na maluso ghakupambana chomene pa nkhani ya 'Native Question' (African black) na maudindo agho ŵakeneranga kuchita mu chalo. Phangano ili mphanyi likaŵa lambura kufiskika kwambura Sir Andrew Cohen, Muteŵeti Wakovwira wa Secretary for African Affairs (ndipo pamanyuma wakaŵa Kazembe wa Uganda). Wakazgoka yumoza wa awo ŵakambiska na kwendeska vyaru ivyo vikaŵa ku chigaŵa cha Federation, ndipo kanandi wakawovwiranga yekha ŵanyawo. Cohen, uyo wakaŵa Muyuda ndipo wakakhuŵara comene cifukwa ca nyifwa ya ŵanthu ŵa mu caru ca America, wakaŵa munthu wakususka mtundu wa ŵanthu kweniso wakuvikilira wanangwa wa ŵanthu ŵa mu Africa. Kweni wakaleka vilato vyake kuti waleke kucita ivyo wakawonanga kuti ni ngozi yikuru comene kuluska kulutilira kwa muwuso wa ŵatuŵa wa ku Southern Rhodesia. Lord Blake, wakulemba mdauko wa ku Oxford, wakalemba kuti: "Mwakuyana waka, mtundu wa Apartheid ndiwo ukapangiska kuti vinthu viŵe makora". Pa Malichi 24, 1953, Nyumba ya Commons yikazomerezga fundo za ungano uwu, ndipo mu Epulero yikapeleka fundo zakukolerana na vyaru vya Northern Rhodesia na Nyasaland. Pa 9 Epulero, ku Southern Rhodesia kukacitika referendum.<ref name=":0" />{{Rp|592}} Pakulondezga kukosera na kukhozga mtima kwa Prime Minister wa Southern Rhodesia, Sir Godfrey Huggins, ŵanthu ŵakujumpha 25,000 ŵa ku Southern Rhodesia ŵakavotera boma la federal, ndipo pafupifupi 15,000 ŵakakana. Ŵanthu ŵanandi ŵa mu vigaŵa vyose vitatu ivi ŵakasuskanga. Wupu uwu ukaŵako apo Nyumba ya Malamulo ya ku United Kingdom yikapeleka dango lakuti Rhodesia and Nyasaland Federation Act, 1953. Dango ili likapeleka mazaza kwa Fumukazi kuti yikhazikiske wupu wa vyaru vitatu ivi. Dango ili likapelekeka pa Ogasiti 1, 1953, ndipo likapangiska kuti malango ghanyake gha mu Dango la Wupu Wakulongozga ghayambe kugwira ntchito. Kazembe mukuru wakwamba, Lord Llewellin, wakamba uteŵeti wake pa Seputembala 4. Pa Okutobala 23, 1953, Llewellin wakalemba chikalata icho chikapeleka ulongozgi unyake wose wa mu Dango.<ref name=":0" />{{Rp|591}} === Ndondomeko ya chalo === Paumaliro, boma la Britain likamba kulamulira mu vyaru vinkhondi. Ivi vikapangiska kuti paŵe kukangana pakati pa maboma gha vigaŵa vyakupambanapambana. Lord Blake wakati, caru ici cikaŵa "cimoza mwa vyaru ivyo vikaŵa na maboma ghawemi comene".<ref>Blake, 284.</ref> Ndondomeko iyi yikapangiska kuti paŵe boma la ku Africa ilo lili na mazaza ghakupambanapambana. Pakaŵa ndondomeko yakuti maboma gha boma na gha vigaŵa ghagaŵane mazaza na milimo yawo. Ndime 97 ya Dango ili yikapeleka mazaza ku wupu wa Federal Assembly kuti usinthe malango gha boma. Kazembe Mukuru ndiyo wakwimira Fumukazi mu Federation. Boma la United States likaŵa na mazaza pa nkhani izo zikakhwaskanga boma. Maufumu gha boma ghakagaŵikana mu "Federal Legislative List" agho wupu wakulongozga malango ghakaŵa na wanangwa wa kupanga malango, na "Concurrent Legislative List" uwo wupu wakulongozga malango wa boma na wa vigaŵa ukaŵa na wanangwa wa kupanga malango.<ref name=":0" />{{Rp|593}}Malango gha boma ghakaŵa ghakuzirwa chomene kuluska malango gha chigaŵa mu vigaŵa vyose ivyo boma likapika mazaza ghakuchitira malango, kusazgapo malango agho ghakalembeka pamoza. Boma likapangika na Kazembe Mukuru, uyo wakimiranga Fumukazi, na Wupu Wakulongozga uwo ukaŵa na Nduna Yikuru na nduna zinyake zinkhondi na zinayi izo zikaŵikika na Kazembe Mukuru. Khoti likuru likapangika na Khoti Likuru Chomene, ilo pamasinda likalembeka na Federal Supreme Court Act, 1955, ilo likapangika na Chief Justice, ŵeruzgi ŵaŵiri ŵa boma, na ŵeruzgi ŵalara ŵa vigaŵa vitatu vya Federation. Khoti ili likamba kugwira ntchito pa Julayi 1, 1955, apo Kazembe-Jenerala wakapeleka chilapo kwa mulara wa khoti na ŵeruzgi ŵanyake. Mu upharazgi uwu mukaŵaso Lord High Chancellor na Chief Justice of the Union of South Africa.:595 Ŵeruzgi ŵalara ŵakaŵa Sir Robert Tredgold, uyo wakaŵa Chief Justice of Southern Rhodesia, uyo wakaŵa Chief Justice of the Federation kufuma mu 1953 mpaka 1961, na Sir John Clayden, kufuma mu 1961 mpaka 1963. Khoti Likuru Chomene likaŵa na mazaza ghakupulikizga madandawuro gha makhoti ghapachanya gha mu vigaŵa vyawo. Kweni pakwamba khoti ili likaŵa na mazaza pa nkhani izi: * Mphindano pakati pa boma na boma la vigaŵa, panji pakati pa maboma gha vigaŵa para mphindano izi zikukhwaska mafumbo (ghawemi panji ghaunenesko) agho ghakukolerana na kuŵako panji ukuru wa wanangwa; * Nkhani izo zikukhwaska malo ghambura maofesi mu Nyumba ya Malango ya chalo na ma petition gha pa mavoti; ndipo * Vinthu ivyo munthu wakukhumba kupeleka dango lakukanizga panji dango lakukanizga mulimo wa boma.<ref name=":0" />{{Rp|596}} Mu 1958, nduna yikuru yikakhazikiska ofesi yakuwona vya mafuko iyo yikadumbiskana ndondomeko, vyakucita, na milimo iyo yikatondeskanga panji kususka ndondomeko ya boma yakuwona vya wanangwa wa ŵanthu. Pa 1 Epulero 1959, nduna yikuru yikimika Secretary of Parliamentary to the Ministry of Home Affairs, uyo wakaŵa na udindo wa nduna yakuwona vya mafuko. [[File:Federation_of_Rhodesia_and_Nyasaland_map_1960.jpg|link=https://en.wikipedia.org/wiki/File:Federation_of_Rhodesia_and_Nyasaland_map_1960.jpg|thumb|Mapu gha charu cha Federation na vigaŵa vyapafupi, pamoza na msumba ukuru wa Southern Rhodesia wa Salisbury.]] Ŵanthu ŵanandi ŵakagomezganga kuti charu cha Southern Rhodesia ndicho chizamuŵa na mazaza pa charu chose. Ivi vikapangiska kuti paŵe maungano ghatali na kusintha malango. Pa nyengo iyo, ŵanthu ŵa mu Africa ŵakasuskanga ŵanyawo pa nkhani za ndyali kweniso ŵakakhumbanga yayi kuti ŵanthu ŵaŵasopenge. Vinthu ivyo vikapangiska kuti wupu uwu uleke kukhazikika vikaŵa mphambano yikuru pakati pa ŵanthu ŵa ku Africa na ŵa ku Europe. Kweniso ŵanthu ŵa ku Europe awo ŵakakhalanga ku Southern Rhodesia ŵakasazgikiranga chomene. Ici cikawovwira comene kuti vinthu vyende makora mu caru ici. Mu 1939, ŵanthu pafupifupi 60,000 ŵa ku Europe ŵakakhalanga ku Southern Rhodesia; pambere wupu wa Federation undaŵeko ŵakaŵa 135,000; apo wupu wa Federation ukaparanyikanga ŵakaŵa 223,000 (nangauli awo ŵiza sono ŵangavota para pajumpha vyaka vitatu). Nyasaland yikaŵa na ŵanthu ŵacoko comene ku Europe na ku Africa. Ntchito yikuru iyo ŵanthu ŵa ku Southern Rhodesia ŵa ku Europe ŵakagwiranga mu CAF yikulongoreka na mulongozgi wawo wakwamba, Sir Godfrey Huggins (uyo wakazgoka Viscount Malvern mu Febuluwale 1955), Prime Minister wa Federation kwa vyaka vitatu vyakwambilira ndipo pambere ivi vindachitike, Prime Minister wa Southern Rhodesia kwa vyaka 23. Huggins wakaleka udindo wa Prime Minister wa Southern Rhodesia kuti watore udindo wa Federal Prime Minister. Ŵanthu ŵanandi ŵakamba kusamira ku vigaŵa vyakuzirwa vya ndyali. Malo gha nduna yikuru ya Southern Rhodesia ghakaŵaso gha nduna yikuru, nga ni umo vikaŵira mu Britain's Ministerial Titles Act of 1933, ndipo ghakaŵa gha nduna yikuru. Garfield Todd, nduna ya vya ndyali ya ku mphepete mwa nyanja iyo yizamuzgoreka. Ŵanthu ŵakaghanaghananga kuti udindo wa Todd na ndyali zake vikaŵa vyambura kuzirwa. Nakuti yikaŵa yakukhumbikwa chomene kuti CAF yimare, kweniso kuti Rhodesian Front yikure. M'malo mwa wupu wakulongozga, nduna yikuru Huggins yikakhumbanga kuti wupu uwu uŵikane pamoza, na kupanga boma limoza. Kweni Nkhondo Yachiŵiri ya pa Charu Chose yikati yamara, Britain yikasuska cifukwa cakuti caru ca Southern Rhodesia cikaŵa na wanangwa wa kupoka katundu na ndalama cifukwa ca unandi wa ŵanthu ŵa ku Europe. Ŵakapanga wupu wakulongozga kuti ulekeske suzgo ili. Ntheura Huggins wakaŵa nduna yikuru yakwamba kufuma mu 1953 mpaka 1956, ndipo wakalondezgana na Sir Roy Welensky, wandale wakuzirwa wa ku Northern Rhodesia, kufuma mu 1956 mpaka apo Federation yikamara mu Disembala 1963. Mu boma la Britain, maofesi ghaŵiri gha ufumu ghakaŵa pa mphindano yikuru ya maghanoghano, ya munthu na ya ntchito. CO ndiyo wakalamuliranga vyaru vya Nyasaland na Northern Rhodesia, apo CRO ndiyo wakalamuliranga Southern Rhodesia. Vyaru vya kumpoto vikasuskanga boma la Rhodesia la kumwera, ilo CRO yikakhozgeranga. Chakuzirwa nchakuti, CO yikakhumba kuti yikhozgere wanangwa wa ŵanthu ŵa ku Africa kuluska CRO, iyo yikakhumba kukhozga vyakukhumba vya ŵanthu ŵa ku Southern Rhodesia (ndipo ku Northern Rhodesia) ŵa ku Europe. Mu 1957, Welensky wakakhumbanga kuti paŵe dipatimenti yimoza iyo yikateŵeterenge vigaŵa vyose vitatu, ndipo Macmillan nayo wakatemwanga kuti CRO ndiyo yiŵe na udindo wa vigaŵa vyose ivi. Kweni Secretary of the Cabinet wakamuphalira kuti ŵanthu ŵa ku Africa na ŵantchito ŵa ku Northern Territories ŵakususka. Mwantheura, mu 1962, milimo ya wupu uwu yikasamira ku dipatimenti yiphya, yakucemeka Central Africa Office, ndipo Rab Butler ndiyo wakaŵa nduna. Ndipouli, ici cikaŵa ca nyengo yicoko waka, cifukwa apo Alec Douglas-Home wakalondezganga Macmillan kuŵa nduna yikuru, udindo wa Federation ukawelera ku CRO na CO, ndipo Duncan Sandys ndiyo wakaŵa na udindo wa wose ŵaŵiri.<ref>Murphy, Philip, [https://books.google.co.uk/books?id=pxCA6zj134AC&newbks=1&newbks_redir=0&lpg=PA199&dq=%22Central%20Africa%20Office%22%20%22Butler%22&pg=PA199#v=onepage&q=%22Central%20Africa%20Office%22%20%22Butler%22&f=false ''Party Politics and Decolonization: The Conservative Party and British Colonial Policy in Tropical Africa 1951-1964''], Clarendon Press, 1995, p. 199.</ref> Cikaŵa cakwenelera kuti Cecil Rhodes wakhazikiske vigaŵa vyose vitatu mu caru cimoza. Kweni kwa Huggins na ŵa ku Rhodesia, cifukwa cikuru ico cikapangiska kuti CAF (panji kuti kuwungana) kuŵepo cikaŵa kuti kumpoto kwa Rhodesia kukaŵa na mkuŵa unandi. Mwakupambana na vyaru vya Rhodesia, charu cha Nyasaland chikaŵavya visulo vinandi, ndipo ŵanthu ŵa ku Europe, ŵanandi ŵakaŵa ŵa ku Scotland. Kuŵanjizga mu wupu wa Federation kukaŵa kacitiro kakuyelezgera kuluska kukhumbikwa. Kuŵikapo mtima uku kukawovwira yayi CAF: Nyasaland na ŵanthu ŵake ŵa ku Africa ndiwo ŵakapangiska kuti CAF yileke kukhazikika, ndipo yikamara..^[<ref>{{Cite book|last=Blake|first=Robert|url=https://books.google.com/books?id=jXp0AAAAMAAJ&q=Its+inclusion+in+the+Federation+was+always+more+a+symbolic+gesture+than+a+practical+necessity.+Ironically,+it+was+to+be+largely+Nyasaland+and+its+African+population+where+the+impetus+for+destabilization+of+the+CAF+arose,+leading+to+its+dissolution|title=A History of Rhodesia|date=1978|publisher=Knopf|isbn=978-0-394-48068-8|language=en}}</ref> {| class="wikitable" align="center" |+'''Chiŵelengero cha ŵanthu ŵazungu na ŵafipa pambere CAF yindambe na apo yikaŵa mukati'''<ref>{{cite book|title=An Introduction to the History of Central Africa|last=Wills|first=A.J.|year=1967|publisher=[[Oxford University Press]]|location=Durban|edition=2nd|isbn=0-620-06410-2|page=Appendix IV|chapter=Three Territories|access-date=10 September 2012|url=https://books.google.com/books?id=TLshAAAAMAAJ}}</ref> ! rowspan="2" |Chaka ! colspan="2" |Southern Rhodesia ! colspan="2" |Northern Rhodesia ! colspan="2" |Nyasaland ! colspan="2" |Unandi |- |Ŵazungu |Ŵafipa |Ŵazungu |Ŵafipa |Ŵazungu |Ŵafipa |Ŵazungu |Ŵazungu |- |'''1927''' |38,200 (3.98%) |922,000 (96.02%) |4,000 (0.4%) |1,000,000 (99.6%) |1,700 (0.13%) |1,350,000 (99.87%) |43,900 (1.32%) |3,272,000 (98.68%) |- |'''1946''' |80,500 (4.79%) |1,600,000 (95.21%) |21,919 (1.32%) |1,634,980 (97.68%) |2,300 (0.10%) |2,340,000 (99.90%) |104,719 (1.84%) |5,574,980 (98.16%) |- |'''1955''' |125,000 (4.95%) |2,400,000 (95.05%) |65,000 (3.02%) |2,085,000 (96.98%) |6,300 (0.25%) |2,550,000 (99.75%) |196,300 (2.71%) |7,035,000 (97.28%) |- |'''1960''' |223,000 (7.30%) |2,830,000 (92.70%) |76,000 (3.14%) |2,340,000 (96.85%) |9,300 (0.33%) |2,810,000 (99.66%) |308,300 (3.72%) |7,980,000 (96.28%) |} == Kukura kwa cuma na wanangwa wa ndyali == [[File:Federation_of_Rhodesia_and_Nyasaland_five_pound_note.jpg|link=https://en.wikipedia.org/wiki/File:Federation_of_Rhodesia_and_Nyasaland_five_pound_note.jpg|right|thumb|320x320px|Ndalama ya Fuko ya mapaundi ghankhondi mu 1961]] Nangauli boma la CAF likaŵa lakusuzga, kweni vinthu vikendanga makora. Mu cilimika cakwamba ca wupu uwu, GDP yake yikaŵa yakuzizwiska ya mapaundi 350 miliyoni; pamanyuma pa vilimika viŵiri yikaŵa pafupifupi mapaundi 450 miliyoni.<ref>Blake, 288.</ref>Kweni ndalama izo munthu wa ku Europe wakasanganga zikapambananga na izo munthu wa ku Africa wakasanganga. Mu 1955, boma likapharazga kuti lipangenge sitima ya Kariba. Chikaŵa cinthu cakuzizwiska comene pakuzenga damu likuru comene pa caru cose pa nyengo iyo. Malo agha ghakavumbura mphindano pakati pa Southern na Northern Rhodesia, ndipo Rhodesia ndiyo yikaŵa malo ghakwenelera kuzenga chiziŵa. CAF yikapeleka vyaka 10 vya wanangwa pa nkhani ya wanangwa wa ŵanthu ŵa ku Africa. Pakaŵa ŵaminisitala ŵacigaŵa ca Africa mu CAF iyo yikaŵa na ŵacigaŵa ca Southern Rhodesia, apo vyaka 10 kumasinda, ŵanthu ŵacigaŵa ca South Rhodesia 70 pera ndiwo ŵakaŵa na wanangwa wa kuvota. Ntheura, CAF yikaŵa na wanangwa wa kupoka katundu na ndalama. Nangauli ivi vikakwenyerezga ŵazungu ŵanandi, kweni ŵakalutilira kulondezga ivyo Huggins wakacita na CAF, comene cifukwa ca kukura kwa cuma. Kweni ŵanthu ŵa ku Africa ŵakakhorwa yayi na fundo iyi, ndipo ŵalongozgi ŵawo ŵakamba kukhumba kuti ŵanthu ŵanandi ndiwo ŵalongozgenge. == Kuwuka kwa kutemwa caru == [[File:RLIassault1963.PNG|link=https://en.wikipedia.org/wiki/File:RLIassault1963.PNG|thumb|Ŵasilikari ŵa CAF ŵa Rhodesia Light Infantry ŵakasambizgika mu 1963]] Ŵanthu ŵa ku Africa ŵakamba kutinkhana na CAF, ndipo nyengo yeneyiyo maboma gha ku Britain ghakatinkhanga umo yikapangikira kweniso chilato chake. Mu Juni 1956, Kazembe wa Northern Rhodesia, Sir Arthur Benson, wakalemba kalata yakubisika chomene yakususka chomene wupu uwu (na dango liphya ilo likanozgekera) kweniso nduna yikuru ya boma, Sir Roy Welensky. Pakati pajumpha vilimika viŵiri, Lord Malvern (uyo wakaŵa Sir Godfrey Huggins mu Febuluwale 1955) wakasanga buku ili na kumupa Welensky. Ubwezi pakati pa Whitehall na nduna za CAF ukaŵa wakuti ungaweleramo yayi. Ivi ndivyo vikapangiska kuti Harold Macmillan, uyo wakaŵa nduna yikuru ya boma la Britain, wamanye kuti mu CAF muli suzgo, kweni wakawona kuti suzgo ili likaŵa lakuzirwa yayi. Nkhani iyi yikamalizgika mwaluŵiro na kusintha malango ghanyake, kweni sono vikumanyikwa kuti Welensky wakaghanaghananga chomene za ndondomeko ya unilateral declaration of independence (UDI) ya federation, nangauli wakasankha yayi. Pa nyengo iyi, kuumaliro wa vyaka 10, ŵanthu ŵa ku Northern Territories, ku Africa, ŵakasuska muwuso wa CAF. Mu Julayi 1958, Hastings Banda, mulongozgi wa Nyasaland African Congress (NAC) (pamanyuma Malawi Congress Party), wakawerako ku Great Britain kuya ku Nyasaland, apo mu Okutobala Kenneth Kaunda wakazgoka mulongozgi wa Zambia African National Congress (ZANC), chigaŵa icho chikapatuka ku Northern Rhodesian ANC. Boma la CAF likakanizga gulu la ZANC mu Malichi 1959, ndipo mu Juni likajalira Kaunda myezi 9. Apo Kaunda wakaŵa mu jele, Mainza Chona, uyo wakaŵa muteŵeti wake wakugomezgeka, wakagwira nchito pamoza na ŵanthu ŵanyake ŵa ku Africa kuti ŵapange United National Independence Party (UNIP). Kukwambilira kwa 1959, ku Nyasaland kukawuka vivulupi, ndipo wakulemba mdauko munyake, Lord Blake, wakati: "Charu ichi chikaŵa mukavu comene pa vyaru vitatu ivi, kweniso chikaŵa na ndyali zinandi comene". Boma la CAF likapharazga kuti kuli suzgo. Dr. Banda na ŵalongozgi ŵanyake ŵa NAC ŵakakakika ndipo gulu lawo likakanizgika. Ŵasilikari ŵa ku Southern Rhodesia ŵakatumika kuti ŵize na ndondomeko. Mbumba ya British Labour MP John Stonehouse yikachimbizgika ku Southern Rhodesia nyengo yicoko waka pambere boma la Nyasaland lindayowoyepo suzgo, ico cikakwiyiska ŵa British Labour Party. Nkhani iyi yikapangiska kuti fundo yose ya wupu uwu yiŵe yakukayikiska, ndipo nanga ni Nduna Yikuru Macmillan nayo wakamba kukayikira usange wupu uwu ungaŵa na nkhongono pa nkhani za ndyali. Komiti ya Ufumu iyo yikapelekanga ulongozgi kwa Macmillan pa ivyo vicitikenge ku CAF, yikalongozgekanga na The 1st Viscount Monckton of Brenchley, QC, uyo kale wakaŵa Paymaster General. Secretary of the Commonwealth, The 14th Earl of Home, wakatumika kuti wakanozge nduna yikuru Welensky, uyo wakakondwa yayi na kwiza kwa komiti iyi. Welensky wakasanga kuti Fumu Home yikukhozgera kuti CAF yilipo. Mwakupambana na ivi, munthu munyake wa ku Scotland, Iain Macleod, uyo wakaŵa Secretary of Colonial Affairs, wakatemwanga wanangwa wa ŵanthu ŵa ku Africa na kumazga wupu uwu. Nangauli pa nyengo iyi Macmillan wakakhozgera Fumu Home, kweni vinthu vikasintha. Ku Britain, Macmillan wakati nchakuzirwa comene kuti "ŵasungiliri ŵa Tory ŵalutilire kucita vinthu mwakukolerana na umo vinthu viliri sono". == Kulekeka == [[File:Rhodesia_and_Nyasaland.png|link=https://en.wikipedia.org/wiki/File:Rhodesia_and_Nyasaland.png|thumb|550x550px|Kusintha kwa Federation of Rhodesia and Nyasaland]] Pa nyengo iyo Macmillan wakendera caru ca Africa mu 1960, apo wakapharazganga ku Nyumba ya Malamulo ku Cape Town, vinthu vikamba kusintha. Kuzakafika mu 1960, vyaru ivyo vikaŵa pasi pa France vikaŵa kuti vyafwatuka kale. Ndipo ŵanthu ŵanandi ŵa ku Europe ŵakachimbira ku Belgian Congo chifukwa cha nkhondo ya pawenenawene. Pa nyengo ya suzgo ya ku Congo, ŵanthu ŵa ku Africa ŵakawonanga kuti Prime Minister wa CAF, Sir Roy Welensky, ni munthu wakususka ndipo wovwiri wake ku Katanga ukaŵa wakusazgirapo. Welensky wakatinkhikanga na ŵanthu ŵa ku woko lamalyero na lamazere wuwo: pati pajumpha vilimika vicoko waka, apo wakacitanga kampeni yakwimikana na chipani ca Rhodesian Front ca Ian Smith, ŵanthu ŵa ku Russia ŵakasuska Welensky uyo wakaŵa wakujiyuyura, kuti ni 'Muyuda wa ndopa,' 'Mukomyunizimu,<nowiki>''</nowiki>muwukirano,' na'munthu wakucita wofi.' Secretary wa Commonwealth, Duncan Sandys, wakadumbiskana za 'Constitution ya 1961', constitution yiphya ya CAF iyo yikakhukiska chomene mazaza gha Britain pa iyo: kweni, mu 1962, British na CAF cabinet ŵakakolerana kuti Nyasaland yikwenera kuzomerezgeka kupatuka, nangauli Prime Minister wa Southern Rhodesia Sir Edgar Whitehead wakajipeleka ku British kuti ŵasunge chisisi ichi mpaka pa mavoti gha 1962 mu chigaŵa ichi. Pakati pajumpha chaka chimoza, charu cha Northern Rhodesia nacho chikapokera wanangwa uwu. Mu 1963, ungano wa Victoria Falls Conference ukacitika, cifukwa cakuti ukaŵa cinthu caumaliro ca kuponoska CAF, kweniso cifukwa cakuti yikaŵa malo ghakupatulirako. Pa Juni 5, 1963, ŵalongozgi ŵa ku Kenya, Tanganyika, na Uganda ŵakayowoya kuti ŵakukhumba kukolerana kuti ŵaŵe mu wupu wa East Africa. Kuumaliro wa Juni 1963, boma ili likawonekanga kuti lileke kunangika. Ndipouli, pati pajumpha myezi yicoko waka, cilindizga ca kukhazikiska wupu uwu cikamara. Pali vifukwa vyakupambanapambana ivyo vikapangiska kuti charu ichi chileke kukolerana, kusazgapo kuti charu cha Uganda chikudandawura chifukwa chakuti ntchakulopwa mu charu ichi, kweniso chifukwa cha ivyo Kwame Nkrumah wakakhumbanga kuti charu cha East Africa chiŵe na wupu ukuru. Ŵanthu ŵanyake nga ni Joseph Nye na Thomas Franck, ŵakalemba vya kutondeka kwa wupu uwu. Pa Disembala 31, 1963, wupu wa Rhodesia na Nyasaland ukamara, ndipo katundu wake wakagaŵika pakati pa maboma gha vigaŵa. Charu cha Southern Rhodesia chikapokera katundu munandi wa ŵasilikari aŵa, kusazgapo katundu wa ŵasilikari ŵa boma. Mu Julayi 1964, charu cha Nyasaland chikajiyimira paŵekha ndipo chikachemekanga Malawi, ndipo mu Okutobala, Northern Rhodesia yikajiyimira paŵekha ndipo yikachemeka Republic of Zambia. Pa Novembala 11, 1965, boma la Southern Rhodesia, lakulongozgeka na nduna yikuru Ian Smith, likapharazga kuti charu cha Rhodesia chili na wanangwa wakujiyimira pawekha. Ici cikapangiska kuti caru cose ciŵe na citima. == Chitetezo == Nduna ya vya kuvikilira yikaŵa mulongozgi wa wupu wa kuvikilira, uwo ukaŵa na ŵasilikari na ŵanthu ŵanyake. The Army, in 1960, consisted of three training formations: * Sukulu ya ŵasilikari ŵakwenda pasi iyo yikaŵa ku Gwelo, ndiyo yikacitiskanga masambiro ghanyake. Gulu ili likaŵa na vigaŵa viŵiri, vya nkhondo na vya ŵasilikari..<ref name=":0" />{{Rp|667}} * Ku malo ghakusungirako ŵasilikari, ku Salisbury, ndiko ŵakasambizgiranga ŵasilikari wose ŵa mitundu yinyake. * Ku Depot, ku Royal Rhodesia Regiment, ŵakasambizganga ŵasilikari ŵa Territorial Force. Gulu ili likasambizgikanga na mawupu gha Rhodesia na Nyasaland Corps of Engineers, Corps of Signals, na Army Service Corps. Mu Meyi 1958, malo ghatatu ghakacemeka na mazina gha "ŵasilikari ŵatatu ŵakumanyikwa comene ŵa ku Central Africa". Msasa wa RAR ku Llewellin ukacemekanga Methuen Camp cifukwa ca zina la Colonel J.A. Methuen. Malo agha ghakacemekanga Cobbe Barracks cifukwa ca zina la Mulara Alexander Cobbe. Malo agha ghakachemeka Stephenson Barracks, pamanyuma pa Mubali A. Stephenson. - Kasi ndiwe? Pa malo ghakucemeka Llewellin Barracks ku Bulawayo pakaŵa cikumbusko ca kazembe mukuru wakwamba wa wupu wa Federation. Nkhondo ya Tug Argan yikakumbukirika mu zina la Tug Argan Barracks mu Ndola. Gulu la ŵasilikari ili likaŵa na mabataliyoni ghanayi gha ku Africa: 1st na 2nd Battalion, King's African Rifles; the Northern Rhodesia Regiment; and the Rhodesian African Rifles.:6681961, the all-White 1st Battalion of the Rhodesian Light Infantry regiment was added. Gulu la ŵanakazi la Rhodesia and Nyasaland Women's Military Air Service (lakucemeka kuti "WAMS") likaŵa gulu la ŵanakazi la Federation. Mu 1957, ŵasilikari ŵakasintha ndondomeko yawo ndipo ŵakamba kuchepeska unandi wa ŵasilikari.<ref name=":0" />{{Rp|671}} == Chiharo == Nangauli wupu wa Rhodesia na Nyasaland ukakhala waka vyaka 10, kweni ukakhwaska comene caru ca Central Africa. Boma la ŵanthu ŵachoko waka ŵatuŵa, apo ŵanthu ŵa ku Europe ŵakukwana 200,000, comenecomene ŵa ku Southern Rhodesia, ŵakalongozganga ŵanthu ŵanandi ŵa mu Africa, ŵakalongozgekanga na ŵanthu awo ŵakakhumbanga kusintha vinthu. Wupu wa Britain uwo ukaŵa pasi pa mazaza gha Britain, ukaŵa wakupambana na wupu unyake wa ku South Africa. Kuwuskika kwa CAF kukavumbura mphambano pakati pa vyaru vyakujiyimira vyene ivyo vikalongozgekanga na Africa nga ni Zambia na Malawi, na Southern Rhodesia (iyo yikalutilira kulamulirika na boma la ŵanthu ŵachoko waka Ŵachizungu mpaka apo vinthu vikasinthira mu 1978). Ku Southern Rhodesia kukaŵa nkhondo pakati pa boma na ŵasilikari ŵa ku Africa, apo Malawi na Zambia vikazgoka vyaru vya chipani chimoza. Pamanyuma pa Southern Rhodesia's Unilateral Declaration of Independence (UDI), nkhondo yikuru yikamba pakati pa vigaŵa viŵiri vya CAF - Zambia (iyo yikukhozgera ŵanthu ŵa ku Africa) na Southern Rhodesia (iyo yikukhozgeka na South Africa) - pamoza na mazgu ghakututuzga gha vyaru vinyake, ndipo nyengo zinyake kukaŵa nkhondo. == Mathebulu ghakutumizga makalata == [[File:Fedrhnld.gif|link=https://en.wikipedia.org/wiki/File:Fedrhnld.gif|right|thumb|Sitampu ya CAF]] Mu 1954, boma la Britain likafumiska mathamalindi ghakwamba agho ghakaŵa na cithuzithuzi ca Fumukazi Elizabeth II. Wonani nkhani yikuru pa Sitampu za ku Rhodesia na Nyasaland. Kweniso ŵakafumiskanga vithuzithuzi vya msonkho. {{Malaŵi}} [[Category:Mdauko wa chalo cha Malaŵi]] == Wonaniso == {{Portal|Malawi|United Kingdom|Zambia}} * [[:en:Governor-General_of_the_Federation_of_Rhodesia_and_Nyasaland|Governor-General of the Federation of Rhodesia and Nyasaland]] * [[:en:Prime_Minister_of_the_Federation_of_Rhodesia_and_Nyasaland|Prime Minister of the Federation of Rhodesia and Nyasaland]] * [[:en:Federation_of_Rhodesia_and_Nyasaland_election,_1953|Federation of Rhodesia and Nyasaland election, 1953]] * [[:en:Federation_of_Rhodesia_and_Nyasaland_election,_1958|Federation of Rhodesia and Nyasaland election, 1958]] * [[:en:Federation_of_Rhodesia_and_Nyasaland_election,_1962|Federation of Rhodesia and Nyasaland election, 1962]] * [[:en:Flag_of_the_Federation_of_Rhodesia_and_Nyasaland|Flag of the Federation of Rhodesia and Nyasaland]] * [[:en:Government_of_the_Federation_of_Rhodesia_and_Nyasaland|Government of the Federation of Rhodesia and Nyasaland]] * [[:en:Rhodesia's_Unilateral_Declaration_of_Independence|Rhodesia's Unilateral Declaration of Independence]] {{clear}} == Vyakulemba == <references group="" responsive="1"></references> == Ukaboni == {{Refbegin|25em}} * Cohen, Andrew. ''The Politics and Economics of Decolonization in Africa: The Failed Experiment of the Central African Federation'' (I. B. Tauris, London, 2017). * Franklin, Henry. ''Unholy wedlock: the failure of the Central African Federation'' (G. Allen & Unwin, London, 1963). * Blake, Robert. ''A History of Rhodesia'' (Eyre Methuen, London 1977). * Hancock, Ian. ''White Liberals, Moderates, and Radicals in Rhodesia, 1953–1980'' (Croom Helm, Sydney, Australia, 1984). * Mason, Phillip. ''Year of Decision: Rhodesia and Nyasaland in 1960'' (Oxford University Press, 1961). * Phillips, C. E. Lucas. ''The vision splendid: the future of the Central African Federation'' (Heinemann, London, 1960). * Leys, Colin and Pratt Cranford (eds.). ''A new deal in Central Africa'' (Heinemann, London, 1960). * Clegg, Edward Marshall. ''Race and politics: partnership in the Federation of Rhodesia and Nyasaland''. (Oxford University Press, 1960). * Gray, Richard. ''The two nations: aspects of the development of race relations in the Rhodesias and Nyasaland'' (Greenwood Press, Westport, Conn., 1960). * Rogaly, Joe. ''Rhodesia: Britain's deep south''. (The Economist, London, 1962). * Hall, Richard. ''The High Price of Principles: Kaunda and the White South'' (Hodder and Stoughton, London, 1969). * [[Guy Clutton-Brock]]. ''Dawn in Nyasaland'' (Hodder and Stoughton, London 1959). * Dorien, Ray. ''Venturing to the Rhodesias and Nyasaland'' (Johnson, London, 1962) * Hanna, Alexander John. ''The story of the Rhodesias and Nyasaland.'' (Faber and Faber, 1965). * Black, Colin. ''The lands and peoples of Rhodesia and Nyasaland'' (Macmillan, NY, 1961). * Sanger, Clyde. ''Central African emergency'' (Heinemann, London 1960). * Gann, Lewis H. ''Huggins of Rhodesia: the man and his country'' (Allen & Unwin, London, 1964). * Gann, Lewis H. ''Central Africa: the former British states'' (Englewood Cliffs, N. J., Prentice-Hall, 1971). * Haw, Richard C. (fwd. by Sir Godfrey Huggins) ''No other home: Co-existence in Africa'' (S. Manning, Bulawayo, Southern Rhodesia, 1960?). * Taylor, Don. ''The Rhodesian: the life of Sir Roy Welensky.'' (Museum Press, London 1965). * Wood, J.R.T. ''The Welensky papers: a history of the federation of Rhodesia and Nyasaland'' (Graham Pub., Durban, 1983). * Welensky, Roy, Sir. ''Welensky's 4000 days: the life and death of the Federation of Rhodesia and Nyasaland'' (Collins, London, 1964). * [[Garry Allighan|Allighan, Garry]]. ''The Welensky story'' (Macdonald, London, 1962). * Alport, Cuthbert James McCall, Lord. ''The sudden assignment: being a record of service in central Africa during the last controversial years of the Federation of Rhodesia and Nyasaland, 1961–1963.'' (Hodder and Stoughton, London, 1965). * Thompson, Cecil Harry. ''Economic development in Rhodesia and Nyasaland'' (D. Dobson, Publisher London, 1954) * Walker, Audrey A. ''The Rhodesias and Nyasaland: a guide to official publications'' (General Reference and Bibliography Division, Reference Dept., Library of Congress: for sale by the Superintendent of Documents, US Govt. Print. Off., 1965). * Irvine, Alexander George. ''The balance of payments of Rhodesia and Nyasaland, 1945–1954.'' (Oxford University Press, 1959.) * United States Bureau of Foreign Commerce, Near Eastern and African Division. ''Investment in the Federation of Rhodesia and Nyasaland: basic information for United States businessmen.'' (U. S. Dept. of Commerce, Bureau of Foreign Commerce, 1956) * Standard Bank of South Africa, Ltd. ''The federation of Rhodesia and Nyasaland: general information for business organisations.'' (London, 1958). * Sowelem, R. A. ''Toward financial independence in a developing economy: an analysis of the monetary experience of the Federation of Rhodesia and Nyasaland, 1952–63.'' (Allen & Unwin, London, 1967). * {{cite book|last1=Shutt|first1=Allison K|title=Manners Make A Nation: Racial Etiquette in Southern Rhodesia, 1910–1963|date=2015|publisher=University of Rochester Press|location=Rochester}} {{Refend}} == Vigaŵa vya kuwalo == * Rhodesia and Nyasaland Army http://www.rhodesia.nl/ceremonialparade.pdf * [http://www.rhodesia.me.uk/ Window on Rhodesia], an archive of the history and life of Rhodesia * {{Cite web |last=King |first=Anthony |date=2001 |title=Identity and Decolonisation: the policy of partnership in Southern Rhodesia 1945-62 |url=https://ora.ox.ac.uk/objects/uuid:676e28d6-223e-482e-ba5c-18198d3b735c/download_file?file_format=pdf&safe_filename=DPhil%2BThesis%2Bfinal%2Bversion%2Bdigital.pdf&type_of_work=Thesis |access-date=2020-05-29 |website=unesdoc.unesco.org |publisher=St. Antony's College, Oxford}} {{British overseas territories||state=expanded}}{{Coord|16|S|29|E|display=title}}{{Authority control}} 9eyb0ixftf8b8qcciozh2kuy71xqa05 0 25468 121839 120719 2026-09-08T16:40:38Z InternetArchiveBot 6449 Add 1 book for [[en:Wikipedia:Verifiability|verifiability]] (20260908)) #IABot (v2.0.9.5) ([[User:GreenC bot|GreenC bot]] 121839 wikitext text/x-wiki {{Infobox settlement | name = Purial | native_name = | native_name_lang = <!-- ISO 639-1 code e.g. "fr" for French. If more than one, use {{lang}} instead --> | settlement_type = Msumba | image_skyline = | imagesize = | image_alt = | image_caption = | image_flag = | flag_alt = | image_seal = | seal_alt = | image_shield = | shield_alt = | etymology = | nickname = | motto = | image_map = El_Purial_OSM.jpg | map_alt = | map_caption = Mapu ya El Purial | pushpin_map = Cuba#Villa Clara Province#Cuba Camajuaní | pushpin_map_alt = | pushpin_map_caption = El Purial in Cuba | pushpin_label_position = | coordinates = {{coord|22|33|05|N|79|44|41|W|region:CU|display=inline,title}} | coor_pinpoint = | coordinates_footnotes = | subdivision_type = Country | subdivision_name = [[Cuba]] | subdivision_type1 = [[Provinces of Cuba|Province]] | subdivision_name1 = [[Villa Clara Province|Villa Clara]] | subdivision_type2 = [[Municipalities of Cuba|Municipality]] | subdivision_name2 = [[Camajuaní]] | subdivision_type3 = Ward | subdivision_name3 = [[Aguada de Moya]] | established_title = | established_date = | founder = | seat_type = | seat = | government_footnotes = | government_type = | governing_body = | leader_party = | leader_title = | leader_name = | leader_title1 = | leader_name1 = | leader_title2 = | leader_name2 = | leader_title3 = | leader_name3 = | leader_title4 = | leader_name4 = | unit_pref = Metric <!-- ALL fields with measurements have automatic unit conversion --> <!-- for references: use <ref> tags -->| area_footnotes = | area_urban_footnotes = <!--<ref> </ref> --> | area_rural_footnotes = <!--<ref> </ref> --> | area_metro_footnotes = <!--<ref> </ref> --> | area_note = | area_water_percent = | area_rank = | area_blank1_title = | area_blank2_title = <!-- square kilometers --> | area_total_km2 = | area_land_km2 = | area_water_km2 = | area_urban_km2 = | area_rural_km2 = | area_metro_km2 = | area_blank1_km2 = | area_blank2_km2 = <!-- hectares --> | area_total_ha = | area_land_ha = | area_water_ha = | area_urban_ha = | area_rural_ha = | area_metro_ha = | area_blank1_ha = | area_blank2_ha = | length_km = | width_km = | dimensions_footnotes = | elevation_footnotes = | elevation_m = 129 | population_footnotes = <ref name=“EcuRed”> [https://www.ecured.cu/Purial_(Camajuan%C3%AD) Purial (Camajuaní) - EcuRed] </ref> | population_as_of = | population_total = 37 | population_density_km2 = auto | population_note = | population_demonym = | timezone1 = | utc_offset1 = | timezone1_DST = | utc_offset1_DST = | postal_code_type = | postal_code = | area_code_type = | area_code = | area_codes = <!-- for multiple area codes --> | iso_code = | website = <!-- {{URL|example.com}} --> | module = | footnotes = | official_name = El Purial }} '''El Purial''', wakuchemekaso '''Purial''', ni muzi wa ku [[Aguada de Moya]], [[Camajuaní]], [[Villa Clara]], [[Cuba]]. <ref>{{cite book |last1=Pardo |first1=Georges |title=The geology of Cuba |year=2009 |publisher=American Association of Petroleum Geologists |location=Tulsa, Okla |isbn=978-0-89181-065-0 |pages=23 |language=English}}</ref><ref>{{cite book |last1=Office of Geography |first1=United States |title=Cuba : Official Standard Names Approved by the U.S. Board on Geographic Names |year=1963 |publisher=U.S. Govt. Print. Off. |location=Washington |pages=460 |language=English}}</ref> Kumwera kwa tawuni iyi kuli tumapiri uto tukucemeka [[Lomas El Purial]] panji Hills El Purial mu Cingelezi. Kumafumiro gha dazi kwa tawuni iyi kuli Aguada de Moya, kumwera kwa tawuni iyi kuli La [[Piedra, Camajuaní|Piedra]]. Kumanjiliro gha dazi kwa tawuni iyi kuli [[La Luz, Cuba|La Luz]], [[CPA Benito Ramírez|CPA "Benito Ramírez"]], na [[Guerrero, Cuba|Guerrero]]. ==Chuma== Kuyana na DMPF (Departamento de control de la Dirección Municipal de Planificación Física) ya Camajuani, El Purial ni malo agho ghakukolerana yayi na chuma panji ntchito. <ref>{{Cite web |last1=Barroso |first1=Joel Jiménez |last2=Figueroa Vidal |first2=Dr. Arq. Carlos. R. |title=Diagnóstico estratégico de la situación habitacional del municipio de Camajuaní |url=https://dspace.uclv.edu.cu/bitstream/handle/123456789/1550/C10009.pdf?sequence=1&isAllowed=y |page=68}}</ref> Msumba uwu uli mu malo gha vyakumera, ndipo ŵanthu ŵanandi ŵakulima. Vinthu vikuru comene vya mu caru ici ni: vyakurya vya shuga, hona, vyakurya vyakupambanapambana na viŵeto. Mu vigaŵa vyapafupi na msumba uwu muli mafakitale ghakujumpha 20, kusazgapo nyama na moŵa, kweniso fakitare yakupangiramo vinthu vyaulimi. <ref name=“EcuRed”/> ==Nyumba== Mu El Purial muli nyumba zinandi za mu tawuni. Pali masukulu ghaŵiri, ni [[Sukulu ya Leoncio Vidal (Camajuaní)|sukulu ya Leoncio Vidal]],<ref>{{cite book |last1=García Triana |first1=Mauro |last2=Eng Herrera |first2=Pedro |title=The Chinese in Cuba, 1847-now |url=https://archive.org/details/chineseincuba1840000garc |date=2009 |publisher=Lexington Books |location=Lanham |isbn=978-0-7391-3343-9 |pages=[https://archive.org/details/chineseincuba1840000garc/page/42 42] |language=English}}</ref> Zina ili lili kupokera kufuma kwa [[Leoncio Vidal]] wa ku Cuba,<ref>{{cite book |last1=Pérez |first1=Francisco |last2=Serrano Rubio |first2=Violeta |title=Máximo Gómez : aproximación a su cronología, 1836-1905 |year=1986 |publisher=Editorial Academia |location=La Habana, Cuba |pages=81 |oclc=1024421297 |url=https://www.worldcat.org/oclc/1024421297 |language=Spanish}}</ref><ref>{{cite book |last1=Franqui |first1=Carlos |last2=Felix |first2=Georgette |last3=Kerrigan |first3=Elaine |last4=Freeman |first4=Phyllis |last5=St. Martin |first5=Hardie |last6=Franqui |first6=Carlos |title=Diary of the Cuban revolution |url=https://archive.org/details/diaryofcubanrevo0000fran |year=1980 |publisher=The Viking Press |location=New York |isbn=978-0-670-27217-4 |pages=[https://archive.org/details/diaryofcubanrevo0000fran/page/34 34]}}</ref> and [[Escuela Primaria Celestino Pacheco (Camajuaní)|Sukulu Yakwamba ya Celestino Pacheco]]. <ref>{{Cite web |title=Portal del Ciudadano en Camajuaní - Educación |url=https://www.soycamajuani.gob.cu/es/educacion/amp |access-date=2022-12-23 |website=www.soycamajuani.gob.cu}}</ref>Chipatala mu chigaŵa ichi ni [[Consultorio Médico 17 (Camajuaní)|Consultorio Médico 17]].<ref>{{Cite web |title=El Purial, Camajuaní |url=https://cuba-streets.openalfa.com/places/el-purial-camajuani |access-date=2022-07-18 |website=cuba-streets.openalfa.com |language=en-US}}</ref><ref>{{Cite web |title=OpenStreetMap |url=https://www.openstreetmap.org/ |access-date=2022-07-18 |website=OpenStreetMap |language=en}}</ref> Ŵanthu ŵa mu cigaŵa ici ŵasanga candulo cikuru comene cifukwa lero ŵali na maofesi gha munkhwala, maofesi gha munthavi gha mazuŵa ghano, na maofesi ghanyake gha munthavi. <ref name=“EcuRed”/> == Malo == Mlonga wa Sagua la Chica na wa Camajuaní ndiwo ni misewu yikuru comene mu tawuni iyi. Malo agha ghakaŵa ghambura kwenda makora, ndipo ghakaŵa na madambo ghanandi. <ref name=“EcuRed”/> Chifukwa cha malo agha, zuŵa lililose mu tawuni iyi mukuŵa chithukivu cha madigiri 30.29 na madigiri 21.66. Mphepo zikufuma kumafumiro gha dazi na kumpoto-kumafumiro gha dazi kwa tawuni iyi ndipo zikujumpha pa 8.3 km pa ora. <ref name=“EcuRed”/> Ku tawuni iyi kukulokwa maji ghanandi chomene pa chaka. <ref name=“EcuRed”/> ==Mbili== Uthenga wakwamba wakulongosora za malo agha ngwakufuma mu 1703. Mu cigaŵa ici, vinthu vikamba kwenda makora comene ndipo vikafika pa vigaŵa vyose vya umoyo wa cuma, ndyali na wa ŵanthu. Pakuyowoya za zina la cigaŵa ico tawuni iyi yili, Camajuaní, pali Mabaibolo ghakupambanapambana, ndipo ghakuzomerezgeka comene ndigho ghakuyowoya za lizgu ili, ilo likufuma ku ŵanthu ŵa mu caru ici, ilo likung'anamura mlonga uwo ukuskamba mu madambo ghake, ndipo likung'anamura, pakati pa vinyake, maji ghakutowa, ghakutowa na ghakwenda. <ref name=“EcuRed”/> Chigaluka chakwamba mu vyaru ivi chikachitika pa Febuluwale 14, 1869, ndipo mulongozgi wake wakaŵa Salome Hernández wa ku [[Venezuela]], uyo wakagwiranga nchito mu caru ici, ndipo wakaŵa mulara wa ŵasilikari. Ŵanthu ŵanyake awo ŵakamanyikwa na nkhondo iyi ŵakaŵa Jesús del Sol, Aquilino Tuñón, na Diego Dorado. <ref name=“EcuRed”/> Pa Epulero 25 wa chaka chenechicho, dokotala Juan Bruno Zayas wakawuka kufuma ku munda wapafupi mu Vega Alta, pamoza na gulu lakwamba la ŵasilikari mu Villa Clara ya mazuŵa ghano. Ŵanthu ŵanyake ŵa ku malo agha ŵakaŵa na nkharo yiwemi, nga ni Mubali Leoncio Vidal Caro, kweniso Mubali Roberto Méndez Peñate na Rafael Casallas. Vidal ndiyo wakalongozga kuwukira kwa Santa Clara pa Malichi 23, 1896. <ref name=“EcuRed”/> Mu vyaka vya Repubulika la New Colonial, ŵanthu ŵakamba kulimbana na ŵantchito. Vyaka ivi vikaŵa vyakukondweska comene cifukwa cakuti ŵantchito ŵa mu vigaŵa vikuruvikuru ŵakacitanga milimo yinandi; ŵantchito ŵa mu vigaŵa vya shuga na hona ŵakacitanga maungano gha mazuŵa ghacoko waka kuti ŵavikilire vilato vyawo, nga ni kunanga kwa ŵantchito ŵa mu vigaŵa vyakwambilira kuti ŵasangire ndalama zakupambana na za ŵantchito ŵa mu vigaŵa vyakwambilira. <ref name=“EcuRed”/> Pakukhumba kuti charu chiŵe na wanangwa, ŵanthu ŵanandi ŵa mu chigaŵa ichi ŵakamba kulimbana na batistato. Ŵanandi ŵa iwo ŵakapeleka umoyo wawo cifukwa ca mulimo uwu. Ŵanthu awo ŵakuzunulika ni Anastasio Cárdenas Ávila, uyo wakafwa ku Trinidad, na Andrés Cuevas Heredia, uyo wakafwa mu nkhondo ya Sierra Maestra, ndipo wakapika udindo wa mulongozgi wa ŵasilikari cifukwa ca nkhongono zake. Cinthu cakuzirwa comene pa umo nkhondo iyi yikendera cikaŵa kuŵapo kwa ŵalongozgi ŵa nkhondo [[Camilo Cienfuegos, Villa Clara|Camilo Cienfuegos]] na Ernesto Che Guevara, mu nyengo yaumaliro ya nkhondo iyi. <ref name=“EcuRed”/> Kufuma waka apo Nkhondo Yakwamba ya Caru Cose yikambira, ŵanthu ŵakujiyuyura ŵa mu tawuni iyi ŵalongora kuti mbakunozgeka kuvikilira tawuni iyi ku ŵasilikari. Ŵakaŵapo pakurwa nkhondo na vigeŵenga, mu Playa Girón na pakuparanya ŵanthu awo ŵakachitanga vivulupi. Ŵanthu ŵa mu chigaŵa ichi ŵakovwira ŵanthu ŵa mu vyaru vinyake pa nkhondo. <ref name=“EcuRed”/> ==Chikhalidwe== Msumba uwu uli na ŵanthu ŵanandi awo ŵakukhala mu malo agha, nga ni Raúl Planas, Omar González, Juan Manuel García, kweniso Leoncio Yanes na Ruperto Delgado Limendux. Wovwirani kuti muzi uwu uŵe na gulu la vyakusanguluska, makhoti gha ŵanthu ŵakutemwa kuvina, malo ghakusungirako vinthu vyakale, na vinyake. <ref name=“EcuRed”/> Chikondwelero chakukhora chomene mu chigaŵa chose ichi ni parranda, chiphikiro icho chikuchitika mu chigaŵa cha pakati pa Cuba, icho chikababikira ku Remedios, ndipo lero ni chiphikiro chakukondweska chomene ku ŵanthu wose ŵa mu chigaŵa ichi, uko kuli sumu, kuvina, vyakusanguluska vya pulasitiki na vyakuponya moto. <ref name=“EcuRed”/> ==Ukaboni== {{Reflist}} [[Category:Aguada de Moya]] mmbvsyyf64kdrblyntp0h7ob5el13fo 0 45705 121840 119923 2026-09-08T17:20:15Z InternetArchiveBot 6449 Add 2 books for [[en:Wikipedia:Verifiability|verifiability]] (20260908)) #IABot (v2.0.9.5) ([[User:GreenC bot|GreenC bot]] 121840 wikitext text/x-wiki {{Infobox artist | name = Tania Bruguera | image = File:Tania Bruguera small.jpg | alt = | caption = | birth_name = Tania Brugueras | birth_date = {{birth year and age|1968}} | birth_place = [[Havana]], [[Cuba]] | death_date = | death_place = | alma_mater = {{ubl | [[Instituto Superior de Arte]] | [[School of the Art Institute of Chicago]] }} | movement = Performance Art, installation and video | awards = {{ubl | Guggenheim Fellowship (1998) | Prince Claus Prize (2000) | {{ill|Velázquez Award for Plastic Arts|es|Premio Velázquez de Artes Plásticas}} }} | elected = | patrons = | website = {{URL|http://www.taniabruguera.com}} | father = [[Miguel Brugueras]] | field = Artist and activist | notable_works = Displacement (1989-99), <br>Untitled (Havana, 2000),<br> Tatlin's Whisper #5 (2008) }} '''Tania Bruguera''' (wakababika mu 1968 ku [[Havana]], [[Cuba]])<ref name="Phaidon Editors">{{cite book |title=Great Women Artists |date=2019 |publisher=Phaidon Press |isbn=978-0714878775 |page=79}}</ref>) ni nkhwantha ya vyakujambura na kujambura vinthu ndipo wakujambura vinthu na kujambura vinthu. Iye wakukhala ku Cambridge uko wakugwira nchito nga ni mutu wa vya manyuzipepara na vyakucita pa [[Harvard University]].<ref>{{Cite web |last=Author 14ymedio |date=2023-05-04 |title=Forced Into Exile, Artist Tania Bruguera Says That She Will Return to Cuba in August |url=https://translatingcuba.com/forced-into-exile-artist-tania-bruguera-says-that-she-will-return-to-cuba-in-august/ |access-date=2023-05-20 |website=Translating Cuba |language=en-GB}}</ref> Bruguera wakaluta ku maungano ghakurughakuru pa caru cose.<ref name="Global" /> Ntchito yake yili mu nyumba zakusungiramo vinthu vya pa caru cose, kusangzapo [[Museum of Modern Art]] na [[Bronx Museum of the Arts]] na [[Museo Nacional de Bellas Artes de La Habana]].<ref name="Global" /> Mulimo wa Bruguera ukulongosora vya mazaza na kuwusa, ndipo milimo yake yinandi yikulongosora vinthu ivyo vikachitika mu Cuba.<ref name="IUAV" /><ref name="Posner">{{Cite book|title=Tania Bruguera: On the political imaginary|url=https://archive.org/details/taniabrugueraonp0000posn|last1=Posner|first1=Helaine|last2=Mosquera|first2=Gerardo|last3=Lambert-Beatty|first3=Carrie|publisher=Charta|year=2009|isbn=978-88-8158-764-3|location=New York, NY}}</ref> Chifukwa cha ivyo wakachitanga, Bruguera wakakakika kanandi waka na kujalirika mu jele. == Mbili == Wakababika na zina lakuti Tania Brugueras, ndipo wakaŵa mwana wa Miguel Brugueras uyo wakaŵa nduna ya boma, kweni wakati wakwaniska vyaka 18, wakasintha zina lake na kuŵa Bruguera.<ref>{{cite web|url=http://www.aljazeera.com/indepth/features/2016/10/tania-bruguera-cuban-artist-fights-free-expression-160930124023219.html|title=Tania Bruguera: Cuban artist fights for free expression|first=Carlos Manuel|last=Alvarez|website=www.aljazeera.com|access-date=21 February 2018}}</ref> Cifukwa cakuti adada ŵake ŵakaŵa nduna ndipo ŵakaŵa mu boma la Fidel Castro, Tania wakasama maulendo ghatatu apo wakaŵa mwana. Adada ŵake ŵakaluta ku Paris (1973-1974), Lebanon (1974-1977), na Panama (1977-1979). Mu 1979, vilimika viŵiri kufuma apo wakasamukira kacitatu, Bruguera wakasankha kuwelera ku Cuba. Bruguera wakasambira ku Instituto Superior de Arte ku Havana ndipo pamasinda wakatora digiri ya M.F.A. ku School of the Art Institute of Chicago.<ref name="CV">{{cite web|url=http://www.taniabruguera.com/PDFdocuments/Resume.pdf|title=Curriculum Vitae|website=taniabruguera.com|access-date=21 February 2018}}</ref><ref name="IUAV">[http://www.iuav.it/Facolta/facolt--di1/English-ve/faculty/teaching-f/Tania-Brug/index.htm IUAV], Faculty of Arts & Design</ref><ref name="Global">{{cite book|last=Reilly and Nochlin|first=Eds|title=Global Feminisms: New Directions in Contemporary Art|year=2007|publisher=Merrell|location=London and New York|page=270}}</ref> Ndiwo wakambiska na kulongozga Catédra Arte de Conducta (sukulu ya maluso gha kachitiro), sukulu yakwamba ya maluso gha kachitiro ku Latin America, iyo yikupangika na Instituto Superior de Arte ku Havana. Kufuma mu 2003 kufika mu 2010, wakaŵa pulofesa mu Dipatimenti ya Visual Arts pa Yunivesite ya Chicago, ku United States ndipo ni pulofesa wakucemeka ku Yunivesite ya Iuav di Venezia ku Venice, [[Italy]]. Mu 2021, Bruguera wakafumako ku Cuba kuti boma lizomerezge kuti ŵakwimira boma awo ŵakakakika mu chaka chenechichi ŵafumemo mu Cuba.<ref>{{Cite web |title=Tania Bruguera Departing Cuba in Exchange for Government Freeing Prisoners |url=https://www.artforum.com/news/tania-bruguera-departing-cuba-in-exchange-for-government-freeing-prisoners-86897 |access-date=2023-05-20 |website=www.artforum.com |language=en-US}}</ref> ==Ntchito== Mu 1985-96, Ana Mendieta wati wafwa, Bruguera wakambiska viphikiro vyakuti Tribute to Ana Mendieta. Mu 1997 Bruguera wakalemba buku lakuti The Burden of Guilt (El peso de la culpa) ilo likulongosora umo ŵanthu ŵanandi ŵa ku Cuba ŵakajiphyera mwakuti ŵaleke kukomeka na ŵanthu ŵa ku [[Spain]].<ref name="guggenheim.org">{{Cite web|url=https://www.guggenheim.org/artwork/artist/tania-bruguera|title = The Guggenheim Museums and Foundation}}</ref><ref>{{Cite book|title=Corpus Delecti: Performance Art of the Americas|url=https://archive.org/details/corpusdelectiper0000unse|last=Fusco|first=Coco|publisher=Routledge|year=2000|isbn=0415194547|location=London|pages=[https://archive.org/details/corpusdelectiper0000unse/page/152 152]–153}}</ref> Bruguera wakalongosora kuti kurya fuvu kukaŵa "nkhondo ya kulimbana na boma". Pa nyengo iyi, Bruguera wakimilira kwambura kuvwara, ndipo thupi la mwana wa mberere likaŵa mu singo yake. Kwa maminiti 45, wakarya dongo lakusazgako maji na mchere, ivyo vikimiranga masozi.<ref>{{Cite web |title=Holy Terrors: Performing Greater Cuba: Tania Bruguera and the Burden of Guilt |url=https://scalar.usc.edu/nehvectors/taylor/performing-greater-cuba-tania-bruguera-and-the-burden-of-guilt |access-date=2023-05-20 |website=Holy Terrors: Latin American Women Perform}}</ref><ref name="Guilt">{{cite web |last=Bruguera |first=Tania |title=The Burden of Guilt |url=http://www.taniabruguera.com/cms/214-0-The+Burden+of+Guilt.htm |access-date=May 17, 2013 |work=Tania Bruguera}}</ref><ref name="Rubin">{{cite web|last=Rubin|first=Edward|title=Art in America Featured Installation by Cuban Artist at Neuberger Museum|url=http://www.artesmagazine.com/2010/03/neuberger-museum-features-installation-art-by-cuban-artist/|work=Artes Magazine|access-date=May 17, 2013|url-status=dead|archive-url=https://web.archive.org/web/20110815164806/http://www.artesmagazine.com/2010/03/neuberger-museum-features-installation-art-by-cuban-artist/|archive-date=August 15, 2011}}</ref> Nga ni umo Edward Rubin wakalongosolera, "cithuzithuzi cakucitiska citima ici cikadankha kulongoreka mu Havana, uko ŵategherezgi ŵakakumbuskika makora kuti wanangwa, wanangwa, na wanangwa wa kujisankhira vyakucita ni vintu vyambura kuwoneka, kweni ni vinthu ivyo vikulongora kuti tili na wanangwa". Mu 1998-1999 Bruguera wakapanga cinthu cakucita cithuzithuzi cakucemeka kuti "Destierro" (Kusamuka). Vinthu ivi vikuyanako na ivyo munthu munyake wankhongono zina lake - Nikis Nkonde -  wakachita ndipo vikulongora kuti boma la Cuba likaŵalayizga vinthu vyawaka ŵanthu ŵake apo likachitanga vinthu vyautesi. Na cinthu ici, Tania wakucema ŵanthu ŵa ku Cuba kuti ŵacitepo kanthu na kupempha boma la ku Cuba kuti licite ivyo laŵalayizga. Mu 2002, Bruguera wakambiska Cátedra Arte de Conducta (Sukulu ya Maluso gha Nkharo) ku Havana kuti wapeleke malo ghakusambizgirako vya maluso ghanyake mu caru ca Cuba. Cátedra iyi yikaŵa na mulimo wa kusambizga ŵawukirano ŵa ku Cuba maluso ghakupambanapambana, na kulongora umo maluso ghangagwilira nchito kuti ghasinthe maghanoghano gha ŵanthu. Kweniso, Cátedra yingapulikikwa nga ni mulimo wa luso mu nthowa ya maboma kususka, social mchitidwe, panji parasitism, na Bruguera reformulating maboma frameworks wa Cuban national art sukulu, the Havana Biennial, ndipo ndalama-ndi-nkongono-fueled mayiko luso dera kuti unintended vilato. Pakugwiliskira nchito malo agho wakaŵa, Bruguera wakawovwira ŵasambiri ŵake kuti ŵaŵe na nkharo yiwemi mwa kuŵalongoraso milimo yawo pa Havana Bienal". Bruguera wakaluta ku Havana ku Havana Biennial of Tatlin's Whisper #6 2009 ndipo wakapangiska kuti ŵanthu ŵayowoye vinandi. Pa nyengo iyo ŵakacitanga cinthu ici, Bruguera wakaŵika maikolofoni na kuphalira ŵanthu kuti ŵayowoyenge cilicose ico ŵakukhumba kwa miniti yimoza. Ŵanthu awo ŵakavwaranga vyakuvwara vya ŵasilikari ŵakaŵikanga tuyuni tuchokotuchoko pa viŵegha vya waliyose uyo wakayowoyanga nkhani, kulongora kuti ŵakakumbukiranga ivyo vikacitika apo nkhunda yikakhala pa viŵegha vya Fidel Castro apo wakayowoyanga nkhani yakulongosora kuti watonda pa nkhondo mu Janyuwale 1959. Ŵanandi awo ŵakaŵapo pa ungano uwu ŵakayowoya mazgu ghakuti "ufulu" na "demokirasi". Yumoza wa ŵanthu aŵa wakaŵa Yoani Sánchez, uyo ni mulembi wa mabulogu.<ref name="Reuters">[https://web.archive.org/web/20090409045549/http://uk.reuters.com/article/internetNews/idUKTRE5306OQ20090401?sp=true Reuters], Cuba accuses blogger of "provocation".</ref><ref name="MHerald">[http://www.miamiherald.com/living/story/976152.html The Miami Herald], Artist's work lets Cubans speak out in Havana for freedom</ref><ref name="Repubblica">[http://www.repubblica.it/2009/03/sezioni/esteri/cuba-usa/performance-liberta/performance-liberta.html La Repubblica], Cuba, blogger sul palco per un grido di libertà.</ref> Boma la ku Cuba likayowoya kuti likususka ivi ndipo likati "ichi ntchiyezgo chakukhozga soni na chambura kuzomerezgeka ku ŵanthu awo ŵakutemwa kujambura vinthu ndipo chikukwiyiska ŵanthu ŵa ku Cuba na ŵa ku vyaru vinyake awo ŵakiza kuzakalongora kuti ŵakukolerana na boma".<ref name="Reuters" /><ref name="Jiribilla">[http://www.lajiribilla.cu/2009/n412_03/412_50.html La Jiribilla:], Declaración del Comité Organizador de la Décima Bienal de La Habana.</ref> IMu 2011, Bruguera adayamba kugwira ntchito pa Immigrant Movement International, ntchito yojambulidwa m'magawo ambiri yomwe ikuyembekezeka kupitilira mu 2015. Mu 2011, Bruguera wakamba kukhala mu nyumba yichoko ku Corona, Queens, na ŵanthu ŵankhondi ŵakufuma ku vyaru vinyake na ŵana ŵawo. Iyo wakakhumbanga kumanya masuzgo agho ŵanthu awo ŵali na vikalata vyambura kuzomerezgeka ŵakukumana nagho para ŵakukhumba kusanga ndalama zinandi yayi kweniso para ŵalije inshuwalansi. Mulimo uwu ukacitikanga na Queens Museum of Art na gulu la ŵanthu awo ŵakakhumbanga kusanga ndalama yayi lakucemeka Creative Time. Mulimo uwu ukaŵangaso wa kujura sitoro ku [[New York]], uko Bruguera wakakhumbanga kuti wacitiskenge masambiro gha luso ku ŵanthu ŵakufuma ku vyaru vinyake, kweni wakasanga kuti ŵanthu ŵanandi awo ŵakizanga ku sitoro iyi ŵakakhumbanga kusambira Cingelezi panji kusanga nchito. Mu chaka cha 2012, wakalemba buku la Surplus Value, ilo likaŵa chigaŵa cha pulogiramu ya Immigrant Movement International ku Tate Modern. Kuti ŵanjire mu cipinda ca Surplus Value, ŵalendo ŵakalindiliranga pa mzere utali, ndipo ŵakakhumbikwiranga kupimika na makina ghakupimira utesi. Pa malo agha pakaŵa vimanyikwiro vinayi vyakuyana na ivyo vikaŵa mu misasa yakuyuzgirako ŵanthu ya Nazi. Mu chaka cha 2013, wakambiska pulogiramu ya The Museum of Arte Útil mu mgwirizano na Queens Museum of Art ku New York na Van Abbemuseum ku Eindhoven (NL). Mu Cisipanishi, lizgu lakuti Arte Útil likung'anamura luso, kweni likung'anamuraso luso panji cinthu cinyake. Arte Útil wakughanaghana, kulenga na kufiska vinthu ivyo vikovwira ŵanthu. Nyumba yakusungiramo vinthu vyakale ya Arte Útil yikapangika na gulu la Asociación de Arte Útil, ilo ni gulu la ŵanthu ŵakufuma mu vyaru vinyake. Alistair Hudson, uyo ni mulara wa sukulu ya Middlesbrough Institute of Modern Art (MIMA) na Bruguera ndiwo ŵakulongozga gulu ili. Mu chaka cha 2017, Bruguera wakajipharazga kuti waŵe mulembi wa chisankho cha pulezidenti wa ku Cuba mu chaka cha 2018 mu vidiyo yakuchemeka #YoMePropongo en Cuba. Mu pulogiramu iyi, wakufumba ŵanthu kuti ŵaghanaghanire ivyo ŵangacita kuti ŵazakaŵe na umoyo uwemi munthazi ku Cuba usange ŵangasankhika kuŵa pulezidenti. M'paka sono, Bruguera wapokera mavidiyo 70 kufuma ku ŵanthu ŵa ku Cuba awo ŵakukhumba kusintha boma la vimbundi ili, kuti ŵaŵape nyumba zakukwana, kweniso kuti ŵasinthe vinthu pa nkhani ya ndalama. Mu chaka cha 2018, wakapokera ntchito ya ku Tate Modern's Turbine Hall. Pa malo agha, Bruguera wakabenekelera cigaŵa cinyake ca pasi na malangi ghafipa. Para ŵalendo ŵakhala panji kugona pa malo agha, ŵakawonanga cithuzithuzi cikuru ca munthu uyo wakacimbira ku Syria. Catherine Wood, uyo wakonkheska malo agha, wakalongosora kuti: "Mukucema ŵanthu kuti ŵacitepo kanthu, cifukwa palije ico mungacita kuti muwonenge cithuzithuzi ici kwambura kukolerana na ŵanthu ŵanandi". Mu chaka cha 2021, nyumba yakusungiramo vinthu vyakale ya Pérez Art Museum ku Miami yikagura ntchito ya Bruguera ya El peso de la culpa (The Burden of Guilt).<ref>{{Cite web |title=El peso de la culpa (The Burden of Guilt) • Pérez Art Museum Miami |url=https://www.pamm.org/en/artwork/2017.073 |access-date=2023-03-07 |website=Pérez Art Museum Miami |language=en-US}}</ref><ref>{{Cite web |last=Valentine |first=Victoria L. |date=2021-08-21 |title=New Acquisitions: Pérez Art Museum Miami Adds 13 Works to Collection, Diverse Slate of Artists Includes Kenturah Davis, Bisa Butler, Karon Davis, Coco Fusco, and Sonia Gomes |url=https://www.culturetype.com/2021/08/20/new-acquisitions-perez-art-museum-miami-adds-13-works-to-collection-diverse-slate-of-artists-includes-kenturah-davis-bisa-butler-karon-davis-coco-fusco-and-sonia-gomes/ |access-date=2023-03-07 |website=Culture Type |language=en-US}}</ref> Bruguera wakaluta ku malo ghanandi ghakupambanapambana, kusazgapo Documenta 11 (2002), Documenta fifteen (2022), Bienal Iberoamericana ku Lima, Peru (2002), Istanbul Biennial (2003), Shanghai Biennale (2004), na Gwangju Biennale ku Gwangju, Korea (2008). Ntchito zake zili mu nyumba zakusungiramo vinthu vya ŵanthu ŵanandi pa charu chose, kusazgapo Museum of Modern Art na Bronx Museum of the Arts ku New York na Museo Nacional de Bellas Artes de La Habana.<ref name="Global" /> === Activism === Bruguera wakakakika na kufumiskika katatu mu nyengo ya Disembala 2014 mpaka Janyuwale 2015 chifukwa cha kupanga chiwonetsero ku Plaza de la Revolución ku Havana. Iyo wakakakika pamoza na ŵanthu ŵanyake ŵa ku Cuba, awo ŵakakhumbanga kuti vinthu visinthe, awo ŵakalembanga mabulogu, na awo ŵakalembanga nkhani mu nyuzipepara, awo ŵakalondezganga kampeni ya 'Yo Tambien Exijo.' Kampeni iyi yikamba pa Disembala 17, 2014, apo Raúl Castro na Barack Obama ŵakapharazga kuti ŵaŵeso paubwezi na caru ca Cuba, ndipo ivi vingapangiska kuti nkhondo iyo yili kuŵapo kwa vyaka 50 yimare. Ŵanthu ŵakwamba kukakika pa Ciŵiri, Disembala 30, pamasinda pakuti Bruguera wapharazga kuti wacitenge maseŵero gha pa wumba na cilato cakuti waŵaleke ŵanthu ŵa ku Cuba kuti ŵayowoye maghanoghano ghawo mwakufwatuka. Mulimo uwu ukacemeka kuti Tatlin's wisper #6  ⁇  Havana Version, ndipo ukacitikapo kale mu 2009 pa nyengo ya 10th Havana Biennial. Mu nyengo ya Tatlin's Whisper #5 (2008), ŵanthu awo ŵakaŵapo pa chiphikiro ichi ŵakasangana na ŵapolisi awo ŵakakweranga pa mahachi.<ref name="guggenheim.org"/> Ŵanthu ŵanandi ŵakayowoyapo nkhani iyi mu manyuzipepara<ref>{{cite web|url=http://hyperallergic.com/173328/how-tania-brugueras-free-speech-performance-was-mishandled-and-misreported-in-cuba/|title=How Tania Bruguera's Free Speech Performance Was Mishandled, and Misreported, in Cuba|website=Hyperallergic|date=7 January 2015|language=en-US|access-date=2016-03-05}}</ref><ref>{{cite web|url=http://www.e-flux.com/announcements/on-the-detention-of-cuban-artist-tania-bruguera-by-coco-fusco/|title=On the detention of Cuban artist Tania Bruguera, by Coco Fusco {{!}} e-flux|website=www.e-flux.com|access-date=2016-03-05}}</ref><ref>{{cite web|url=https://news.artnet.com/art-world/how-tania-brugueras-whisper-became-the-performance-heard-round-the-world-213637|title=Tania Bruguera's 2014 Whisper Performance – artnet News|website=artnet News|date=8 January 2015|language=en-US|access-date=2016-03-05}}</ref><ref>{{cite web|url=http://www.art-agenda.com/reviews/tania-bruguera%25E2%2580%2599s-tatlin%25E2%2580%2599s-whisper-6-and-the-hannah-arendt-international-institute-for-artivism/|title=Tania Bruguera's Tatlin's Whisper #6 and the Hannah Arendt International Institute for Artivism {{!}} Art Agenda|website=www.art-agenda.com|access-date=2016-03-05}}</ref><ref>{{Cite news|url=https://www.theguardian.com/artanddesign/2015/oct/13/frieze-tania-bruguera-artist-cuba-torture-interview|title=Tania Bruguera: the more the secret police torture me, the better my art gets|last=Hoby|first=Hermione|date=2015-10-13|newspaper=The Guardian|language=en-GB|issn=0261-3077|access-date=2016-03-05}}</ref> ndipo ŵanthu ŵakujumpha 1,000 pa caru cose ŵakalemba na kusayinira kalata yakukhozgera Tania iyo yikalembekera Raúl Castro. Kalata iyi yikayowoya kuti: "Tikugomezga kuti kumukaka na kukanizga pasipoti yake ya ku Cuba, ni nthowa zambura kwenelera zakucitira vinthu na munthu uyo wakakhumbanga waka kuti ŵanthu ŵayowoyepo". Pamanyuma ŵakamufumiska ndipo boma la Cuba likamuwezgera pasipoti yake pa Julayi 10, 2015, myezi 6 kufuma apo ŵakayipokelera. Mu Disembala 2015, Bruguera wakapharazga kuti wangaweleraso ku Cuba. Iyo wakati apo wakaŵa mu jele wakazomera kuti wafumenge pekha para wapika vinthu viŵiri: kuti awo ŵakakolerana nayo yayi na boma awo ŵakakakika pamasinda pakuti wawonelerapo ivyo wakacita pa Revolution Square ŵafumiskike; ndiposo kuti boma la Cuba limupeko kalata yakusachizga kuti wawelerenge ku Cuba. Pa 3 March, 2016, iye wakambiska kampeni ya Kickstarter kuti wasange ndalama za INSTAR (Institute of Artivism Hannah Arendt). Wupu uwu ukukhumba kuti ŵanthu ŵaŵe paubwezi, ŵacitenge vinthu mwamtende kweniso mwamahara para vinthu vyasuzga, kweniso kuti ŵanthu awo ŵali na maghanoghano ghakupambana pa nkhani ya ndyali ŵakumanenge pamoza kuti ŵazenge caru ciwemi. Awo ŵakalemba pulogiramu iyi ŵakaphalirika kuti ŵapeleke uthenga wawo ku boma la Cuba apo Bruguera wakanizgikanga. Mu Okutobala 2017, Tania Bruguera wakapharazga kuti wazamupharazga nga ni "Purezidenti wa ku Cuba", para Pulezidenti Raul Castro (munyamata wa Fidel Castro) wafumapo pa udindo. Bruguera wakayowoya kuti mulimo wa kuseka uwu ni mulimo wa kuvumbura kuti Cuba ni boma la chipani chimoza ilo ŵanthu ŵakulisora yayi. Iyo wakugomezga kuti wasinthenge vinthu mwa kuvumbura unenesko uwu, na kuwuskapo cikhaliro ca wofi. Bruguera wakakakika mu Disembala 2018 pambere wandachite chipharazgo chakususkana na dango la ku Cuba (Docree 349) ilo likukhumba kuti awo ŵakucita vyakusanguluska ŵapemphe boma kuti liŵapenge malaisensi. Pa Disembala 6, 2018, Bruguera wakafumiskika mu jele pamanyuma pa mazuŵa ghatatu pamoza na ŵanthu ŵanyake 12 awo ŵakakanizganga ŵanthu kugwiliskira nchito vinthu vyakupambanapambana. Ndipouli, mudumbu wake wakaphalira nyuzipepara ya The Art Newspaper kuti boma la Cuba likumujalira mu nyumba ndipo likukhumba kuti wamukome. Bruguera wakadandawura ku boma la ku Cuba kuti likamuyowoyera vyauzeleza pamasinda pakusindikizga nkhani izo zikakhumbanga "kumuŵinya [mwanakazi uyu] na mbumba yake, mu maghanoghano, mu umoyo, na mu nchito yake". Nkhani izi zikaŵa mu nyuzipepara ya Gramma, Razones de Cuba, na La Jiribilla. Mu Okutobala 2020, Bruguera wakadandawura kuti wakapulikanga vyakuŵinya vinandi chifukwa cha kupoma uko wakapulika mu nyumba yake ku Havana.<ref name = "CiberCuba">{{cite web |url=https://www.cibercuba.com/noticias/2020-10-18-u1-e20037-s27061-tania-bruguera-denuncia-malestares-fisicos-sonido-parecido-al |title=Tania Bruguera denuncia malestares físicos y un sonido parecido al de un grillo electrónico en su casa |work=CiberCuba |author=CiberCuba |date=October 18, 2020 |access-date=October 21, 2020}}</ref>Vimanyikwiro vya matenda agha vikuyana waka na ivyo vikucitika para munthu wali na nthenda ya ku Havana. == Ukaboni == {{Reflist}} == Vigaŵa vya kuwalo == * Art21 episode featuring Tania Bruguera https://art21.org/artist/tania-bruguera/ *[https://www.moma.org/magazine/articles/22 Dignity Does Not Rest: An Interview with Tania Bruguera, MoMA Magazine] * [https://www.moma.org/calendar/exhibitions/3898?locale=en Tania Bruguera, Untitled (Havana 2000) at The Museum of Modern Art] * [https://www.moma.org/audio/playlist/47 Hear Bruguera speak about her work Untitled (Havana 2000)] * [http://www.taniabruguera.com/ Official webpage of the artist] *[https://web.archive.org/web/20150607153816/http://bombmagazine.org/article/10071/tania-bruguera Interview with Paul O'neil in Bomb Magazine] *[https://www.theguardian.com/artanddesign/2015/oct/13/frieze-tania-bruguera-artist-cuba-torture-interview Tania Bruguera: the more the secret police torture me, the better my art gets, The Guardian] *[http://worldfellows.yale.edu/tania-bruguera Tania Bruguera: Yale World Follows] *[https://web.archive.org/web/20160501202035/http://www.wmagazine.com/culture/art-and-design/2015/12/tania-bruguera-cuban-artist/photos Tania Bruguera: Rebel with a Cause] {{Webarchive|url=https://web.archive.org/web/20160501202035/http://www.wmagazine.com/culture/art-and-design/2015/12/tania-bruguera-cuban-artist/photos |date=2016-05-01 }} {{Authority control}} {{DEFAULTSORT:Bruguera, Tania}} [[Category:1968 births]] [[Category:Living people]] [[Category:20th-century Cuban women artists]] [[Category:21st-century Cuban women artists]] [[Category:Women performance artists]] [[Category:Cuban contemporary artists]] [[Category:Artists from Havana]] [[Category:School of the Art Institute of Chicago alumni]] [[Category:Women installation artists]] [[Category:Instituto Superior de Arte alumni]] jeez4kh4a5cogm9w2svw9wayqhptrzt 0 48466 121838 119837 2026-09-08T16:29:34Z InternetArchiveBot 6449 Add 4 books for [[en:Wikipedia:Verifiability|verifiability]] (20260908)) #IABot (v2.0.9.5) ([[User:GreenC bot|GreenC bot]] 121838 wikitext text/x-wiki {{Short description|Kampani ya malonda ya ku East India ya ku Netherlands, 1602–1799}} {{other uses|Kampani ya East India (kuzatula)}} {{Use British English|date=March 2026}} {{Use dmy dates|date=November 2018}} {{Infobox company | name = Kampani Yakukolerana ya East India{{nobold|1602–1799}} | logo = VOC.svg | logo_size = 100 | image = Flag of the Dutch East India Company.svg | image_caption = Mbendera ya kampani (1630) | native_name = {{ubli|Vereenigde Oostindische Compagnie|Generale Vereenichde Geoctrooieerde Compagnie {{lang|en|italic=no|(zina lakwamba)}}|Vereenigde Nederlandsche Geoctroyeerde Oostindische Compagnie {{noitalic|(zina lakovwira pa malango)}} }} | native_name_lang = nl | type = Kampani yakulongozgeka na boma na ŵanthu | fate = [[Kumazga (malango)|Yikamazgika]] ndipo [[Kwenjilira boma|yikapokeka na boma]] kuŵa [[Dutch East Indies]] | predecessor = {{collapsible list|bullets=y|title={{nobold|{{lang|nl|[[Voorcompagnie]]ën}}{{}}Makampani ghakwamba (1594–1602){{efn|Makampani agho ghakuchemeka {{lang|nl|voorcompagnieën}} (panji makampani ghakwamba) ghakusazgapo: {{lang|nl|italic=no|[[Compagnie van Verre]]}} (Amsterdam, 1594–1598), {{lang|nl|italic=no|[[Voorcompagnie|Nieuwe Compagnie]]}}, {{lang|nl|italic=no|[[Voorcompagnie|Eerste Verenigde Compagnie op Oost-Indië]]}} (Amsterdam, 1598–1601), {{lang|nl|italic=no|[[Voorcompagnie|Oude Oost-Indische Compagnie]]}} (Amsterdam, 1598–1601), {{lang|nl|italic=no|Verenigde Amsterdamse Compagnie}}, {{lang|nl|italic=no|Nieuwe of Tweede Compagnie}}, {{lang|nl|italic=no|[[Brabantsche Compagnie]]}}, {{lang|nl|italic=no|[[Nieuwe Brabantsche Compagnie]]}}, {{lang|nl|italic=no|Magelhaensche Compagnie{{}}Rotterdamse Compagnie}}, {{lang|nl|italic=no|Middelburgse Compagnie}}, {{lang|nl|italic=no|[[Veerse Compagnie]]}} (Zeeland, 1597), {{lang|nl|italic=no|Verenigde Zeeuwse Compagnie}} (Middelburg & Veere, 1600), {{lang|nl|italic=no|[[Compagnie van De Moucheron]]}} (Zeeland, 1600), na {{lang|nl|italic=no|[[Voorcompagnie|Delftse Vennootschap]]}}. Niels Steensgaard wakalemba kuti, "the {{lang|nl|voorcompagnieën}} were not [[Incorporation (business)|incorporated]], but were run by a number of {{lang|nl|bewindhebbers}}, who were joined together like partners in a simple company, i.e. traded on joint account".{{cite book |last=Steensgaard |first=Niels |title=The Asian Trade Revolution of the Seventeenth Century |url=[https://archive.org/details/asiantraderevolu0000stee](https://archive.org/details/asiantraderevolu0000stee) |url-access=registration |publisher=University of Chicago Press |year=1974 |isbn=0-226-77139-3}}}}}} |{{lang|nl|italic=no|[[Compagnie van Verre]]}}|{{lang|nl|italic=no|[[Brabantsche Compagnie]]}}|{{lang|nl|italic=no|[[Compagnie van De Moucheron]]}}|{{lang|nl|italic=no|[[Veerse Compagnie]]}}}} | founded = {{start date and age|df=y|1602|03|20}},{{cite web|url=[http://entoen.nu/voc/en|title=The](http://entoen.nu/voc/en|title=The) Dutch East India Company (VOC)|publisher=Canon van Nederland|access-date=19 March 2011|archive-url=[https://web.archive.org/web/20101201212719/http://entoen.nu/voc/en|archive-date=1](https://web.archive.org/web/20101201212719/http://entoen.nu/voc/en|archive-date=1) December 2010|url-status=dead}} na [[States General of the Netherlands|Konsili Yikuru ya Netherlands]] kuyunganizga [[Voorcompagnie|makampani agho ghakaŵako]]/makampani ghakwamba | defunct = {{end date and age|df=y|1799|12|31}} | founder = [[Johan van Oldenbarnevelt]] na [[States General of the Dutch Republic|Konsili Yikuru ya Dutch Republic]] | hq_location_city = {{plainlist| * [[Amsterdam]], [[Dutch Republic]] (likuru la kampani pa charu chose) * [[Batavia, Dutch East Indies|Batavia]], Dutch East Indies (likuru lachiŵiri panji malo ghakulamulirako ku vyaru vinyake)}} | area_served = {{hlist|[[South East Asia]]|[[South Asia]]|[[Asia–Pacific]]|[[Southern Africa]]}} | key_people = {{plainlist| * {{ill|Heeren XVII|nl|Heren XVII}}{{}}Ŵalongozgi 17{{efn|Kuŵa komiti ya ŵalongozgi}} (Dutch Republic, 1602–1799) * [[Governors-general of the Dutch East Indies]]{{efn|Kuŵa ''de facto'' [[ŵalongozgi ŵakuru ŵa kampani]]}} ([[Batavia, Dutch East Indies|Batavia]], 1610–1800)}} | industry = [[Kampani yakusazgapo mabizinesi|Kampani yakwamba yakusazga mabizinesi]] | products = [[Malonda gha vyakununkhira|Vakununkhira]], [[silika]], [[porcelain]], [[visulo]], [[viŵeto]], [[tiyi]], [[tirigu]], [[mpunga]], [[soya]], [[makampani gha shuga|nzimbe]], [[South African wine|vinyu]], [[Coffee production in Indonesia|khofi]], [[ŵazga]] }} [[File:Michiel Jansz van Mierevelt - Johan van Oldenbarnevelt.jpg|thumb|upright=0.9|Kampani ya United East India Company yikapangika na [[Johan van Oldenbarnevelt]], munthu wakuzirwa chomene mu ndyale za Dutch Republic.]] [[File:SA 3025-De binnenplaats van de Beurs van Hendrick de Keyser.jpg|alt=|thumb|Msika wa malonda wa Hendrick de Keyser]] '''United East India Company'''{{efn|Kung'anamulira mwakudunjika zina la Chidachi {{lang|nl|Vereenigde Oostindische Compagnie}} ni ''Kampani Yakukolerana ya East India''. Pa mazina ghakupambanapambana gha malonda gha VOC mu Chingelezi, wonani nkhani izi: [[East India Company (disambiguation)|Kampani za East India]]; [[Greater India|India Yikuru]]; [[East India|East India]]; [[East Indies|East Indies]]; [[Dutch East Indies|East Indies ya Chidachi]]; [[Dutch India|India ya Chidachi]]; [[Voorcompagnie|Makampani ghakwambilira]]; [[List of Dutch East India Company trading posts and settlements|Mndandanda wa malo gha malonda na maderahene gha Kampani ya Dutch East India]].}} ({{langx|nl|Vereenigde Oostindische Compagnie}} {{IPA|nl|vərˈeːnɪɣdə oːstˈɪndisə kɔmpɑˈɲi|}}; {{abbr.}}'''VOC''' {{IPA|nl|veː(j)oːˈseː|}}), iyo yikudziŵika chomene kuti '''Kampani ya Dutch East India''', yikaŵa [[chartered company|kampani yakupika chiphaso]] yakuchita [[trading company|malonda]] kweniso yikaŵa yimoza mwa [[joint-stock companies|makampani ghakwamba gha masheya]] pa charu chapasi. Likapangika pa 20 Malichi 1602 na [[States General of the Netherlands|Wupu wa Ŵalongozgi wa Netherlands]] ukusazga pamoza [[Voorcompagnie|makampani agho ghakaŵako kale]], ndipo likapika [[monopoly|ufumu wa malonda wakuŵikika yekha]] wa vyaka 21 kuti lichite malonda ku Asia. Masheya gha kampani iyi ghakaŵa ghakugulika na nzika yiliyose ya [[Dutch Republic|Dutch Republic]] ndipo ghakaguliskikanga pa misika yakuwonekera kwa wose ya [[secondary markets|masheya agho ghaguliskikaso]], ndipo umoza wa misika iyi ukazgoka [[Amsterdam Stock Exchange|Msika wa Masheya wa Amsterdam]]. Kampani iyi yikaŵa na nkhongono zakuyana na za boma, kusazgapo nkhongono zakuchita nkhondo, kuŵika ŵakayidi mu jele na kuŵakoma, kupanga mapangano, kupanga [[Coinage of the Dutch East India Company|ndalama zake]], na kukhazikiska maderahene. Chifukwa chakuti yikachitanga malonda pakati pa maderahene na vyaru vinandi vya ku East na West, VOC nyengo zinyake yikuwoneka kuti yikaŵa [[multinational corporation|kampani yakwamba pa charu chose chapasi yakuchita ntchito mu vyaru vinandi]]. Mbiri ya Ulamuliro wa Ŵachidachi] {{Webarchive|url=[https://web.archive.org/web/20150207085730/http://www.kb.nl/themas/geschiedenis-en-cultuur/koloniaal-verleden/voc-1602%E2%80%931799](https://web.archive.org/web/20150207085730/http://www.kb.nl/themas/geschiedenis-en-cultuur/koloniaal-verleden/voc-1602%E2%80%931799) |date=7 February 2015 }} VOC ku [[National Library of the Netherlands|Laibulare ya Charu ya Netherlands]] (mu Chidachi) Kuwoneska mu 1602 kuti yisange phindu mu [[Maluku Islands|malonda gha vyakununkhira gha ku Maluku]], VOC yikakhazikiska likuru lake mu msumba wa madoko wa [[Jayakarta]] mu 1619 ndipo yikasintha zina lake kuŵa [[Batavia, Dutch East Indies|Batavia]], uwo sono ukuchemeka [[Jakarta]]. Mu vyaka viŵiri vyakulondezgapo, kampani iyi yikasanga madoko ghanyake kuŵa malo ghake gha malonda ndipo yikavikilira vyakukhumba vyake mwa kupoka malo agho ghakaŵa kuzingilira. Yikalutilira kuŵa kampani yakuzirwa ya malonda ndipo yikapelekanga vigawanyo vya phindu vya chaka na chaka ivyo pa avareji vikaŵa pafupi 18% ya ndalama zakuguliskira kampani iyi kwa vyaka pafupifupi 200. Chifukwa cha uzgaŵa wa malonda, vimbundi na kukwera kwa ndalama zakulongozgera kampani mu vyaka vyakumalizga vya m'ma 18, kampani iyi yikafilisika ndipo yikamazgika mwalamulo mu 1799. Katundu wake na ngongole zake vikapokeka na boma la Dutch [[Batavian Republic]]. ==Zina la kampani, chimanyikwilo na mbendera== [[File:17th century plaque to Dutch East India Company (VOC), Hoorn.jpg|thumb|upright=1.36|Chizindikiro cha m'ma 17 cha Kampani Yakukolerana ya East India, VOC, ku [[Hoorn]]]] [[File\:VOC-Amsterdam.svg|thumb|upright|Chimanyikwilo cha [[Amsterdam]] Chamber ya VOC]] Mu Chidachi, zina la kampani iyi likaŵa ''Vereenigde Nederlandsche Geoctroyeerde Oostindische Compagnie'', ilo likachemekanga mwakufupikiska kuti VOC, ndipo likung'anamura kuti 'Kampani Yakukolerana ya Dutch Yakupika Chiphaso ya East India' (Kampani Yakukolerana ya East India). Chimanyikwilo cha kampani iyi chikaŵa na ''V'' yikuru, na ''O'' kumazere ndipo ''C'' ku chigaŵa cha kumanjiliro, ndipo panji chikaŵa chimanyikwilo chakwamba cha kampani icho chikamanyikwa pa charu chose. Chikawonekanga pa vinthu vya kampani, nga ni mbendera, mizinga na ndalama. Kalata yakwamba ya zina la msumba uko chipinda cha kampani chikachitira ntchito yikaŵikikanga pachanya. Kusinthasintha, kupulikikwa makora, kuphweka, kuyana kwa vigaŵa, kuleka kuchita ukalamba na uthenga wa chimanyikwilo ichi vikuwoneka kuti ni vinthu vyakuzirwa vya chimanyikwilo cha VOC icho chikapangika mwaluso. Vinthu ivi vikawovwira kuti chimanyikwilo ichi chizomerezeke pa nyengo iyo fundo ya [[chimanyikwilo cha kampani]] yikamanyikwanga viŵi yayi. Munthu wakulima mpheska ku Australia wagwiliskira ntchito chimanyikwilo cha VOC kufuma kuumaliro wa vyaka vya m'ma 20, wati walembeskaso zina la kampani iyi na chilato ichi. Pa charu chose, chomene mu vyaru ivyo vikuyowoya Chingelezi, VOC yikumanyikwa chomene kuti ni 'Kampani ya Dutch East India'. Zina lakuti 'Kampani ya Dutch East India' likugwiliskirika ntchito kupambaniska kampani iyi na [ya ku Britain] [[Kampani ya East India]] (EIC) na makampani ghanyake gha ku East India, nga ni [[Kampani ya Danish East India]], [[Kampani Yakwamba ya French East Indies|Kampani ya French East India]], [[Kampani ya Portuguese East India]], na [[Kampani ya Swedish East India]]. Mazina ghanyake agho kampani iyi yikumanyikwira nagho ghakusazgapo 'Kampani ya Dutch East Indies', 'Kampani Yakukolerana ya East India', 'Kampani ya Jan', panji 'Jan Compagnie'. Kampani ya Dutch East India] {{Webarchive|url=[https://web.archive.org/web/20150906121307/http://european-heritage.org/netherlands/alkmaar/dutch-east-india-company](https://web.archive.org/web/20150906121307/http://european-heritage.org/netherlands/alkmaar/dutch-east-india-company) |date=6 September 2015}}, ''European Heritage Project.'' ==Mbili== ===Kwambira=== {{See also|Ulendo wa Ŵachi Dutch Wakwamba ku Indonesia|Ulendo wa Ŵachi Dutch Wachiŵiri ku Indonesia|Voorcompagnie}} {{Further|Malonda gha vyakununkhira|Njira ya Cape}} Pambere pa [[Dutch Revolt|kuwukira kwa ŵa Dutch]], uko kukamba mu 1566/68, msumba wa Brabant wa [[Antwerp]] ukachita ntchito yakuzirwa nga ni malo ghakugawirako katundu kumpoto kwa [[Europe]]. Pamanyuma pa 1591, Ŵapwitikizi ŵakagwiliskira ntchito gulu la malonda la vyaru vinandi la ŵa German [[Fugger family|Fugger]] na [[Welser family|Welser]], pamoza na makampani gha ku [[Spain]] na Italy, agho ghakagwiranga ntchito kufuma ku [[Hamburg]] nga ni doko likuru la kumpoto lakugawirako katundu wawo, mwakuti ŵamalonda ŵa ku Dutch ŵakatolekera kuwalo kwa malonda. Pa nyengo yeneyiyo, dongosolo la malonda la Ŵapwitikizi likatondeka kusazgirako katundu kuti likwaniriske kusazgikira kwa khumbo, chomene khumbo la pepper. Khumbo la vyakununkhira likaŵa [[Price elasticity of demand|lakusuzga kusintha mwakuyana na mtengo]]; ntheura, kuchedwa kulikose pa kupereka pepper kukapangiska kuti mitengo ya pepper yikwere chomene. Mu 1580, [[Kingdom of Portugal|ufumu wa Portugal]] ukakolerana mu [[personal union|umoza wa mafumu]] na [[Spanish crown|ufumu wa Spain]], uwo ukamanyikwa kuti [[Iberian Union]]. Pa nyengo iyi [[Dutch Republic]] yikaŵa pa nkhondo na Spain. Ntheura, [[Portuguese Empire|Ufumu wa Portugal]] ukazgoka chilato chakwenelera cha nkhondo za ŵa Dutch. Vinthu ivi vikapangiska ŵamalonda ŵa ku Dutch kuti nawo ŵambe kuchita malonda gha vyakununkhira pakati pa makontinenti. Kweniso, ŵamalonda na ŵakupenja vinthu ŵanandi ŵa ku Dutch, nga ni [[Jan Huyghen van Linschoten]] na [[Cornelis de Houtman]], ŵakasanga umanyi waŵeneŵene wa nthowa za malonda na nthowa za ntchito za Ŵapwitikizi "zachisisi", ndipo ivi vikapeleka mwaŵi unyake ku ŵa Dutch kuti ŵanjire mu malonda agha.{{sfn|De Vries|Van der Woude |1997 |page=383}} Mwaŵi ukaŵa wakunozgeka kuti ŵa Dutch ŵambe maulendo ghawo ghakupenja ku [[Indonesia|visiwa vya Indonesia]], kuyambira na [[Cornelis de Houtman]] mu 1595 ndipo mu 1598, [[Jacob Corneliszoon van Neck|Jacob Van Neck]] mu 1598, pakati pa ŵanyake. Pa ulendo wakupenja wa zombo vinayi uwo ukalongozgeka na [[Frederick de Houtman]] mu 1595 ku [[Bantam (city)|Banten]], doko likuru la pepper ku West Java, ŵalendo ŵa mu sitima ŵakasangana na Ŵapwitikizi na ŵa ku Java. Ulendo wa Houtman ukalutilira kuya kumafumiro gha dazi mumphepete mwa nyanja ya kumpoto kwa [[Java]], ndipo ŵanthu 12 ŵa mu gulu lake ŵakakomeka pa nkhondo na ŵa ku Java ku Sidayu, uku iwo ŵakakoma mulongozgi wa malo ku [[Madura]]. Hafu ya gulu la ŵalendo ŵakaŵa kuti ŵatayika pambere ulendo uwu undafike ku Netherlands mu 1596, kweni ŵakiza na vyakununkhira vinandi ivyo vikaŵapa phindu likuru.{{sfn|Ricklefs |1993 |page=27}} [[File\:De terugkomst in Amsterdam van de tweede expeditie naar Oost-Indië, Hendrik Cornelisz Vroom, 1599, Rijksmuseum SK-A-2858.jpg|thumb|260px|Kuwelera kwa [[Ulendo wa Ŵa Dutch Wachiŵiri ku Indonesia|ulendo wachiŵiri wa ku Asia]] wa [[Jacob van Neck]] mu 1599, wakajambulika na [[Cornelis Vroom]]]] Mu 1598, magulu gha zombo ghakupambanapambana ghakatumika na magulu gha ŵamalonda ghakupambanapambana kufuma mu Netherlands yose. Zombo vinyake vikazgeŵeka, kweni vinandi vikafika makora, ndipo maulendo ghanyake ghakapanga phindu likuru. Mu 1598, [[Ulendo wa Ŵa Dutch Wachiŵiri ku Indonesia|gulu la zombo vinayi]] ilo likalongozgeka na [[Jacob van Neck]] likaŵa gulu lakwamba la zombo za ku Dutch kufika ku 'Visiwa vya Vyakununkhira' vya Maluku, ivyo vikamanyikwangaso kuti Moluccas, ndipo likasindika ŵamalonda ŵa pakati ŵa ku Java. Zombo izi zikawelera ku Europe mu 1599 na 1600, ndipo ulendo uwu ukapanga phindu la 400%.{{sfn|Ricklefs |1993 |page=27}} Mu 1600, ŵa Dutch ŵakakolerana na [[Hitu people|ŵa Hitu]] Ŵasilamu pa [[Ambon Island]] mu phangano lakulimbana na Ŵapwitikizi. Pa phangano ili, ŵa Dutch ŵakapika wanangwa wakugura vyakununkhira kufuma kwa ŵa Hitu pera. Ŵa Dutch ŵakamba kulamulira Ambon apo Ŵapwitikizi ŵakajipeleka na kupereka linga lawo ku Ambon ku phangano la ŵa Dutch na ŵa Hitu. Mu 1613, ŵa Dutch ŵakafumiska Ŵapwitikizi ku linga lawo la [[Solor]], kweni nkhondo yinyake ya Ŵapwitikizi yikapangiska kuti ulamuliro usinthe kachiŵiri. Pamanyuma pa kupokaso linga ili, ŵa Dutch ŵakapokaso Solor mu 1636.{{sfn|Ricklefs |1993 |pages=25–28}} Kumafumiro gha dazi kwa [[Solor]], pa chisumbu cha [[Timor]], kuluta panthazi kwa ŵa Dutch kukakanizgika na gulu lakujilamulira ilo likaŵa na nkhongono la Ŵapwitikizi ŵa ku Eurasia ilo likachemekanga [[Topasses]]. Iwo ŵakalutilira kulamulira malonda gha [[Sandalwood|mtengo wa sandalwood]]. Kukanizgika kwawo kukalutilira mu vyaka vya m'ma 17 na 18, ndipo ichi chikapangiska kuti [[Portuguese Timor]] chilutilire kuŵa pasi pa ulamuliro wa Ŵapwitikizi.{{in lang|pt}} Matos, Artur Teodoro de (1974), ''Timor Portugues, 1515–1769'', Lisboa: Instituto Histórico Infante Dom Henrique.{{in lang|nl}} Roever, Arend de (2002), ''De jacht op sandelhout: De VOC en de tweedeling van Timor in de zeventiende eeuw'', Zutphen: Walburg Pers. ===Vyaka vyakwambilira=== [[File\:Sd2-baggala.JPG|thumb|[[Mughal Bengal]]'s baghlah yikaŵa mtundu wa sitima uwo ŵamalonda ŵa ku Dutch ŵakagwiliskiranga ntchito chomene mu [[Indian Ocean]], [[Arabian Sea]], [[Bay of Bengal]], [[Strait of Malacca]] na [[South China Sea]].]] [[File\:COLLECTIE TROPENMUSEUM Reproductie van een plattegrond van Batavia uit circa 1627 TMnr 496-3.jpg|thumb|Chithuzithuzi chakubwerezga mapu gha msumba wa Batavia pafupi na{{nbsp}}1627, mu [[Wereldmuseum Amsterdam]]]] [[File\:Waere affbeeldinge Wegens het Casteel ende Stadt BATAVIA gelegen opt groot Eylant JAVA Anno 1681.jpg|thumb|Batavia ya ŵa Dutch mu 1681, yakazengeka pa malo agho sono ni [[North Jakarta]]]] Pa nyengo iyi, chikaŵa chizolowezi kuti kampani yipelekekenge ndalama kwa nyengo ya ulendo umoza pera ndipo yimazgikenge apo gulu la zombo lawelera. Kugwiliskira ntchito ndalama pa maulendo agha kukaŵa kwakofya chomene chifukwa cha vyakofya vya kawirikawiri vya ŵankhondo ŵa panyanja, matenda na kusweka kwa sitima, kweniso chifukwa cha kusangana kwa [[inelastic demand|khumbo ilo likusintha viŵi yayi mwakuyana na mtengo]] na [[elastic supply|katundu uyo wakusangika mwaluso]]{{efn|Mu nyengo yapakati, apo ŵapereki ŵaphya ŵanganjira mu msika. Mu nyengo yifupi, katundu uyo wakusangika nawo ukaŵa wakusintha viŵi yayi mwakuyana na mtengo.}} gha vyakununkhira, uko kukapangiskanga kuti mitengo yiwile chomene na kuparanya chigomezgo cha kupanga phindu. Kuti ŵalamulire ngozi iyi, kupanga [[cartel|gulu la makampani ghakukolerana]] kuti lilamulire katundu uyo wakuperekeka kukawoneka kuti ni nthowa yakwenelera. Mu 1600, Ŵaingelezi ndiwo ŵakaŵa ŵakwamba kugwiliskira ntchito nthowa iyi mwa kusazga vinthu vyawo mu kampani yakukhala na ulamuliro wa yekha, [[East India Company|Kampani ya East India ya ku England]], ndipo ivi vikawofya ŵapikisana nawo ŵa ku Dutch kuti ŵangaparanyika.{{sfn|De Vries|Van der Woude |1997 |pages=384–385}} Mu 1602, boma la Dutch likalondezga nthowa iyi, likawovwira kukhazikiska "Kampani Yakukolerana ya East Indies" yimoza iyo yikapikikaso ulamuliro wa yekha pa malonda gha ku Asia.{{Cite book |url=[https://www.nationaalarchief.nl/onderzoeken/archief/1.04.02/invnr/1/file/NL-HaNA\_1.04.02\_1\_01](https://www.nationaalarchief.nl/onderzoeken/archief/1.04.02/invnr/1/file/NL-HaNA_1.04.02_1_01) |title=Octrooi verleend door de Staten-Generaal betreffende de alleenhandel ten oosten van Kaap de Goede Hoop en ten westen van de Straat van Magallanes voor de duur van 21 jaar |year=1602 |publication-place=Amsterdam |pages=5 |language=nl |trans-title=Patent granted by the States General concerning exclusive trade east of the Cape of Good Hope and west of the Strait of Magallanes for a period of 21 years |quote='Dese vereenichde Compaignie sal beginnen ende aenvanck nemen met desen Jaere xvi C ende twee ende sal gedurende den tyt van eenentwintich Jaren achter (This United Company shall commence operations in the year of 1602, and shall continue for a period of twenty-one consecutive years)' |access-date=22 April 2022 |orig-date=20 March 1602 |via=Nationaal Archief |archive-date=22 April 2022 |archive-url=[https://web.archive.org/web/20220422184915/https://www.nationaalarchief.nl/onderzoeken/archief/1.04.02/invnr/1/file/NL-HaNA\_1.04.02\_1\_01](https://web.archive.org/web/20220422184915/https://web.archive.org/web/20220422184915/https://www.nationaalarchief.nl/onderzoeken/archief/1.04.02/invnr/1/file/NL-HaNA_1.04.02_1_01) |url-status=live}} Kwa nyengo yinyake mu vyaka vya m'ma 17, yikakwaniska kulamulira malonda gha nutmeg, mace na cloves, na kuguliska vyakununkhira ivi mu maufumu gha ku Europe na mu [[Mughal Empire]] wa Emperor [[Akbar the Great]] pa mitengo iyo yikaŵa yakukwera maulendo 14–17 kuluska mtengo uwo yikaguliranga ku [[Indonesia]].{{Cite book|title=Southeast Asia in the Age of Commerce, 1450–1680|last=Reid|first=Anthony|publisher=Yale University Press|year=1993|location=New Haven, Connecticut|pages=290}} Apo phindu la ŵa Dutch likakweranga chomene, chuma cha ku Visiwa vya Vyakununkhira chikaparanyika, chifukwa nga ni mugulisi yumoza pera, VOC yikachichizga kuti mitengo iyo ŵalimi ŵa ku Visiwa vya Vyakununkhira ŵakapokeranga yiŵe yichoko chomene. Na ndalama zakwamba za 6,440,200 [[guilder]]s{{cite book|first=John|last=Bruce|title=Annals of the Honourable East-India Company |url=[https://archive.org/details/annalshonorable00brucgoog|year=1810|publisher=Black](https://archive.org/details/annalshonorable00brucgoog|year=1810|publisher=Black), Parry, and Kingsbury|page=[[https://archive.org/details/annalshonorable00brucgoog/page/n42](https://archive.org/details/annalshonorable00brucgoog/page/n42) 28]}} (yakuyana na {{Euro|{{Inflation|NL|{{#expr:6440200/10^6}}|1600|r=0}}{{nbsp}}million|link=yes}} mu {{Inflation/year|NL}}), chiphaso cha kampani yiphya chikayipa mazaza ghakuzenga malinga, kusungilira ŵasilikari, na kuchita mapangano na ŵawusi ŵa ku Asia. Chikapeleka mwaŵi wa kampani iyo yikeneranga kulutilira kwa vyaka 21, kweni kuŵerengera vya ndalama kukeneranga kuchitika paumaliro wa chaka chilichose cha vyaka 10.{{sfn|De Vries|Van der Woude |1997 |pages=384–385}} [[File\:Willem Blaeu00.jpg|thumb|Early map of the Maluku Islands made during the [[Age of Discovery]], by [[Willem Blaeu]], 1630. North is on the right, with [[Sultanate of Ternate|Ternate]] as the rightmost followed by [[Sultanate of Tidore|Tidore]], both were known as the [[Spice Islands]] (trade secret, outposts of the VOC). |left]] Mu Febuluwale 1603, kampani iyi yikapoka [[Santa Catarina (ship)|''Santa Catarina'']], sitima ya malonda ya Ŵapwitikizi ya matani 1,500, pafupi na mphepete mwa nyanja ya [[Malay Peninsula]]. Mu chaka cheneko, gulu lakukolerana la ŵa Dutch na Ŵaingelezi likapoka sitima yinyake ya malonda ya Ŵapwitikizi kufupi na [[Macau]].{{cite book |author-link=C. R. Boxer |last=Boxer |first=C. R. |title=Fidalgos in the Far East, 1550–1770 |publisher=Martinus Nijhoff |location=The Hague |date=1948 |page=50}} Ndalama izo zikapatika pakuguliska katundu wa mu sitima ziŵiri izi zikaŵa zakujumpha 50% ya ndalama zakwamba izo ŵanthu ŵakaŵika mu VOC.{{cite book |last=Boyajian |first=James C. |title=Portuguese Trade in Asia under the Habsburgs, 1580–1640 |url=[https://books.google.com/books?id=C0lrDYYzMyAC&pg=PA151](https://books.google.com/books?id=C0lrDYYzMyAC\&pg=PA151) |page=151 |publisher=JHU Press |date=2008 |isbn=978-0-8018-8754-3 |access-date=2 June 2016 |archive-date=11 April 2023 |archive-url=[https://web.archive.org/web/20230411160033/https://books.google.com/books?id=C0lrDYYzMyAC&pg=PA151](https://web.archive.org/web/20230411160033/https://books.google.com/books?id=C0lrDYYzMyAC\&pg=PA151) |url-status=live}} Mu 1603, malo ghakwamba gha malonda gha Ŵa Dutch agho ghakaŵa ghakukhazikika ku Indonesia ghakakhazikiskika ku [[Banten]], [[West Java]]. Mu 1611, ghanyake ghakakhazikiskika ku [[Jayakarta]] (pamanyuma likachemekanga "Batavia" ndipo pamanyuma "Jakarta").{{sfn|Ricklefs |1993 |page=29}} Mu 1610, VOC yikakhazikiska udindo wa [[governor-general of the Dutch East Indies|mulongozgi mukuru]] kuti yikwaniske kulamulira makora nkhani zake ku Asia. Kuti walangure na kulamulira ngozi ya [[despotism|ulamuliro wankhaza]] wa ŵalongozgi ŵakuru, [[Council of the Indies (Dutch)|Khonsolo ya Indies]] (''Raad van Indië'') yikapangika. Mulongozgi mukuru wakazgoka mulongozgi mukuru wa ntchito za VOC ku Asia. ''Heeren XVII'', gulu la ŵanthu 17 awo ŵakaŵa na magawo gha kampani ndipo ŵakimiranga vipinda vyakupambanapambana, likalutilira kuŵa na ulamuliro wose pa kampani iyi mwalamulo.{{sfn|Ricklefs |1993 |pages=25–28}} [[File\:Amboina. 17th century print, most likely English..jpg|thumb|''Chisumbu cha Amboina'', chithuzithuzi cha [[17th century|m'ma 17]], panji chikajambulika na Mungwelezi]] Likuru la VOC likaŵa ku [[Governorate of Ambon|Ambon]] mu nyengo ya ŵalongozgi ŵakuru ŵatatu ŵakwamba (1610–1619), kweni malo agha ghakaŵa ghambura kwenelera. Nangauli ghakaŵa pakati pa malo agho vyakununkhira vikapangikanga, ghakaŵa kutali na nthowa za malonda gha ku Asia na malo ghanyake agho VOC yikachitirangako ntchito, kufuma ku Africa kuya ku India na Japan. Om Prakash, ''The Dutch East India Company and the Economy of Bengal, 1630–1720'' (Princeton University Press, 1985)William De Lange, ''Pars Japonica: the first Dutch expedition to reach the shores of Japan'', (2006) Ntheura, malo gha kumadzulo kwa chigaŵa ichi ghakapenjeka. [[Straits of Malacca]] ghakaŵa ghakuzirwa pa nkhani za nkhondo na malonda kweni ghakamba kuŵa ghakofya pamanyuma pa kupoka na Ŵapwitikizi, ndipo malo ghakwamba gha VOC ghakukhazikika ku Banten ghakaŵa pasi pa ulamuliro wa mulongozgi wa ku malo uyo wakaŵa na nkhongono, kweniso ghakakumana na chipikano chikuru kufuma kwa ŵamalonda ŵa ku China na Ŵaingelezi.{{sfn|Ricklefs |1993 |pages=25–28}} Mu 1604, ulendo wachiŵiri wa Ŵaingelezi wa [[Kampani ya East India]] uwo ukalongozgekanga na [[Sir Henry Middleton]] ukafika ku visiwa vya [[Ternate]], [[Tidore]], [[Ambon Island|Ambon]] na [[Banda Islands|Banda]]. Ku Banda, ŵakasangana na kususka kukuru kufuma ku VOC, ndipo ichi chikapangiska chipikano cha ŵa Dutch na Ŵaingelezi pa nkhani ya kusanga vyakununkhira. Kufuma mu 1611 mpaka 1617, Ŵaingelezi ŵakakhazikiska malo gha malonda ku [[Sukadana]] (kumwera chakumafumiro gha dazi kwa [[Kalimantan]]), [[Makassar]], [[Jayakarta]] na [[Jepara]] ku [[Java]], kweniso Aceh, [[Pariaman]] na [[Jambi]] ku [[Sumatra]], ndipo ivi vikawofya khumbo la ŵa Dutch lakuti ŵaŵe na ulamuliro wawo watekha pa malonda gha East Indies.{{sfn|Ricklefs |1993 |page=29}} Mu 1620, mapangano gha ubwezi mu Europe ghakapanga nyengo ya kukolerana pakati pa malonda gha vyakununkhira gha ŵa Dutch na Ŵaingelezi.{{sfn|Ricklefs |1993 |page=29}} Ivi vikamalira pa [[Amboyna massacre|kupharazgana na kukoma ŵa Amboyna]], apo Ŵaingelezi 10 ŵakakakika, ŵakayuzgika ndipo ŵakadumulika mitu chifukwa cha kuyuzgika kuti ŵakapangana kugalukira boma la Dutch.{{cite book |editor-last=Miller |editor-first=George |title=To The Spice Islands and Beyond: Travels in Eastern Indonesia |publisher=Oxford University Press |year=1996 |location=New York|pages=xvi |isbn=967-65-3099-9 |no-pp=true}} Nangauli ivi vikapangiska ukali ukuru mu Europe na suzgo la ubwezi pakati pa vyaru, Ŵaingelezi mwakufwasa ŵakafumapo mu vinandi mwa vyakuchita vyawo ku Indonesia, kweni ŵakalutilira kuguliska malonda ku Banten, ndipo ŵakaŵika mtima pa vyakukhumba vinyake ku Asia. ===Kukura=== [[File\:Melaka-St-Paul-Dutch-graves-2182.jpg|thumb|Manda gha ŵanthu ŵakuzirwa ŵa ku Dutch mu mabwinja gha [[St. Paul's Church, Malacca]], mu [[Dutch Malacca]] yakale]] [[File\:De handelsloge van de VOC in Hougly in Bengalen Rijksmuseum SK-A-4282.jpeg|thumb|260px|Fakitale ya Kampani ya Dutch East India ku [[Hugli-Chuchura]], [[Mughal Bengal]] — Hendrik van Schuylenburgh (1665)]] Mu 1619, [[Jan Pieterszoon Coen]] wakimikika kuŵa mulongozgi mukuru wa VOC. Wakamanya kuti VOC yingazgoka nkhongono ku Asia, pa nkhani za ndale kweniso chuma. Pa 30 Meyi 1619, Coen, wakovwirika na gulu la zombo 19, wakaluta ku Jayakarta mwankhondo, wakachimbizga ŵasilikari ŵa Banten; ndipo kufuma pa mabwinja gha msumba uwu wakakhazikiska [[Batavia, Dutch East Indies|Batavia]] kuŵa likuru la VOC. Mu vyaka vya m'ma 1620, pafupifupi ŵanthu wose ŵa ku [[Banda Islands]] ŵakachimbizgika, ŵakafa na njala, panji ŵakakomeka pakuyezga kuŵikapo minda ya ŵa Dutch.{{sfn|Ricklefs |1993 |page=30}} Minda iyi yikagwiliskirikanga ntchito pakulima [[nutmeg]] kuti yiguliskike ku vyaru vinyake. Coen wakakhumbanga kusamuska ŵanthu ŵanandi ŵa ku Dutch kuti ŵakakhale ku East Indies, kweni ndondomeko iyi yikafika yayi pa chilato chake, chomene chifukwa ŵa Dutch ŵachoko chomene ŵakaŵa ŵakunozgeka kusamukira ku Asia. ''The Dutch Seaborne Empire 1600–1800'', page 218 Chinthu chinyake icho Coen wakachita chikenda makora chomene. Suzgo likuru mu malonda gha ku Europe na Asia pa nyengo iyi likaŵa lakuti Ŵaevulopu ŵakaŵavya katundu munandi uyo ŵanthu ŵa ku Asia ŵakakhumbanga, kupatulapo siliva na golide. Ntheura ŵamalonda ŵa ku Europe ŵakeneranga kulipira vyakununkhira na visulo vyamtengo, ivyo vikaŵa vichoko ku Europe, kupatulapo ku Spain na [[Portugal]]. Ŵa Dutch na Ŵaingelezi ŵakeneranga kusanga visulo ivi mwa kupanga malonda ghakujumpha na vyaru vinyake vya ku Europe. Coen wakasanga nthowa yakupulikikwa ya kumazgira suzgo ili: kwambiska dongosolo la malonda pakati pa vyaru vya ku Asia, ilo phindu lake likatenge ligwiliskikenge ntchito kulipilira malonda gha vyakununkhira na Europe. Mu nyengo yitali, ivi vikamazga kufipa mtima na kufumiska visulo vyamtengo kufuma ku Europe, nangauli pakwamba vikakhumbanga kuti pakhale ndalama zinandi za malonda ku Indies. VOC yikawelerangaso kuŵika chigaŵa chikuru cha phindu lake mu chilato ichi mu nyengo yakufika ku 1630.{{sfn|De Vries|Van der Woude |1997 |page=386}} The VOC yikachitanga malonda mu Asia yose, ndipo yikasanga phindu likuru chomene ku [[Bengal]]. Zombo izo zikafumanga ku Netherlands kuya ku Batavia zikanyamuranga vinthu vyakukhumbikwa ku malo gha VOC mu Asia. Siliva na mkuwa kufuma ku Japan vikagwiliskirikanga ntchito kuchita malonda na maufumu ghakukhupuka chomene pa charu, [[India ya Mughal]] na [[China ya Qing]], kuti ŵasange silika, thonje, porcelain na vyakuvwara. Katundu uyu wakagulikanga mu Asia kuti ŵasange vyakununkhira ivyo ŵanthu ŵakakhumbanga chomene, panji wakanyamulika kuwelera ku Europe. VOC yikaŵaso yakuzirwa chomene pakwambiska maghanoghano gha ku Europe na tekinoloje ku Asia. Kampani iyi yikawovwiranga ŵamisiri ŵa Chikhristu ndipo yikachitanga malonda gha tekinoloje yiphya na China na Japan. Malo gha malonda gha VOC gha mtende ku [[Dejima]], [[chisumbu chakupangika na ŵanthu]] icho chili kufupi na [[Nagasaki, Nagasaki|Nagasaki]], ghakaŵa kwa vyaka vyakujumpha 200 malo ghakwamba pera agho Ŵaevulopu ŵakazomerezgekanga kuchitira malonda na [[Japan]].{{cite book|title=The Globe Encompassed: The Age of European Discovery, 1500–1700|url=https://archive.org/details/globeencompassed0000ames|author=Ames, Glenn J.|year=2008|page=[https://archive.org/details/globeencompassed0000ames/page/115 115]}} Apo VOC yikayezga kugwiliskira ntchito nkhongono za nkhondo kuti yikakamizge [[Ming dynasty|mafumu gha Ming]] kuzomerezga malonda na ŵa Dutch, Ŵachina ŵakathereska ŵa Dutch mu [[Sino–Dutch conflicts|nkhondo ya visiwa vya Penghu]] kufuma mu 1623 mpaka 1624, ndipo VOC yikachichizgika kuleka [[Penghu]] na kuluta ku [[Taiwan]]. Ŵachina ŵakathereskaso VOC pa [[Battle of Liaoluo Bay|Nkhondo ya ku Liaoluo Bay]] mu 1633. Ŵalongozgi ŵa Vietnam ŵa [[Nguyen lords|Nguyen]] ŵakathereska VOC mu [[Battle of the Gianh River (1643)|nkhondo ya 1643]] pa nyengo ya [[Trịnh–Nguyễn War|Nkhondo ya Trịnh–Nguyễn]], ndipo ŵakaphulika sitima ya Ŵa Dutch. Ŵa Cambodia ŵakathereska VOC mu [[Cambodian–Dutch War|Nkhondo ya Cambodia na Dutch]] kufuma mu 1643 mpaka 1644 pa Mlonga wa Mekong. [[File\:Dutch settlement at Chunchura on the Hugli river, West Benga Wellcome V0050427 (cropped).jpg|thumb|260px|Malo ghakukhala gha ŵa Dutch mu [[Suba ya Bengal]]]] Mu 1640, VOC yikasanga dowoko la [[Galle]], [[Ceylon ya Dutch|Ceylon]], kufuma kwa Ŵapwitikizi ndipo yikamazga ulamuliro wawo watekha pa malonda gha [[cinnamon|sinamoni]]. Mu 1658, [[Gerard Pietersz Hulft]] wakazingilizga [[Colombo]], ndipo msumba uwu ukapokeka na wovwiri wa Fumu [[Rajasinghe II]] ya [[Kandy]]. Mu 1659, Ŵapwitikizi ŵakaŵachimbizga mu vigaŵa vya mumphepete mwa nyanja, ivyo pamanyuma vikapokeka na VOC, ndipo ichi chikawovwira VOC kuŵa na ulamuliro wawo watekha pa malonda gha sinamoni. Kuti Ŵapwitikizi panji Ŵaingelezi ŵaleke kupokaso [[Sri Lanka]], VOC yikalutilira kupoka [[Dutch Malabar|Malo gha Malabar]] ghose kufuma ku Ŵapwitikizi, ndipo pafupifupi yikaŵachimbizga wose ku mphepete mwa nyanja ya kumanjiliro gha dazi kwa India. Mu 1652, [[Jan van Riebeeck]] wakakhazikiska malo ghakupumulirapo na kusazgirako vyakukhumbikwa pa [[Cape of Storms]] (kumwera chakumafumiro gha dazi kwa Africa, sono [[Cape Town]], South Africa) kuti ghawovwire zombo za kampani pa ulendo wawo kuya na kufuma ku East Asia. Pamanyuma, cape iyi yikachemekaso [[Cape of Good Hope]] chifukwa cha kuŵapo kwa malo agha. Nangauli zombo izo zikaŵavya ubwezi na kampani zikazomerezgekanga kugwiliskira ntchito malo agha, zikakhomeskekanga ndalama zinandi chomene. Pamanyuma malo agha ghakazgoka koloni lakukwana, [[Dutch Cape Colony|Cape Colony]], apo ŵa Dutch na ŵa ku Europe ŵanyake ŵakamba kukhala kwenekura. Mu vyaka vya m'ma 17, malo gha malonda gha VOC ghakakhazikiskikaso ku [[Persia]],{{Cite web |title=Dutch era |url=[https://www.nla.ae/en/our-history/historical-periods/dutch-era/](https://www.nla.ae/en/our-history/historical-periods/dutch-era/) |access-date=2026-04-08}} [[Dutch Bengal|Bengal]], [[Dutch Malacca|Malacca]], [[Thailand|Siam]], [[Dutch Formosa|Formosa]] (sono Taiwan), kweniso ku mphepete mwa nyanja ya [[Dutch Malabar|Malabar]] na [[Dutch Coromandel|Coromandel]] ku India. Kufika mwakudunjika ku China mainland kukiza mu 1729 apo [[Canton Factories|fakitale]] yikakhazikiskika ku [[Guangzhou|Canton]].{{cite journal |last1=Hertroijes |first1=Frasie |title=Meeting the Dutch: cooperation and conflict between Jesuits and Dutch merchants in Asia, 1680–1795 |journal=Paper Presented at the Conference of ENIUGH, London |year=2011 |page=10 |url=[http://research.uni-leipzig.de/eniugh/congress/fileadmin/eniugh2011/dokumente/Going\_Dutch\_Hertroijs\_2011\_4\_7.pdf](http://research.uni-leipzig.de/eniugh/congress/fileadmin/eniugh2011/dokumente/Going_Dutch_Hertroijs_2011_4_7.pdf) |access-date=28 July 2018 |archive-date=7 April 2022 |archive-url=[https://web.archive.org/web/20220407020410/http://research.uni-leipzig.de/eniugh/congress/fileadmin/eniugh2011/dokumente/Going_Dutch_Hertroijs_2011_4_7.pdf](https://web.archive.org/web/20220407020410/http://research.uni-leipzig.de/eniugh/congress/fileadmin/eniugh2011/dokumente/Going_Dutch_Hertroijs_2011_4_7.pdf) |url-status=dead }} Mu 1661, mulongozgi wa [[Ming dynasty|Ming]] Koxinga wakalongozga gulu la zombo kuti lithere ŵa Dutch. Ŵati ŵanthu ŵakugomezgeka ku Ming ŵathereska ŵasilikari ŵakuwovwira ŵa Dutch awo ŵakafuma ku Java mu 1662, Frederick Coyett, mulongozgi wa ŵa Dutch, wakapereka Taiwan.{{cite book|last=Andrade|author1-link=Tonio Andrade|first=Tonio|title=How Taiwan Became Chinese: Dutch, Spanish and Han Colonization in the Seventeenth Century|publisher=Columbia University Press|year=2005|url=[http://www.gutenberg-e.org/andrade/andrade11.html#s02/|access-date=16](http://www.gutenberg-e.org/andrade/andrade11.html#s02/|access-date=16) May 2012|archive-date=19 April 2021|archive-url=[https://web.archive.org/web/20210419085256/http://gutenberg-e.org/andrade/andrade11.html#s02/|url-status=live](https://web.archive.org/web/20210419085256/http://gutenberg-e.org/andrade/andrade11.html#s02/|url-status=live)}} (''wonani'' [[History of Taiwan]]). Mu 1663, VOC yikasayina "Pangano la Painan" na ŵalongozgi ŵa ku malo ŵanandi mu chigaŵa cha [[Painan]] awo ŵakagalukira [[Aceh Sultanate]]. Phangano ili likazomerezga VOC kuzenga malo gha malonda mu chigaŵa ichi ndipo pamanyuma kuŵa na ulamuliro wawo watekha pa malonda, chomene malonda gha golide.{{Cite web |date=31 July 1982 |title=170 tahun kepahlawanan minangkabau |url=[http://majalah.tempointeraktif.com/id/arsip/1982/07/31/BK/mbm.19820731.BK47129.id.html](http://majalah.tempointeraktif.com/id/arsip/1982/07/31/BK/mbm.19820731.BK47129.id.html) |url-status=dead |archive-url=[https://web.archive.org/web/20120314193208/http://majalah.tempointeraktif.com/id/arsip/1982/07/31/BK/mbm.19820731.BK47129.id.html](https://web.archive.org/web/20120314193208/http://majalah.tempointeraktif.com/id/arsip/1982/07/31/BK/mbm.19820731.BK47129.id.html) |archive-date=14 March 2012 |access-date=11 March 2012 |website=Majalah Tempo Online |language=indonesian}} Kufika mu 1669, VOC yikaŵa kampani yakukhupuka chomene ya ŵanthu ŵapadera iyo charu chikaŵa nacho kufika pa nyengo iyo, ndipo yikaŵa na zombo za malonda zakujumpha 150, zombo za nkhondo 40, ŵantchito 50,000, ŵasilikari ŵake 10,000, kweniso [[dividend|malipiro gha phindu]] gha 40% pa ndalama zakwamba izo zikaŵikika.{{efn|The share price had appreciated significantly, so in that respect the dividend was less impressive.}} Ŵantchito ŵanandi ŵa VOC ŵakasangananga na ŵanthu ŵa ku malo ndipo ŵakasazgiranga chiŵelengero cha ŵanthu ŵa [[Indos in pre-colonial history|Indo mu mbili ya nyengo ya ukoloni undandambe]].{{cite web |last=De Witt |first=D. |work=Children of the VOC at |title=The Easternization of the West: The Role of Melaka, the Malay-Indonesian archipelago and the Dutch (VOC). (International seminar by the Melaka State Government, the Malaysian Institute of Historical and Patriotism Studies (IKSEP), the Institute of Occidental Studies (IKON) at the National University of Malaysia (UKM) and the Netherlands Embassy in Malaysia. Malacca, Malaysia, 27 July 2006 |url=[http://www.dutchmalaysia.net/press/Easternization.html](http://www.dutchmalaysia.net/press/Easternization.html) |access-date=14 February 2010 |archive-url=[https://web.archive.org/web/20090814022910/http://www.dutchmalaysia.net/press/Easternization.html](https://web.archive.org/web/20090814022910/http://www.dutchmalaysia.net/press/Easternization.html) |archive-date=14 August 2009 |url-status=dead}}{{cite book |last=Blusse |first=Leonard |title=Strange Company: Chinese Settlers, Mestizo Women and the Dutch in VOC Batavia. (Dordrecht-Holland; Riverton, US, Foris Publications, 1986. xiii, 302p.) number: 959.82 B659}} ===Kusintha kwa nkhani=== Kuzingira mu 1670, vinthu viŵiri vikapangiska kuti malonda gha VOC ghaleke kukura. Chakwamba, malonda ghakupindulitsa chomene na Japan ghakamba kuchepa. Kutayika kwa malo gha VOC pa [[Formosa]] chifukwa cha [[Koxinga]] mu [[siege of Fort Zeelandia|kuzingilizga Fort Zeelandia]] mu 1662, pamoza na masuzgo gha mukati mwa [[China]] (apo [[Ming dynasty]] yikasinthikanga na [[Qing dynasty|ufumu wa Qing]] wa China), kukamazga malonda gha silika pamanyuma pa 1666. Nangauli VOC yikagwiliskira ntchito silika wa [[Mughal Bengal|Bengal ya Mughal]] m'malo mwa silika wa ku China, vinthu vinyake vikakhwaska umo siliva na golide wa ku Japan vikafikiranga ku malonda. [[Shogunate|Shogunate]] yikakhazikiska nthowa zinandi zakukanizgira kufumiskika kwa visulo ivi vyamtengo, ndipo pakuchita nthena yikakanizga mwaŵi wa VOC wa malonda na kusazgirapo kuŵinya kwa malonda. Ntheura, Japan yikaleka kuŵa chinthu chakuzirwa chomene mu malonda gha VOC pakati pa vyaru vya Asia kufika mu 1685.{{sfn|De Vries|Van der Woude |1997 |pages=434–435}} Chinthu chakuzirwa chomene ntchakuti, [[Third Anglo-Dutch War|Nkhondo yachitatu ya Anglo-Dutch]] yikakanizga kwa nyengo yichoko malonda gha VOC na Europe. Ivi vikapangiska kuti mtengo wa pepper ukwere chomene, ndipo vikakopa [[English East India Company|Kampani ya East India ya Ŵaingelezi]] (EIC) kuti yinjire mwankhongono mu msika uwu mu vyaka vyakafuma pamanyuma pa 1672. Pambere apa, chimoza mwa malango gha VOC pa kuŵika mitengo chikaŵa chakuti ŵaŵikenge pepper yinandi pachoko mu msika kuti ŵachitiske mitengo kukhira pasi pa mlingo uwo ŵamalonda ŵanyake ŵangakhumbiranga kunjira mu msika (m'malo mwa kupenja [[Profit maximization|phindu likuru chomene]] mu nyengo yichoko). Vinjeru vya ndondomeko iyi vikawoneka apo pakawuka nkhondo yikuru ya mitengo na EIC, apo kampani iyi yikazuzga msika na katundu wuphya kufuma ku India. Mu chipikano ichi cha kutora chigaŵa chikuru cha msika, VOC (iyo yikaŵa na ndalama zinandi chomene) yikakwaniska kulindilira mpaka EIC yileke nkhongono. Nadi, kufika mu 1683, EIC yikaŵa pafupi kusoŵa ndalama; mtengo wa magawo ghake ukakhira kufuma pa 600 kuya pa 250; ndipo purezidenti wake [[Josiah Child]] wakachichizgika kwa kanyengo kufumapo pa udindo.{{sfn|De Vries|Van der Woude |1997 |pages=430–433}} Kweni vimanyikwilo vya suzgo vikamba kuwoneka. Makampani ghanyake, nga ni [[Louis XIV's East India Company|Kampani ya East India ya Ŵafaransa]] na [[Danish East India Company|Kampani ya East India ya ŵa Denmark]], nagho ghakamba kunjira mu dongosolo la ŵa Dutch. Ntheura VOC yikajara malo ghakuzura malonda gha pepper agho ghakaŵa ghakuchita makora ku [[Bantam (city)|Bantam]] kwizira mu phangano ilo likachitika na Sultan mu 1684. Kweniso, pa [[Dutch Coromandel|mphepete mwa nyanja ya Coromandel]], yikasamuska malo ghake ghakuru ghakukhora kufuma ku [[Pulicat]] kuya ku [[Nagapattinam]], kuti yisungilire ulamuliro wawo watekha pa malonda gha pepper mwakukwenyerezga Ŵafaransa na ŵa Denmark.{{efn|During the [[War of the Grand Alliance|Nine Years' War]], the French and Dutch companies came to blows on the Indian Subcontinent. The French sent naval expeditions from metropolitan France, which the VOC easily countered. On the other hand, the VOC conquered the important fortress of [[Puducherry (city)|Pondicherry]] after a siege of only 16 days by an expedition of 3,000 men and 19 ships under Laurens Pit from [[Nagapattinam]] in September 1693. The Dutch then made the defenses of the fortress impregnable, which they came to regret when the Dutch government returned it to the French by the [[Peace of Ryswick]] in exchange for tariff concessions in Europe by the French.{{sfn|Chaudhuri|Israel|1991|page=424}}}} Kweni, pa nyengo iyi kuzirwa kwa katundu wa mtundu uwu mu malonda gha pakati pa Asia na Europe kukamba kuchepa mwaluŵiro. Ndalama izo VOC yikeneranga kugwiliskira ntchito pa nkhondo kuti yisungilire ulamuliro wawo watekha zikaŵa zambura kwenelera kuyana na phindu ilo likafumanga mu malonda agha agho ghakamba kuchepa.{{sfn|De Vries|Van der Woude |1997 |pages=433–434}} Nangauli vikaŵa nthena, kusambira kwa VOC pa nkhani iyi kukachedwa, ndipo pakwamba VOC yikapanga chakusankha cha ndondomeko chakuti yinozge malo ghake gha nkhondo pa [[Dutch Malabar|mphepete mwa nyanja ya Malabar]] (na chilindizga chakuti yichepeskenge nkhongono za Ŵaingelezi mu chigaŵa ichi na kumazga kutayika kwa ndalama zake chifukwa cha kugwiliskira ntchito magulu gha ŵasilikari gha ku Malabar) mwa kugwiliskira ntchito nkhongono kukakamizga [[Saamoothiri|Zamorin]] wa [[Kozhikode|Calicut]] kuti wajilambike ku ulamuliro wa ŵa Dutch. Mu 1710, Zamorin wakachichizgika kusayina phangano na VOC ilo likamuphaliranga kuti wachitire malonda mwapadera na VOC pera na kuchimbizga ŵamalonda ŵanyake wose ŵa ku Europe. Kwa kanyengo kachoko, ichi chikawoneka kuti chikusazgiranga mwaŵi wa kampani. Kweni mu 1715, na chikhukhumaliro cha EIC, Zamorin wakakana phangano ili. Nangauli ŵasilikari ŵa Dutch ŵakakwaniska kuzimazga kugaluka uku kwa kanyengo, Zamorin wakalutilira kuchita malonda na Ŵaingelezi na Ŵafaransa, ndipo ichi chikapangiska kuti malonda gha Ŵaingelezi na Ŵafaransa ghakwere chomene. VOC yikaghanaghana mu 1721 kuti chikaŵaso chakwenelera yayi kusuzgika kuyezga kulamulira malonda gha [[Malabar pepper|pepper na vyakununkhira vya Malabar]]. Chisankho cha ndondomeko chikapangika chakuti ŵachepeske ŵasilikari ŵa Dutch na kusiya chigaŵa ichi pasi pa chikoka cha EIC.{{sfn|Chaudhuri|Israel|1991|pages=428–429}} [[File:De Lannoy Surrender.JPG|250px|thumb|[[Eustachius De Lannoy]] wa Kampani ya Dutch East India wakujipereka kwa Maharaja [[Marthanda Varma]] wa [[Kingdom of Travancore|Ufumu wa Travancore]] wa ku India pamanyuma pa [[Battle of Colachel|Nkhondo ya Colachel]] (chithuzithuzi ku [[Padmanabhapuram Palace]]).]] Mu [[Battle of Colachel|Nkhondo ya Colachel]] ya 1741, ŵankhondo ŵa [[Travancore]] pasi pa Fumu [[Marthanda Varma]] ŵakathereska ŵa Dutch. Mulongozgi wa ŵa Dutch, Kaputeni [[Eustachius De Lannoy]], wakakakika. Marthanda Varma wakazomera kuleka umoyo wa kaputeni wa Dutch pa sharti lakuti wanjire mu gulu lake la ŵasilikari na kusambizga ŵasilikari ŵake maluso gha nkhondo gha mazuŵa ghano. Kuthereska uku mu [[Travancore–Dutch War|Nkhondo ya Travancore–Dutch]] kukuwoneka kuti ntchakuwonerapo chakwamba cha nkhongono ya ku Asia yakukhazikika kuthera tekinoloje na nthowa za nkhondo za ku Europe; ndipo kukalongora kwamba kwa kuchepa kwa nkhongono za ŵa Dutch ku India.{{efn|However, the VOC had been defeated many times before. On the Indian subcontinent, the EIC had suffered a resounding defeat in its [[Anglo-Mughal War (1686–1690)|war]] against the Mughals.{{sfn|Chaudhuri|Israel|1991|pages=435–436}}}} Ntheura, kuyezga kulutilira kuchita vinthu nga kale nga kampani ya malonda ya katundu wuchoko kweni phindu likuru, iyo yikakhazikika pa malonda gha vyakununkhira, kukatondeka. Kweni kampani iyi yikaŵa kuti yamba kale (nangauli yikakhumbanga yayi) kulondezga chakuwonerapo cha ŵapikisanawo ŵa ku Europe mwa kusazgirako katundu munyake wa ku Asia, nga ni tiyi, khofi, thonje, vyakuvwara na shuga. Katundu uyu wakaperekanga phindu lichoko, ntheura wakakhumbanga kuti ŵaguliske vinandi kuti ŵasange ndalama zakuyana. Kusintha uku kwa mtundu wa katundu mu malonda gha VOC kukamba mu vyaka vya m'ma 1680, pamanyuma pakuti EIC yikagwa kanyengo mu 1683, ndipo ichi chikapeleka mwaŵi uwemi chomene wa kunjira mu misika iyi. Chifukwa cheneko cha kusintha uku, kweni, chikaŵa mu vinthu viŵiri vyakukhwaskana na kapangidwe ka nyengo yiphya. Chakwamba, kukachitika kusintha kukuru chomene mu vinthu ivyo ŵanthu ŵa ku Europe ŵakakhumbanga, chomene pa vyakuvwara vya ku Asia, khofi na tiyi, kuzungulira kwamba kwa vyaka vya m'ma 18. Chachiŵiri, nyengo yiphya ya ndalama zinandi chomene zakukhazikika pa chiwongolero chichoko yikamba mwamabuchi pa nyengo iyi. Chinthu chachiŵiri ichi chikawovwira kampani kuti yipeze ndalama mwambura kusuzga kuti yikuzge malonda ghake mu vigaŵa viphya.{{efn|It was also helpful that the price war with the EIC in the early decade had caused the accumulation of enormous inventories of pepper and spices, which enabled the VOC to cut down on shipments later on, thereby freeing up capital to increase shipments of other goods.{{sfn|De Vries|Van der Woude |1997 |page=436}}}} Pakati pa vyaka vya m'ma 1680 na 1720, VOC yikakwaniska kunozga na kuŵika ŵanthu ŵakukwana mu zombo zake zinandi, kweniso kugura visulo vinandi vyamtengo kuti yilipire kugula katundu munandi wa ku Asia kuti wanyamulike kuya ku Europe. Ivi vikapangiska kuti kukula kwa kampani kukwere pafupifupi kaŵiri.{{sfn|De Vries|Van der Woude |1997 |pages=436–437}} Kulemera kwa zombo izo zikaŵeranga kuwelera kunyumba kukakwera na 125% mu nyengo iyi. Kweni ndalama izo kampani yikasanganga chifukwa cha kuguliska katundu uyo wakafikanga ku Europe zikakwera na 78% pera. Ivi vikulongora kusintha kukuru mu umo VOC yikaŵira: sono yikachitanga ntchito mu misika yiphya ya katundu uyo ŵanthu ŵakakhumbanga chomene para mtengo ukusintha, ndipo yikeneranga kuphalizgana mwakuyana na ŵalonda ŵanyake. Ivi vikapangiska kuti phindu liŵe lichoko.{{sfn|De Vries|Van der Woude |1997 |pages=437–440}} Ndondomeko za malonda za nyengo iyo zikapangiskanga kuti chiŵe chakusuzga kwa ŵalongozgi ŵa kampani kumanya vinthu ivi, ndipo ichi chingalongosora mwakudunjika vifukwa vya vinthu vinyake ivyo ŵakabudiska pakuwona ivyo vikachitika pamanyuma. Kusoŵa kwa chidziŵitso uku katenge kungamazgika (nga umo vikaŵira mu nyengo zakwamba za mbili ya VOC) na luso lwa ŵalongozgi pa malonda. Kweni pa nyengo iyi, ŵalongozgi aŵa pafupifupi wose ŵakasankhikanga kufuma mu gulu la ndale la ''[[Regenten|ŵalongozgi ŵa regent]]'', ilo likaŵa kuti lataya kale ubwezi wake wapafupi na magulu gha ŵamalonda.{{sfn|De Vries|Van der Woude |1997 |pages=441–442}} Maupangiro ghachoko gha phindu pera ghakulongosora yayi kuchepa kwa ndalama izo kampani yikasanganga. Pa mulingo ukuru, ndalama za ntchito za VOC zikaŵa na kawonekero ka "fixed" (malo gha nkhondo; kusungilira zombo na vinyake). Ntheura, viŵelengero vya phindu mphanyi vikulutilira kuŵa vyakukhora usange kukura kwa malonda agho ghakachitikanga mphanyi kwapangiska [[Economies of scale|kusunga ndalama chifukwa cha kukura kwa ntchito]]. Kweni, nangauli zombo zikuru zikanyamura vinthu vinandi ivyo vikakuranga, ntchito ya ŵantchito yikakura yayi mwakukwana kuti yipange phindu ili. Mwakawiro, ndalama zose za kampani zikakuranga pamoza na kukura kwa malonda; kuchepa kwa phindu lakupambura ndalama kukapangiska mwakudunjika kuchepa kwa phindu la ndalama izo zikaŵikikamo. Nyengo ya kukura yikaŵa ya "kukura kwambura phindu".{{sfn|De Vries|Van der Woude |1997 |page=447}} Mwakudunjika: "[t]he long-term average annual profit in the VOC's 1630–70 'Golden Age' was [[guilder|ƒ]]2.1 M (±{{Euro|{{Inflation|NL|{{#expr:2100000/10^6}}|1650|r=0}}{{nbsp}}M}} in {{Inflation/year|NL}}), of which just under half was distributed as dividends and the remainder reinvested. The long-term average annual profit in the 'Expansion Age' (1680–1730) was ƒ2.0 M (±{{Euro|{{Inflation|NL|{{#expr:2000000/10^6}}|1700|r=0}}{{nbsp}}M}} in {{Inflation/year|NL}}), of which three-quarters was distributed as dividend and one-quarter reinvested. In the earlier period, profits averaged 18% of total revenues; in the latter period, 10%. The annual return of invested capital in the earlier period stood at approximately 6%; in the latter period, 3.4%."{{sfn|De Vries|Van der Woude |1997 |page=447}} Ndipouli, pamaso pa ŵakuŵikamo ndalama, VOC yikachita viheni chomene yayi. Mtengo wa magawo ghake ukalutilira kuŵa pafupi na 400 kufuma pakati pa ma 1680 (kupatula kusintha pachoko pa [[Glorious Revolution|Kusintha kwa Ulemerero]] mu 1688), ndipo ukafika pachanya chomene pa 642 mu ma 1720. Magawo gha VOC pa nyengo iyi ghakaperekanga phindu la 3.5%, ilo likaŵa pachoko waka kuluska phindu la ma bond gha boma la Netherlands.{{sfn|De Vries|Van der Woude |1997 |page=448}} \===Kuchepa na kumara=== [[File\:Chinezenmoord Van Stolk.jpg|thumb|A print of the [[1740 Batavia massacre]]]] [[File\:The East Indiaman General Goddard capturing Dutch East Indiamen, June 1795, by Thomas Luny.jpg|thumb|The British East Indiaman ''[[General Goddard (ship)|General Goddard]]'' attacking seven VOC East Indiamen on 14 June 1795]] Pamanyuma pa 1730, vinthu vya VOC vikamba kuchepa. Pali vinthu vinkhondi vikuru ivyo vikapangiska kuti kampani iyi yimare nkhongono mu vyaka 50 pakati pa 1730 na 1780:{{sfn|De Vries|Van der Woude |1997 |pages=449–455}} - Pakaŵa kuchepa kwambura kuleka kwa malonda gha pakati pa vyaru vya ku Asia chifukwa cha kusintha kwa ndale na chuma mu Asia, uko VOC yikaŵa na nkhongono yichoko waka yakuchitapo kanthu. Vinthu ivi pachokopachoko vikachichizga kampani kufuma ku Persia, [[Dutch Suratte|Suratte]], ku Malabar Coast, na Bengal. Kampani yikeneranga kuchepeska ntchito zake ku chigaŵa icho yikaŵa nacho mwakuthupi, kufuma ku Ceylon kwizira mu visumbu vya Indonesia. Ntheura, unandi wa malonda agha gha pakati pa vyaru vya ku Asia na phindu lake vikeneranga kuchepa. - Umo kampani yikaŵikikira mu Asia (pakati pa malo ghake ghakuru ku Batavia), uko pakwamba kukaŵa kwakovwira pakusanga nkhani za misika, kukamba kuŵa suzgo mu vyaka vya m'ma 18 chifukwa cha kulephera kwa kutumiza vinthu vyose dankha ku malo agha ghakuru. Suzgo ili likawoneka chomene mu malonda gha tiyi, apo ŵapikisano nga ni EIC na [[Ostend Company|Kampani ya Ostend]] ŵakatumizanga vinthu mwakudunjika kufuma ku China kuya ku Europe. - "Venality" ya ŵantchito ŵa VOC (mu ng'anamuro la uryarya na kuleka kuchita ntchito), nangauli yikaŵa suzgo ku makampani ghose gha East India pa nyengo iyo, yikuwoneka kuti yikasuzga VOC pa mulingo ukuru kuluska ŵapikisano ŵake. Kuyowoya unenesko, kampani yikaŵa "mwenezi muwemi" yayi. Malipiro ghakaŵa ghachoko, ndipo "malonda pa nkhani ya munthu" ghakaŵa ghakuzomerezgeka yayi mwalamulo. Ghakamba kusazgikira mu vyaka vya m'ma 18, ndipo ivi vikapangiska kuti ntchito ya kampani yichepe.{{efn|Chakuluska chomene chikaŵa cha "[[Amfioen Society]]". Iyi yikaŵa bizinesi ya ŵantchito ŵapachanya ŵa VOC iyo yikapika ulamuliro wakwendeska malonda gha opium pa Java, pa nyengo iyo VOC yikeneranga kulipira mitengo yapachanya ku EIC kuti yigule opium ku Bengal.}} Kwambira pafupifupi mu ma 1790, mazgu ghakuti ''perished under corruption'' (''vergaan onder corruptie'', agho ghakafupikiskikanga kuŵa VOC mu Chidachi) ghakamba kugwiriskirika ntchito kulongosora ivyo vikachitikira kampani iyi. - Suzgo yinyake iyo VOC yikasangananga nayo pamoza na makampani ghanyake yikaŵa viŵelengero vyapachanya vya ŵantchito kufwa na kulwara. Ivi vikamalanga ŵantchito ŵa kampani na kuchepeska nkhongono za ŵanthu ŵanandi awo ŵakapona. - Suzgo yinyake yikachitika chifukwa cha [[dividend policy|ndondomeko ya kampani yakugaŵira phindu]]. Ma dividend agho kampani yikagaŵanga ghakajumphanga ndalama zakusazgikira izo yikasanganga ku Europe mu vyaka vyose kufuma mu 1690 mpaka 1760 kupatula 1710–1720. Kweni, mu nyengo yakufika mu 1730, ŵalongozgi ŵakatumizga vinthu ku Asia kuti ŵakwezge ndalama za malonda kwenekuko. Ntheura, ma buku gha ndalama ghakuphatikizika mphanyi ghakalongora kuti phindu lose likajumphanga ma dividend. Kweniso, pakati pa 1700 na 1740 kampani yikafumiskamo ƒ5.4 M (±{{Euro|{{Inflation|NL|{{#expr:5400000/10^6}}|1720|r=0}}{{nbsp}}M}} mu {{Inflation/year|NL}}) ya ngongoli ya nyengo yitali. Ntheura, kampani yikaŵa pa malo ghakukhora gha ndalama mu vyaka ivi. Ivi vikasintha pamanyuma pa 1730. Apo phindu likagwa chomene, ''bewindhebbers'' ŵakachepeska waka pachoko ma dividend kufuma pa mulingo wa kale. Ntheura, ma dividend agho ghakagaŵikanga ghakajumphanga ndalama izo zikasangikanga mu vyaka vyose kupatula chimoza (1760–1770). Kuti ŵafiske kuchita ivi, ndalama za kampani izo zikaŵikika ku Asia zikeneranga kuchepetskeka na ƒ4 M pakati pa 1730 na 1780, ndipo ndalama zakusungika izo zikaŵapo ku Europe zikachepa na ƒ20 M mu nyengo yeneyiyo. Ntheura, ŵalongozgi ŵakachichizgika kusazgirapo ndalama zakugwiliskirika ntchito za kampani mwa kukopa ndalama za nyengo yifupi kufuma ku ngongoli zakudikirira, izo zikakhazikiskikanga pa ndalama izo zikayembekezekanga kufuma ku zombo izo zikaŵeranga ku nyumba.Gaastra, Femme (2003), ''The Dutch East India Company: Expansion and Decline'' (Zutphen: Walberg Pers). Nangauli pakaŵa masuzgo agha, mu 1780 VOC yikaŵa nipera kampani yikuru chomene. Chuma chake mu Republic, icho chikaŵa na sitima na katundu wakusungika, chikaŵa ƒ28 M (±{{Euro|{{Inflation|NL|{{#expr:28000000/10^6}}|1780|r=0}}{{nbsp}}M}} mu {{Inflation/year|NL}}); chuma chake mu Asia, icho chikaŵa na ndalama zakugwiliskira ntchito pa malonda kweniso katundu uyo wakaŵa paulendo kuluta ku Europe, chikaŵa ƒ46 M (±{{Euro|{{Inflation|NL|{{#expr:46000000/10^6}}|1780|r=0}}{{nbsp}}M}} mu {{Inflation/year|NL}}). Chuma chose, para wangabwisikapo ngongole zose izo zikaŵa zindabwezgeke, chikaŵa ƒ62 M (±{{Euro|{{Inflation|NL|{{#expr:62000000/10^6}}|1780|r=0}}{{nbsp}}M}} mu {{Inflation/year|NL}}). Ntheura, nyengo iyi kampani yikaŵa yikuru chomene ndipo vinthu vyake vikaŵa vyakuti vingalutilira, usange nthowa yimoza ya kunozga kampani yikatekeleka makora. Mu 1780, [[Nkhondo ya Nayi ya Anglo-Dutch]] yikamba, ndipo pa nyengo ya nkhondo ŴaBritain ŵakawukira kampani ya Dutch East India, ŵakachepeska sitima za VOC na hafu ndipo ŵakalopweska chomene nkhongono zake mu Asia. Chifukwa cha nkhondo iyi, VOC yikaluza ndalama zakukwana ƒ43 M (±{{Euro|{{Inflation|NL|{{#expr:43000000/10^6}}|1780|r=0}}{{nbsp}}M}} mu {{Inflation/year|NL}}). Ngongole izo zikaperekeka kuti kampani yilutilire kugwira ntchito zikapangiska kuti chuma chake chose chambura ngongole chifike pa ziro.{{sfn|De Vries|Van der Woude |1997 |pages=454–455}} Kwambira mu 1720, msika wa shuga wakufuma ku Indonesia ukamba kuchepa chifukwa mpikisano wa shuga wa mtengo waku [[Brazil]] ukakura. Misika ya ku Europe yikazura na shuga. Ŵamalonda ŵa shuga ŵa ku China ŵakukwana makumi ghanandi ŵakafika pa ubankirapuse, ndipo ichi chikapangiska kuti ŵanthu ŵanandi ŵaleke ntchito. Pamanyuma pake, magulu gha ŵantchito ŵa ku Asia awo ŵakaŵavya ntchito ghakamba kupanga. Boma la Netherlands ku Batavia likatondeka kuchitapo kanthu mwakukwana pa masuzgo agha. Mu 1740, mphekesera zakuti magulu gha ŵanthu agha ghachimbizgikenge mu chigaŵa cha Batavia zikapangiska chipolowe chikuru. Ŵasilikari ŵa Netherlands ŵakasanda nyumba za Ŵachina ku Batavia kuti ŵapenje vilwero. Nyumba yinyake yati yaphya mwangozi, ŵasilikari na ŵanthu ŵakavu ŵakamba kukoma na kupoka katundu wa Ŵachina.{{cite book|author=Kumar, Ann|title=Java and Modern Europe: Ambiguous Encounters|year=1997|page=32}} [[Kukoma Ŵachina ku Batavia mu 1740|Kukoma Ŵachina]] uku kukawoneka kuti kukaŵa kwakofya chomene mwakuti bungwe la ŵalongozgi ŵa VOC likamba kufufuza mwalamulo Boma la Dutch East Indies kwa ulendo wakwamba mu mdauko wake. Nkhondo ya Nayi ya Anglo-Dutch yati yamara mu 1783, masuzgo gha ndalama gha VOC ghakakura chomene. Pamanyuma pa kuyezga kwambura phindu kunozga kampani kwizira mu maboma gha zigawo za [[Holland]] na [[Zeeland]], bungwe la ŵalongozgi ŵa VOC likachimbizgika mu 1796 ndipo kayendetsedwe ka kampani kakaperekeka ku ''Komiti ya Vinthu vya Malonda gha ku East Indies na Vinthu Vyake'' ({{langx|nl|Komiti ya vinthu vya malonda gha ku East Indies na vinthu vyake}}).{{Citation |last=Koenders |first=Pieter |chapter=TANAP And The Co-Operation Between ANRI And Nationaal Archief |date=2007-01-01 |title=The Archives of the Dutch East India Company (VOC) and the Local Institutions in Batavia (Jakarta) |pages=169–180 |chapter-url=[http://dx.doi.org/10.1163/ej.9789004163652.1-556.9](http://dx.doi.org/10.1163/ej.9789004163652.1-556.9) |access-date=2024-01-27 |publisher=BRILL |doi=10.1163/ej.9789004163652.1-556.9 |isbn=978-90-474-2179-5|chapter-url-access=subscription }}{{Cite web |title=VOC – Kampani Yakukolerana ya Dutch East India {{!}} Nyumba ya Vyakale ya Western Australia |url=[http://museum.wa.gov.au/explore/dirk-hartog/voc-united-dutch-east-india-company](http://museum.wa.gov.au/explore/dirk-hartog/voc-united-dutch-east-india-company) |access-date=2024-01-27 |website=Nyumba ya Vyakale ya Western Australia |language=Tum}} Kuyamba kwa [[Nkhondo za French Revolutionary|Nkhondo za ku France za Kusintha Boma]] kukamazga umaliro wa VOC, chifukwa kugwa kwa [[Republic ya Netherlands]] na kusinthika kwake kuŵa [[Republic ya Batavia]] mu 1795 kukapangiska kuti ŴachiDutch na ŴaBritain ŵambe nkhondo. Kuwukira kwa ŴaBritain pa sitima na makoloni gha VOC kukapangiska kuti kampani iyi yitaye vinthu vinandi, ndipo nangauli chikalata cha VOC chikawonjezgeka kanandi, chikazomerezgeka kumara pa 31 Disembala 1799, ndipo kampani yikazgoka ya boma. TANAP, Umaliro wa VOC ==Kapangidwe ka kampani== [[File\:Simon\_Fokke,\_Afb\_010097014121.jpg|thumb|Ŵalongozgi Makumi Ghanomwe, mu chipinda cha ŵalongozgi pa [[East India House (Amsterdam)|Nyumba ya East India]] ku Amsterdam.]] Nangauli VOC yikagwiranga ntchito chomene mu chigaŵa icho pamanyuma chikazgoka [[Dutch East Indies|Dutch East Indies]] (lero ni [[Indonesia]]), kampani iyi yikaŵaso na ntchito zakuzirwa mu vigaŵa vinyake. Yikagwiranga ntchito ŵanthu ŵakufuma ku makontinenti na mitundu yakupambanapambana pa ntchito na malo ghakugwilira ntchito ghakuyana. Nangauli yikaŵa kampani ya ŴachiDutch, ŵantchito ŵake ŵakaŵa ŵakufuma ku Netherlands pera yayi, kweni ŵanandi ŵakafumanga ku Germany na vyaru vinyake. Padera pa ŵantchito ŵakupambanapambana ŵakufuma ku kumpoto na kuzambwe kwa Europe awo VOC yikawalembanga ntchito mu [[Dutch Republic|Republic ya Netherlands]], VOC yikagwiliskiranga ntchito chomene misika ya ŵantchito ŵa ku Asia. Ntheura, ŵantchito ŵa maofesi ghakupambanapambana gha VOC mu Asia ŵakaŵa ŴaEurope na ŴaAsia. Ŵantchito ŵa ku Asia panji [[Eurasian|Ŵa ku Europe na Asia]] ŵakagwiranga ntchito nga mbasekera sitima, ŵasilikari, ŵalembi, ŵakuduka mathabwa, ŵakupanga vinthu vya chisulo, panji ŵantchito ŵambura luso.{{sfn|De Vries|Van der Woude |1997 |page=462}} Pa nyengo iyo VOC yikaŵa pa nkhongono zake zikuru, yikaŵa na ŵantchito 25,000 awo ŵakagwiranga ntchito mu Asia na ŵanyake 11,000 awo ŵakaŵa paulendo.{{sfn|De Vries|Van der Woude |1997 |page=462}} Kweniso, nangauli ŵanandi mwa [[shareholder|ŵeneŵa ŵa magawo gha kampani]] ŵakaŵa ŴachiDutch, pafupifupi chigaŵa chimoza pa vigaŵa vinayi vya ŵeneŵa ŵakwamba ŵa magawo gha kampani ŵakaŵa ŵa ku Southern Netherlands (ŵanthu ŵakufuma ku chigaŵa icho sono chikusazgapo Belgium na [[Luxembourg]]), ndipo pakaŵaso Ŵachijeremani ŵakukwana makumi ghanandi. VOC yikaŵa na mitundu yiŵiri ya ŵeneŵa ŵa magawo gha kampani: ''participanten'', awo ŵangawoneka nga mbamembala awo ŵakalongozganga kampani yayi, na ''bewindhebbers'' 76 (pamanyuma ŵakachepeskeka kufika pa 60), awo ŵakagwiranga ntchito nga mbalongozgi ŵa kampani. Uwu ukaŵa umo kampani za ku Netherlands zakuguliska magawo gha kampani zikapangikanga pa nyengo iyo. Chinthu chiphya pa VOC chikaŵa chakuti udindo wa kulipira ngongole wa ''participanten'' pera yayi, kweniso wa ''bewindhebbers'', ukaŵa wakukolerana na ndalama izo ŵakaŵikamo (kanandi, ''bewindhebbers'' ŵakaŵa na udindo wambura mphaka). Ntheura VOC yikaŵa [[limited company|kampani iyo udindo wa ŵeneŵo pa ngongole ukaŵa wakupimika]]. Kweniso, ndalama zikeneranga kukhala ''zakukhazikika'' mu nyengo yose ya umoyo wa kampani. Chifukwa cha ichi, ŵakuŵika ndalama awo ŵakakhumbanga kufumiska ndalama zawo pakati pa nyengo ya kampani ŵakeneranga kuguliska gawo lawo ku ŵanyake pa [[Euronext Amsterdam|Msika wa Magawo gha Amsterdam]].{{sfn|De Vries|Van der Woude |1997 |page=385}} ''Confusion of Confusions'', buku la 1688 la mazungumizgo ilo likalembeka na Muyuda wa Sephardi [[Joseph de la Vega|Joseph de la Vega]], likalongosora umo msika uwu wa magawo ghamoza ukagwiriranga ntchito. VOC yikaŵa na Maofesi 6 (''Kamers'') mu misumba ya madoko: [[Amsterdam]], [[Delft]], [[Rotterdam]], [[Enkhuizen]], [[Middelburg, Zeeland|Middelburg]], na [[Hoorn]]. Ŵimiliri ŵa maofesi agha ŵakakumananga nga ni ''Heeren XVII'' (Ŵalongozgi panji Ŵanthu 17). Ŵakasankhikanga kufuma mu gulu la ŵeneŵa ŵa magawo gha kampani la ''bewindhebbers''.{{sfn|De Vries|Van der Woude |1997 |pages=384–385}} Pa ''Heeren XVII'', ŵimiliri 8 ŵakafumanga ku Ofesi ya Amsterdam (mumoza waka wakuchepa kuti ŵaŵe ŵanandi paŵekha), ŵanayi ŵakafumanga ku Ofesi ya Zeeland, ndipo yumoza wakafumanga ku ofesi yiliyose mwa maofesi ghachoko, apo mpando wa 17 ŵakuperekanga mwakupambanapambana ku Ofesi ya Middelburg-Zeeland panji ŵakasinthananga pakati pa maofesi ghachoko ghankhondi. Ntheura Amsterdam ndiyo yikaŵa na mazgu ghakuzirwa chomene. Ŵanthu ŵa ku Zeeland chomene ŵakaŵa na vyenjezgo pa ndondomeko iyi pakwamba. Wofi uwu ukaŵa wambura chifukwa yayi, chifukwa mu ntchito zikang'anamuranga kuti Amsterdam ndiyo yikakhazikiskanga ivyo vikeneranga kuchitika. Maofesi ghankhondi na limoza ghakawuska ndalama zakwambira za Dutch East India Company: {| class="wikitable" ! rowspan="2" |Ofesi!! colspan="2" |Ndalama |- ! align="center" |[[Dutch guilder|Ma-guilder]] (ƒ) ! align="center" |± [[Euro|Yuro]] (€)<br>yakuyana mu {{Inflation/year|NL}} |- |Amsterdam || align="center" |3,679,915 | align="center" |{{Inflation|NL|{{#expr:3679915/10^6}}|1600|r=0}}{{nbsp}}M |- |Middelburg || align="center" |1,300,405 | align="center" |{{Inflation|NL|{{#expr:1300405/10^6}}|1600|r=0}}{{nbsp}}M |- |Enkhuizen || align="center" |540,000 | align="center" |{{Inflation|NL|{{#expr:540000/10^6}}|1600|r=0}}{{nbsp}}M |- |Delft || align="center" |469,400 | align="center" |{{Inflation|NL|{{#expr:469400/10^6}}|1600|r=0}}{{nbsp}}M |- |Hoorn || align="center" |266,868 | align="center" |{{Inflation|NL|{{#expr:266868/10^6}}|1600|r=0}}{{nbsp}}M |- |Rotterdam || align="center" |173,000 | align="center" |{{Inflation|NL|{{#expr:173000/10^6}}|1600|r=0}}{{nbsp}}M |- !Jumla:!!6,424,588 ! align="center" |{{Inflation|NL|{{#expr:6424588/10^6}}|1600|r=0}}{{nbsp}}M |} Kuwuska ndalama ku Rotterdam kukenda makora yayi. Chigaŵa chikuru cha ndalama izo chikafuma kwa ŵanthu ŵa ku [[Dordrecht]]. Nangauli Enkhuizen yikawuska ndalama zichoko kuluska Amsterdam panji Middelburg-Zeeland, ndiyo yikaŵa na chigaŵa chikuru chomene cha ndalama za [[Share (finance)|magawo]] gha VOC. Pa ŵanthu 358 ŵakwamba awo ŵakagura magawo, pakaŵa ŵamalonda ŵachoko ŵanandi awo ŵakajipeleka kuyezga [[risk|chiwawa cha kutaya ndalama]]. Ndalama zakuchepera izo munthu wakeneranga kuŵikamo mu VOC zikaŵa ƒ3,000, ndipo ichi chikapangiska kuti magawo gha kampani ghaŵe ghakugulika na ŵamalonda ŵanandi.{{cite book|title=The Globe Encompassed: The Age of European Discovery, 1500–1700|url=https://archive.org/details/globeencompassed0000ames|author=Ames, Glenn J.|year=2008|page=[https://archive.org/details/globeencompassed0000ames/page/103 103]}} [[File:AMH-5460-NA Uniform for VOC soldiers (cropped).jpg|thumb|{{circa|1783}} Chithuzithuzi cha ŵasilikari ŵatatu ŵa VOC mu Dutch East Indies]] Pakati pa ŵeneŵa ŵa magawo gha VOC ŵakwambilira, ŵalendo ŵakaŵa na ntchito yikuru. Pa ŵanthu 1,143 awo ŵakapereka ndalama, pakaŵa [[German people|Ŵachijeremani]] 39 na ŵanthu 301 ŵakufuma ku [[Southern Netherlands|Southern Netherlands]] (pafupifupi Belgium na Luxembourg mazuŵa ghano, ivyo panyengo iyo vikaŵa pasi pa ulamuliro wa [[Habsburg|Ŵa Habsburg]]), ndipo [[Isaac le Maire]] ndiyo wakaŵa munthu uyo wakaŵika ndalama zinandi chomene, ƒ85,000. ''Heeren XVII'' (Ŵalongozgi 17) ŵakakumananga mwakusintha: vyaka 6 ku Amsterdam na vyaka 2 ku Middelburg-Zeeland. Ŵakasankhanga ndondomeko zikuru za VOC na kugaŵa ntchito pakati pa maofesi. Maofesi ghakachitanga ntchito zose zakukhumbikwa, ghakapanganga sitima zawo na malo ghakusungiramo katundu, kweniso kuguliska na kugura katundu. ''Heeren XVII'' ŵakatumanga ŵalongozgi ŵa sitima na ulongozgi wakupulikikwa makora wa nthowa iyo ŵakeneranga kwendamo, mphepo izo zikaŵa zikulamulira, mikhaliro ya maji, malo ghakuzika sitima na vimanyikwiro vya pa nyanja. VOC yikapanganga so [[nautical charts|mapu gha pa nyanja]] ghake. Mu nkhani ya [[Dutch–Portuguese War|Nkhondo ya ŴachiDutch na Ŵapwitikizi]], kampani yikakhazikiska likulu lake ku Batavia, pa [[Java island|chirwa cha Java]] (sono ni [[Jakarta]], Indonesia). Malo ghanyake gha ukoloni ghakakhazikiskikaso mu [[East Indies|East Indies]], nga ni pa [[Maluku Islands|Virwa vya Maluku]], ivyo vikusazgapo [[Banda Islands|Virwa vya Banda]], uko VOC yikalamuliranga mwankhaza kuti yisunge ulamuliro wa yekha pa malonda gha [[nutmeg|muskat]] na [[mace (spice)|mace]]. Nthowa izo zikagwiliskirika ntchito kuti ŵasungilire ulamuliro uwu zikazganga [[extortion|kukakamizga ŵanthu kupereka ndalama panji katundu]] na kupondereza mwankhaza ŵanthu ŵakwawo, kusazgapo [[mass murder|kukoma ŵanthu ŵanandi]].<ref>[[Hanna, Willard A.]] (1991). ''Indonesian Banda: Colonialism and its Aftermath in the Nutmeg Islands''. Bandanaira: Yayasan Warisan dan Budaya Banda Naira.</ref> Kweniso, ŵimiliri ŵa VOC nyengo zinyake ŵakagwiliskiranga ntchito nthowa ya kuwotcha makuni gha vyakununkhira kuti ŵachichizge ŵanthu ŵakwawo kulima vyakurya vinyake, ndipo ivi vikachepeskanga mwadala unandi wa vyakununkhira nga ni muskat na ma clove.<ref>{{cite book|title=The Globe Encompassed: The Age of European Discovery, 1500–1700|url=https://archive.org/details/globeencompassed0000ames|author=Ames, Glenn J.|year=2008|page=[https://archive.org/details/globeencompassed0000ames/page/111 111]}}</ref> ==Ŵeneŵa ŵa magawo na nkhani za ulamuliro== [[File:VOC duit.jpg|thumb|upright=0.7|Mbali zose ziŵiri za [[duit|duit]], [[Coinage of the Dutch East India Company|ndalama iyo yikapangika mu 1735 na VOC]]]] Ŵamalonda ŵa ku Netherlands ŵa mu vyaka vya m'ma 1600, chomenechomene awo ŵakaŵikamo ndalama mu VOC, ŵakwenera kuŵa ŵaŵezi ŵakwamba kulembedwa mu mdauko awo ŵakaghanaghanirapo mwakuzirwa za masuzgo gha [[corporate governance|ulamuliro wa makampani]]. Isaac Le Maire, uyo wakumanyikwa kuti wakaŵa munthu wakwamba kulembedwa mu mdauko kuchita [[short selling|kuguliska magawo mwachidule]], wakaŵaso yumoza wa ŵanthu awo ŵakaŵikamo ndalama zinandi mu VOC. Mu 1609, wakadandawura za ulamuliro uheni wa kampani wa VOC. Pa 24 Janyuwale 1609, Le Maire wakapeleka pempho lakususkana na VOC, ndipo ichi chikaŵa chinthu chakwamba kulembedwa mu mdauko cha [[shareholder activism|ntchito ya ŵalembeka magawo yakususkana na kampani]]. Mu mphindano yakwamba kulembeka mu mdauko yakukhwaskana na ulamuliro wa kampani, Le Maire wakasuzga mwakuzomerezgeka kuti wupu wakulongozga wa VOC (Heeren XVII) ukakhumbanga "kusunga ndalama za munyake kwa nyengo yitali panji kuzituma mu nthowa yinyake yakupambana na khumbo la mwenecho", ndipo wakapempha kuti VOC yimazgike mwakuyana na umo malonda ghakachitikira nyengo iyo. Gelderblom, Oscar; De Jong, Abe; Jonker, Joost (2010). ''Putting Le Maire into Perspective: Business Organization and the Evolution of Corporate Governance in the Dutch Republic, 1590–1610'', mu J. Koppell, ed., ''Origins of Shareholder Advocacy''. (New York: Palgrave Macmillan) Mueller, Dennis C. (ed.), (2012). ''The Oxford Handbook of Capitalism'', peji 333. (New York: Oxford University Press) Pambere wakaŵa mwenecho wa magawo ghanandi chomene mu VOC kweniso ''bewindhebber'' uyo wakakhalanga pa wupu wakulongozga, Le Maire wakuwoneka kuti wakayezga kupatuska phindu la kampani kuti liŵe lake mwa kuchita maulendo 14 mu zina lake m'malo mwa zina la kampani. Pakuti magawo ghake ghanandi ghakaŵavya nkhongono yikuru yakuvota, mu 1605 Le Maire wakachimbizgika na ŵalongozgi ŵanyake chifukwa cha milandu ya kwiba ndalama za kampani, ndipo wakachichizgika kusayina phangano lakuti waleke kupikisana na VOC. Wakati wasungilira magawo mu kampani pamanyuma pa nkhani iyi, mu 1609 Le Maire wakaŵa mulembi wa icho chikuchemeka kuti "mazgu ghakwamba kulembeka mu mdauko gha ŵakuŵikamo ndalama ghakuvikilira wanangwa wawo mu kampani iyo magawo ghake ghakuguliskika pa msika". Frentrop, Paul (2009). ''The First Known Shareholder Activist: The Colorful Life and Times of Isaac le Maire (1559–1624)'', mu Frentrop/Jonker/Davis 2009, 11–26 Frentrop, Paul; Jonker, Joost; Davis, S. (ed.), (2009). ''Shareholder Rights at 400: Commemorating Isaac Le Maire and the First Recorded Expression of Investor Advocacy'' (The Hague: Remix Business Communications, 2009) Hansmann, Henry; Pargendler, Mariana (2013). ''The Evolution of Shareholder Voting Rights: Separation of Ownership and Consumption''. (Yale Law Journal, Volume 123, pages 100–165, 2014) Mu 1622, ŵakuŵikamo ndalama mu VOC ŵakachitikasongaso chiŵembu chakwamba kulembeka mu mdauko cha [[shareholder revolt|kuwukira kwa ŵakuŵikamo ndalama]], ŵeneŵo ŵakadandawura kuti mabuku gha ndalama gha kampani "ghakapakika mafuta gha nyama" mwakuti "ghadyeke na ŵapusu". Ŵakuŵikamo ndalama ŵakakhumbanga "reeckeninge", kung'anamura kufufuza mwakwenelera kwa ndalama za kampani. Ntchito ya ŵakuŵikamo ndalama mu VOC mu 1622 yikulongora umo [[corporate social responsibility|kampani yikamba kupulikira udindo wake ku ŵanthu]], apo ŵakuŵikamo ndalama ŵakachitanga viwawa vyakususka mwa kugaŵira mapepala ghakupharazga na kudandawura za kujipangira usambazi kwa ŵalongozgi kweniso kubisa vinthu. ==Malo ghakuru gha malonda, malo ghakukhala ŵanthu, na makoloni== {{Main|Mndandanda wa malo gha malonda na malo ghakukhala ŵanthu gha Kampani ya East Indies ya ku Netherlands}} {{See also|\:Category\:Malo ghakukhala ŵanthu na makoloni gha Kampani ya East Indies ya ku Netherlands agho ghakale|l1=Malo ghakukhala ŵanthu na makoloni gha Kampani ya East Indies ya ku Netherlands agho ghakale (VOC)}} {{See also|\:Category\:Malo gha malonda gha Kampani ya East Indies ya ku Netherlands agho ghakale|l1=Malo gha malonda gha Kampani ya East Indies ya ku Netherlands agho ghakale (VOC)}} {{See also|\:Category\:Malo ghakukhala ŵanthu agho ghakakhazikiskika na Kampani ya East Indies ya ku Netherlands|l1=Malo ghakukhala ŵanthu agho ghakakhazikiskika na Kampani ya East Indies ya ku Netherlands (VOC)}} {{See also|Ulamuliro wa kampani mu East Indies ya ku Netherlands}} Likulu likuru la kampani pa charu chose likaŵa ku [[Amsterdam]], ndipo yikaŵaso na malo ghanyake mu misumba ya ku Netherlands ya [[Delft]], [[Enkhuizen]], [[Hoorn]], [[Middelburg, Zeeland|Middelburg]] na [[Rotterdam]]. Ku Africa, malo gha malonda na makoloni ghakaŵa mu [[Mauritius ya ku Netherlands]] mu 1638–1658 na 1664–1710, kweniso mu [[Koloni ya Cape ya ku Netherlands]] pakati pa 1652 na 1806. Malo gha malonda na makoloni gha kampani ku South Asia na Indonesia ghakaŵa mu [[Batavia, Dutch East Indies|Batavia]], [[Coromandel ya ku Netherlands]] mu 1806–1825, [[Suratte ya ku Netherlands]] mu 1616–1825, [[Bengal ya ku Netherlands]] kufuma mu 1827 kufika 1825, [[Ceylon ya ku Netherlands]] kufuma mu 1640 kufika 1796, na [[Malabar ya ku Netherlands]] kufuma mu 1661 kufika 1795. Malo gha ku Japan ghakaŵa ku [[Hirado, Nagasaki]] kufuma mu 1609 kufika 1641, kweni ghakasamuskika ku [[Dejima]] kufuma mu 1641 kufika 1853. Ku Taiwan, kampani yikaŵa na malo ghake ku [[Anping, Tainan|Anping]] ([[Fort Zeelandia (Taiwan)|Fort Zeelandia]]), [[Tainan]] ([[Fort Provincia]]), [[Wang-an, Penghu]] pa [[Pescadores Islands|Viwumba vya Pescadores]] (Fort Vlissingen; 1620–1624), [[Keelung]] ([[Santisima Trinidad (Taiwan)|Fort Noord-Holland]] na Fort Victoria) na [[Tamsui]] ([[Fort Antonio]]). Ku Malaysia, kampani yikaŵa ku [[Malacca ya ku Netherlands]] mu 1641–1795 na 1818–1825. Ku Thailand, kampani yikaŵa mu [[Ufumu wa Ayutthaya]] mu 1608–1767. Ku Vietnam, kampani yikaŵa ku [[Hanoi]]/Tonkin mu 1636–1699, na ku [[Hội An (city)|Hội An]] mu 1636–1741. [[File\:Fort Rotterdam, Makassar, Indonesia - 20100227-02.jpg|thumb|[[Fort Rotterdam]] ku [[Makassar]], wakazengeka na VOC mu 1673]] [[File\:Melaka-Dutch-Square-2201.jpg|thumb|upright|Dutch Square ku [[Malacca]], pamoza na [[Christ Church, Malacca|Tchalitchi cha Christ]] (pakati) na [[Stadthuys]] (ku malyero)]] [[File\:Kasteel de Goede Hoop Gateway.JPG|thumb|upright|Chipata cha [[Castle of Good Hope]], linga lakukhora lakuzingilizgika ilo likazengeka na VOC mu vyaka vya m'ma 1600]] ==''Mawonekero gha VOC''== {{Cquote| (...) Nkhupulikiska chifukwa icho mose mukuyowoya vinthu viheni na vyakukwiyiska nthena. Tiyeni tikondwenge pamoza. Tiyeni tiyowoyeso kuti "Netherlands yingachita" nga umo tikayowoyeranga: mawonekero gha VOC. Laŵiskani ivyo vili kujumpha mphaka zithu. Kuchita vinthu mwamphu! Asi mukuwona?|200px||[[Jan Pieter Balkenende]], uyo panyengo iyi wakaŵa [[Mlongozgi wa Boma wa Netherlands]], wakazgora ivyo ŵakamususka pa ndondomeko ya boma lake pa nkhani ya nyumba ya malango mu Seputembala 2006{{efn|Jan Peter Balkenende: "Nkhupulikiska chifukwa icho mose mukuyowoya vinthu viheni na vyakukwiyiska nthena. Tiyeni tikondwenge pamoza. Tiyeni tiyowoyeso kuti: 'Netherlands yingachita nadi!', mawonekero gha VOC. Laŵiskani ivyo vili kujumpha mphaka! Kuchita vinthu mwamphu! Asi?" [Mazgu ghakwamba mu Chidachi, ghafwatulika mwakuyanako na ivyo vikawonekanga mu vidiyo]}}Oostindie, Gert: ''Postcolonial Netherlands Sixty-Five Years of Forgetting, Commemorating, Silencing''. (Amsterdam: Amsterdam University Press, 2010, {{ISBN|9789089643537}}), peji 252Jonsson, Stefan; Willén, Julia (eds.): ''Austere Histories in European Societies: Social Exclusion and the Contest of Colonial Memories''. (London: Routledge, 2016), peji 67}} Mdauko wa VOC (chomenechomene vigaŵa vyake viheni) nyengo zose waŵa chinthu icho chingapangiska mphindano. Mu 2006, apo [[Mlongozgi wa Boma wa Netherlands]] [[Jan Pieter Balkenende]] wakayowoya za mzimu wa upayiniya wa malonda na [[work ethic|mtheto wa ntchito]] wa [[ŵanthu ŵa ku Netherlands]] na [[Dutch Republic|Republic ya ku Netherlands]] mu [[Dutch Golden Age|nyengo yawo ya usambazi]], wakapangiska lizgu lakuti "mawonekero gha VOC" (''[[Nl\:VOC-mentaliteit|VOC-mentaliteit]]'' mu Chidachi).{{efn|Balkenende: "Tiyeni tiŵe ŵakugomezga! Tiyeni tiyowoye kuti, 'Ku Netherlands vinthu vingachitikaso!' Mawonekero gha VOC agha: kuluta kujumpha mphaka na kuchita vinthu mwamphu!" [Lafwatulika kufuma ku mazgu ghakwamba gha Chidachi].}} Kwa Balkenende, VOC yikimiranga [[business acumen|mahara gha malonda]] gha ŵa ku Netherlands, [[entrepreneurship|mzimu wa kuchita bizinesi]], mzimu wa kusambira vinthu vipya na kuŵa na mtima wakusankha vinthu mwakukhora. Kweni mazgu agha ghakakwiyiska ŵanthu ŵanandi, chifukwa kuwona mwakukondwera nyengo ya Dutch Golden Age kukuzerezga vinthu ivyo vikayanana nayo mu mdauko, nga ni [[colonialism|ulamuliro wa makoloni]], [[exploitation of labour|kuphindulira ŵantchito mwankhaza]] na nkhaza. Pamanyuma Balkenende wakalongosora kuti "chikaŵa chinthu icho wakakhumbanga yayi kuyowoyapo napachoko". Kweni nangauli ŵanthu ŵakayisuskanga, "mawonekero gha VOC", nga ni chigaŵa cha umo ŵanthu ŵanyake ŵakuwonera mdauko wa Dutch Golden Age, kwa vyaka vinandi ghakaŵa chinthu chakuzirwa mu ndondomeko ya chikhalidwe cha Netherlands. ==Kususka== [[File\:Natives of Arrakan sell slaves to the Dutch East India Company (1663).jpg|thumb|Ŵanthu ŵa ku [[Rakhine State|Arakan]] ŵakuguliska ŵazga ku Kampani ya East Indies ya ku Netherlands, pafupifupi{{nbsp}}1663 CE.]] Kampani iyi yikususkika chifukwa cha vyakufumapo vya [[quasi-absolute monopoly|umaliro wapafupi wa ulamuliro wa malonda wawoŵene]], [[colonialism|ulamuliro wa makoloni]], [[exploitation of labour|kuphindulira ŵantchito mwankhaza]] (kusazgapo kugwiliskira ntchito [[slave labour|ŵazga ngati ŵantchito]]), [[History of slavery|malonda gha ŵazga]], kugwiliskira ntchito nkhaza, [[environmental destruction|kunanga chilengedwe]] (kusazgapo [[deforestation|kutema misitu]]), kweniso chifukwa cha umo kampani iyi yikaŵira na [[bureaucratic|malango na maofesi ghanandi chomene]]. Batavia, iyo sono ni Jakarta, yikaŵa likulu la Kampani ya East Indies ya ku Netherlands, ndipo mu koloni iyi mukaŵa ndondomeko yakukhwima ya magulu gha ŵanthu. Kuyana na Marsely L. Kahoe mu ''The Journal of Historians of Netherlandish Art'', "ntchakwambura kwenelera kupulikiska Batavia, nga umo ŵakusambira ŵanyake ŵachitira, kuti yikaŵa ndondomeko yakukhazikika na kuyana kwa ŵanthu iyo pamanyuma yikanangika chifukwa cha vinthu vya ulamuliro wa makoloni. M'malo mwake, kupatukana kwa ŵanthu mu magulu na kuŵapatula mu Batavia kukafumanga mu nthowa zinyake mwakudunjika mu ndondomeko ya ŵa ku Netherlands." Pakaŵa chiŵerengero chikuru chomene cha ŵantchito ŵa VOC awo ŵakafwanga chifukwa cha ngozi za ngalawa, matenda nga ni scurvy na dysentery, kweniso kukakirana na makampani ghanyake gha malonda na ŵakupoka katundu mu nyanja. Pakati pa 1602 na 1795, pafupifupi ŵasekelaŵa na ŵamisiri miliyoni yimoza ŵakafuma ku Holland, kweni ŵaŵiri pera pa ŵatatu ŵakaŵerako. J.L. van Zanden wakulemba kuti "VOC 'yikamalanga' ŵanthu pafupifupi 4,000 chaka chilichose." ===Ulamuliro wa makoloni, ulamuliro wa malonda wawoŵene na nkhaza=== {{Further|Gulu\:Mdauko wa nkhondo wa Kampani ya East Indies ya ku Netherlands|l1=Mdauko wa nkhondo wa Kampani ya East Indies ya ku Netherlands|Gulu\:Nkhondo izo Kampani ya East Indies ya ku Netherlands yikachitamo|l2=Nkhondo izo Kampani ya East Indies ya ku Netherlands yikachitamo|Ukoloni wa ŵa ku Europe mu Africa|Ulamuliro wa ŵa ku Western mu Asia|Ukoloni wa ŵa ku Europe mu Southeast Asia|Nkhondo za vyakununkhira|Kupha ŵanthu ku Amboyna|Kupha ŵanthu ku Batavia|Kupha ŵanthu pa Chirwa cha Lamey}} {{Cquote|Ŵakulu ŵinu mukumanya kufuma mu ivyo mwawona kuti malonda mu Asia ghakwenera kuchitika na kusungika pasi pa civikiliro na chovwiro cha vilwero vya ŵakulu ŵinu, ndipo vilwero ivi vikwenera kulipilika na phindu lakufuma mu malonda; ntheura tingachita malonda yayi kwambura nkhondo, nesi nkhondo kwambura malonda.|200px||[[Jan Pieterszoon Coen]], uyo wakaŵa mulongozgi mukuru wa VOC ''de facto'' [mu [[East Indies|East Indies]]], ku [[Heeren XVII]], wupu wakulongozga wa VOC [mu [[Dutch Republic|Republic ya ku Netherlands]]], mu 1614}} Malamulo gha VOC ghakazomerezga kuti ichite vinthu nga ni boma ilo likaŵa na mazaza ghakujiyimira, ndipo likachita nkhondo zakukora malo mwankhaza.{{cite book|author=Nicholas Tarling|url=[https://books.google.com/books?id=GIz4CDTCOwcC&pg=PA86|title=The](https://books.google.com/books?id=GIz4CDTCOwcC\&pg=PA86|title=The) Cambridge History of Southeast Asia|publisher=Cambridge University Press|year=1999|isbn=978-0-521-66370-0|pages=86–|author-link=Nicholas Tarling|access-date=8 March 2021|archive-date=11 April 2023|archive-url=[https://web.archive.org/web/20230411160028/https://books.google.com/books?id=GIz4CDTCOwcC&pg=PA86|url-status=live](https://web.archive.org/web/20230411160028/https://books.google.com/books?id=GIz4CDTCOwcC\&pg=PA86|url-status=live)}} Chimoza ntchimoza chikaŵa [[Kukora kwa Ŵadachi Visiwa vya Banda|kukora kwa Ŵadachi Visiwa vya Banda]], pakati pa 1609 na 1621, pamanyuma pakuti visiwa ivi vikakana kupereka mafuta gha nutmeg kwa Ŵadachi pera. Ŵadachi ŵakatuma ŵasilikari kuti ŵalange ŵanthu, ndipo nkhondo izi zikapangiska kuti umoyo wa ŵanthu ŵa ku Banda unangike pafupi chose.{{Cite journal|last=Ittersum|first=Martine Julia van|date=2016-05-18|title=Debating Natural Law in the Banda Islands: A Case Study in Anglo–Dutch Imperial Competition in the East Indies, 1609–1621|journal=History of European Ideas|volume=42|issue=4|pages=459–501|doi=10.1080/01916599.2015.1101216|issn=0191-6599|doi-access=free}} Ŵakadukira chirwa chikuru cha [[Visiwa vya Banda|Banda]], icho chikaŵa [[Lontor (chirwa)|Lontor]], mu 1621. Ŵanthu ŵakukwana 2,800 ŵa ku Banda ŵakakomeka, ŵanandi chifukwa cha njara, ndipo ŵanthu 1,700 ŵakazgoka ŵazga pa nyengo ya kuwukira uku.{{Cite book |last=Straver |first=Hans |date=2018 |title=Vaders en dochters: Molukse historie in de Nederlandse literatuur van de negentiende eeuw en haar weerklank in Indonesië |url=[https://books.google.com/books?id=5wJGDwAAQBAJ&pg=PA90](https://books.google.com/books?id=5wJGDwAAQBAJ\&pg=PA90) |location=Hilversum |publisher=Uitgeverij Verloren |pages=90–91 |isbn=9789087047023 |access-date=17 June 2020 |quote=Om hierin naar behooren te voorzien is het noodig dat Banda t'eenemaal vermeesterd en met ander volk gepeupleerd worde. |language=nl |archive-date=11 April 2023 |archive-url=[https://web.archive.org/web/20230411160029/https://books.google.com/books?id=5wJGDwAAQBAJ&pg=PA90](https://web.archive.org/web/20230411160029/https://books.google.com/books?id=5wJGDwAAQBAJ\&pg=PA90) |url-status=live}} Ŵanthu wose pa visiwa ivi ŵakayanayika kuti ŵakaŵa 15,000 pambere ŵandakoreke. Nangauli chiŵelengero cheneko chichali chambura kumanyikwa makora, ŵakupima kuti ŵanthu pafupifupi 14,000 ŵakakomeka, ŵakapangika ŵazga panji ŵakachimbilira ku malo ghanyake, ndipo ŵanthu 1,000 pera ŵa ku Banda ndiwo ŵakapona pa visiwa ivi. Ŵanthu ŵakupulumuka ŵakaŵikika mu minda ya nutmeg nga mbantchito ŵakukakamizgika.{{cite journal|first=Vincent C.|last=Loth|date=1995|title=Pioneers and Perkeniers: The Banda Islands in the 17th Century|journal=[[Cakalele (magazini)|Cakalele]]|volume=6|publisher=[[University of Hawaiʻi at Mānoa|Yunivesite ya Hawaiʻi ku Mānoa]]|location=Honolulu|hdl=10125/4207|pages=13–35}} Ŵazga ŵakachitirika nkhaza chomene ndipo chiŵelengero cha ŵanthu ŵa ku Banda chikakhira kufika pa 1,000 mu 1681. Ŵazga 200 ŵakazizwanga chaka chilichose kuti ŵasungire chiŵelengero cha ŵazga pafupifupi 4,000.{{Cite book|last=van Zanden |first=J. L.|title=The rise and decline of Holland's economy : merchant capitalism and the labour market|url=https://archive.org/details/risedeclineofhol0000zand |date=1993|publisher=Manchester University Press|page=[https://archive.org/details/risedeclineofhol0000zand/page/77 77]|oclc=654324718}} Mu 1623 pa [[Chirwa cha Ambon|Ambon]] (Amboina), ŵalara ŵa VOC ŵakakaka, ŵakasuzga na kukoma ŵantchito 10 ŵa [[Kampani ya Ŵangerezi ya East India]], pamoza na ŵanthu ŵa ku Japan na Portugal awo ŵakawovwiranga, chifukwa cha kukayikira kuti ŵakachita chiŵembu. Chochitika ichi chikumanyikwa nga ni [[Kukomeka kwa Amboyna]], ndipo chikamazga kukolerana pakati pa Ŵangerezi na Ŵadachi mu Moluccas kweniso chikalongora umo Kampani iyi yikagwiliskiranga ntchito makhoti na chilango kuti yivikilire malonda ghake gha monopoly.{{cite book |last=Clulow |first=Adam |title=Amboina, 1623: Fear and Conspiracy on the Edge of Empire |publisher=Columbia University Press |year=2019 |isbn=978-0231175128}}{{Page needed|date=September 2025}} Mu 1740, apo chuma cha shuga ku Batavia chikakhira chomene, ŵasilikari ŵa VOC na ŵasilikari ŵanyake awo ŵakakolerananga nawo ŵakakoma ŵanthu ŵa ku China ŵanandi chomene. Ŵakufufuza ŵakupereka chiŵelengero cha ŵanthu awo ŵakakomeka kufuma pa 5,000 kufika pa ŵanthu ŵakujumpha 10,000 mu chochitika icho chikaŵa chikumanyikwa nga ni [[Kukomeka kwa Batavia mu 1740|Kukomeka kwa Batavia]].{{cite book |title=The Cambridge History of Southeast Asia, Volume 2|publisher=Cambridge University Press|year=1999|isbn=9780521663700|editor-last=Tarling|editor-first=Nicholas|pages=86–88}} Pambere ivi vindachitike, mu 1636, ŵasilikari ŵa VOC ŵakachita ulendo wakulanga pa [[Kukomeka kwa Chirwa cha Lamey|Chirwa cha Lamey]] (Lamay) icho chili pafupi na Taiwan pamanyuma pa ngozi za sitima. Ŵanthu ŵanandi ŵa pachilwa ŵakakomeka panji ŵakachimbizgika, ndipo chirwa ichi chikakhala pafupi chambura ŵanthu.{{cite book |last=Andrade |first=Tonio |title=How Taiwan Became Chinese: Dutch, Spanish and Han Colonization in the Seventeenth Century|publisher=Columbia University Press|year=2008|isbn=9780231144601}} ===Malonda gha ŵazga gha Ŵadachi na uzga mu nyengo ya ulamuliro wa VOC=== {{Further|Mbiri ya uzga|Uzga ku South Africa|Kupanduka kwa ŵazga pa Meermin}} Panyengo iyo malo ghakukhazikikapo ŵanthu ghakaŵikika pa [[Koloni ya Ŵadachi ya Cape|Cape]] mu 1652, VOC yikaŵa kuti yakhala kale na vyaka vinandi yikuchita [[uzga]] mu [[East Indies]]. [[Jan van Riebeeck]] wakamanya mukati mwa myezi yiŵiri pera kufuma apo malo ghakukhazikikapo ŵanthu gha ku Cape ghakakhazikiskikira kuti [[ntchito ya ŵazga|ntchito ya ŵazga]] yikakhumbikwiranga pa ntchito zakusuzga chomene na zakufipiska chomene. Pakwamba, VOC yikaghanaghananga kuti yingazgora ŵanalume ŵa mtundu wa [[Khoikhoi]] ŵa ku malo agha kuŵa ŵazga, kweni maghanoghano agha ghakakanika chifukwa cha kughanaghana kuti ndondomeko iyi yikaŵa yakudura kweniso yakofya. Ŵanandi ŵa Khoikhoi ŵakasankha kuleka kugwira ntchito ya Ŵadachi chifukwa cha malipiro ghachoko na vinthu vyakusuzga pa ntchito. Pakwamba, ŵakukhazikika ŵakachitanga malonda na Khoikhoi, kweni vinthu vyakusuzga pa ntchito na malipiro ghachoko ivyo Ŵadachi ŵakaŵika vikapangiska nkhondo zinandi. Chiŵelengero cha ŵanthu ŵa ku Europe chikakhalanga pasi pa 200 mu vyaka vinkhondi vyakwamba vya malo agha, ndipo kuchita nkhondo na ŵazengezgani awo ŵakaŵa ŵakujumpha 20,000 mphanyi kukaŵa kupusa. Kweniso, Ŵadachi ŵakawopanga kuti ŵanthu ŵa Khoikhoi usange ŵazgika ŵangachimbilira nyengo zose ku ŵanthu ŵanyawo, apo ŵalendo ŵangasuska chomene kuti ŵachimbire na kupona panji kuleka kukakika so.{{cite book |last=Byrnes |first=Rita |title=South Africa: A Country Study |publisher=GPO for the Library of Congress |year=1996 |location=Washington |pages=Kukhazikiska chuma chakuthemba pa uzga |url=[http://countrystudies.us/south-africa/5.htm](http://countrystudies.us/south-africa/5.htm) |access-date=10 August 2018 |archive-date=11 August 2018 |archive-url=[https://web.archive.org/web/20180811031816/http://countrystudies.us/south-africa/5.htm](https://web.archive.org/web/20180811031816/http://countrystudies.us/south-africa/5.htm) |url-status=live}} Pakati pa 1652 na 1657, ŵakachita viyezgo vinandi vyambura kufiskika vyakutolera ŵanalume kufuma ku [[Dutch East Indies|East Indies]] na ku [[Mauritius]]. Kweni mu 1658, VOC yikafika na sitima ziŵiri za ŵazga ku Cape. Yimoza yikaŵa na ŵanthu ŵakujumpha 200 awo ŵakiza kufuma ku [[Dahomey]] (pasono [[Benin]]), ndipo yinyake yikaŵa na ŵanthu pafupifupi 200, ŵanandi ŵaŵo ŵakaŵa ŵana, awo ŵakakoleka kufuma pa sitima ya Ŵaportugal yakunyamura ŵazga pafupi na mphepete mwa nyanja ya Angola. Kupatulako ŵanthu ŵachoko waka, aŵa ndiwo ŵakaŵa ŵazga ŵekha awo ŵakizikapo ku Cape kufuma ku West Africa. Kufuma mu 1658 mpaka kuumaliro wa ulamuliro wa kampani, ŵazga ŵanandi chomene ŵakizanga ku Cape nyengo na nyengo mu nthowa zakupambanapambana, chomenechomene kwizira mu maulendo ghakunyamura ŵazga agho kampani yikawovwiranga na ŵazga awo ŵakizanga ku Cape mu sitima zake zakuwelera. Kufuma ku malo agha kweniso chifukwa cha kubabika kwawo, chiŵelengero cha ŵazga chikakura kufuma pa ziro mu 1652 kufika pafupifupi 1,000 mu 1700. Mu vyaka vya m'ma 1700, chiŵelengero cha ŵazga chikakura chomene kufika pa 16,839 mu 1795. Pamanyuma pakuti malonda gha ŵazga ghayambika, ŵazga wose awo ŵakizanga ku Cape mpaka apo Britain yikakhazikiskira [[Slave Trade Act 1807|Dango la Malonda gha Ŵazga la 1807]] ŵakafumanga ku East Africa, Mozambique, Madagascar, South na Southeast Asia. Ŵanthu ŵanandi ŵakizanga kufuma ku [[Dutch Ceylon|Ceylon]] na ku visiwa vya Indonesia. Ŵakayidi ŵakufuma ku vyaru vinyake mu ufumu wa VOC nawo ŵakazgikanga. Chiŵelengero cha ŵazga, icho chikajumpha cha ŵakukhazikika ŵa ku Europe mpaka mu kotala lakwamba la vyaka vya m'ma 1800, chikaŵa chomene cha ŵanalume, ntheura chikakhumbikwiranga ŵazga ŵaphya nyengo zose kuti chisungike na kukura. Mu vyaka vya m'ma 1660, malo ghakukhazikikapo ŵanthu gha ku Cape ghakamba kuzaniska ŵazga kufuma ku Ceylon, Malaya (Malaysia), na Madagascar kuti ŵagwire ntchito pa minda.{{cite book |last=Appiah |first=Anthony |author2=Henry Louis Gates |title=Africana: The Encyclopedia of the African and African American Experience |publisher=Oxford University Press |year=2004 |pages=732 |isbn=978-0-19-517055-9 |url=[https://books.google.com/books?id=TMZMAgAAQBAJ&dq=slave+trade+%22dutch+east+india+trading+company%22&pg=PA732](https://books.google.com/books?id=TMZMAgAAQBAJ\&dq=slave+trade+%22dutch+east+india+trading+company%22\&pg=PA732) |archive-url=[https://web.archive.org/web/20220407031804/https://books.google.com/books?id=TMZMAgAAQBAJ&dq=slave+trade+%22dutch+east+india+trading+company%22&pg=PA732](https://web.archive.org/web/20220407031804/https://books.google.com/books?id=TMZMAgAAQBAJ\&dq=slave+trade+%22dutch+east+india+trading+company%22\&pg=PA732) |url-status=dead |archive-date=7 April 2022}} Kukanirana pakati pa ŵalimi ŵa Ŵadachi na Khoikhoi kukamba apo ŵa Khoikhoi ŵakamanya kuti Ŵadachi ŵakaŵa kuti ŵiza kuti ŵakhalenge kwenekuko, ndipo ŵakakhumbanga kutora malo gha ŵaliski. Mu 1659, Doman, wa mtundu wa Khoikhoi uyo wakagwiranga ntchito nga ni wakung'anamura wa Ŵadachi ndipo wakaŵa kuti waluta mpaka ku Java, wakalongozga chiwukirano cha ŵasilikari kuti ŵachimbizge Ŵadachi pa chigaŵa cha Cape. Chiŵukirano ichi chikatherera, nangauli nkhondo yikalutilira mpaka apo mtende wambura kumazga nkhani ukakhazikiskika chaka chakulondezgapo. Mu vyaka vyakhumi ivyo vikarongeka pamanyuma, suzgo pa Khoikhoi likakura apo Ŵadachi ŵanandi ŵakazgoka ŵalimi ŵakujiyimira, ŵakakuliska malo ghawo, ndipo ŵakapenjanga malo gha kuliskapo viŵeto vyawo ivyo vikakuranga. Nkhondo yikambaso mu 1673 ndipo yikalutilira mpaka 1677, apo kukana kwa Khoikhoi kukathereskeka chifukwa cha kusazgikana kwa vilwero vyapachanya vya ku Europe na nthowa ya Ŵadachi yakugwiliskira ntchito kugaŵikana kwa ŵanthu ŵa ku malo agha. Pamanyuma pa ichi, umoyo wa ŵanthu ŵa Khoikhoi ku Western Cape ukambaso kusweka. Ŵanyake ŵakasanga ntchito nga mbaliski pa minda ya ŵa ku Europe; ŵanyake ŵakakana ulamuliro wa ŵalendo ndipo ŵakafumapo ku Cape. Chilango chikuru chomene kwa ŵanandi chikiza mu 1713 apo sitima ya Ŵadachi yikiza na nthenda ya nthomba ku Cape. Pakwamba nthenda iyi yikaŵa yambura kumanyikwa mu malo agha, ndipo yikaparanya ŵanthu ŵa Khoikhoi awo ŵakakhalapo, na kukoma 90% ya ŵanthu. Mu vyaka vyose vya m'ma 1700, malo ghakukhazikikapo ŵanthu ghakalutilira kukura chifukwa cha kuwanda kwa ŵanthu ŵa ku Europe kweniso kulutilira kuzaniska ŵazga. Ŵanthu pafupifupi 3,000 ŵa ku Europe na ŵazga awo ŵakaŵa ku Cape mu 1700 ŵakaŵa pafupifupi 20,000 ŵa ku Europe na ŵazga pafupifupi 25,000 kuumaliro wa vyaka ivi. ==Malo ghakusungirako mbiri na malembere== Ivyo VOC yikachitanga (malo gha malonda na makoloni) vikapanga malo ghakusungirako vinthu ghakuzura na viŵegha, khofi, tiyi, malaya, vyakuŵikamo vinthu vya porcelain na silika, kweniso sitima izo zikasazganga malemba ghanandi. Mauthenga ghakukhwaskana na vinthu vya ndale, chuma, chikhalidwe, chisopa na umoyo wa ŵanthu kufuma ku chigaŵa chikuru chomene ghakendanga pakati pa malo gha VOC, likuru la malonda ku [[Batavia, Dutch East Indies|Batavia]] (pasono [[Jakarta]]), na wupu wa ŵalongozgi (a [[Heeren XVII|Ŵalongozgi Ŵakukwana 17]]) mu Dutch Republic. Balk, G.L.; van Dijk, F.; Kortlang, D.J.; Gaastra, F.S. ''et al.'': ''The Archives of the Dutch East India Company (VOC) and the Local Institutions in Batavia (Jakarta)''. (BRILL, 2007, {{ISBN|9789004163652}}) Masamba 25 miliyoni gha malemba gha VOC ghachali kusungika, ndipo ghali ku Jakarta; [[Colombo]], Sri Lanka; [[Chennai]], India; [[Cape Town]], South Africa; na [[The Hague]], Netherlands. Mu 2003, [[UNESCO]] yikasazga malemba agha pa [[Memory of the World Programme|ndandanda wa pacharu chose wa Memory of the World]].{{cite web |title=Archives of the Dutch East India Company [Documentary heritage submitted by Netherlands and recommended for inclusion in the Memory of the World Register in 2003] |url=[https://www.unesco.org/en/memory-world/archives-dutch-east-india-company](https://www.unesco.org/en/memory-world/archives-dutch-east-india-company) |access-date=2 February 2017 |publisher=UNESCO Memory of the World Programme}} * [[East India Company (disambiguation)|Kampani ya East India (kupambaniska maina)]] * [[Muscovy Company|Kampani ya Muscovy]] * [[Levant Company|Kampani ya Levant]] * [[British East India Company|Kampani ya Ŵabritishi ya East India]] * [[Danish East India Company|Kampani ya Ŵadanishi ya East India]] * [[Dutch West India Company|Kampani ya Ŵachidachi ya West India]] * [[Portuguese East India Company|Kampani ya Ŵapwitikizi ya East India]] * [[Compagnie des Indes (disambiguation)|Compagnie des Indes (kupambaniska maina)]] * [[Danish West India Company|Kampani ya Ŵadanishi ya West India]] * [[Hudson's Bay Company|Kampani ya Hudson's Bay]] * [[Mississippi Company|Kampani ya Mississippi]] * [[South Sea Company|Kampani ya South Sea]] * [[Ostend Company|Kampani ya Ostend]] * [[Swedish East India Company|Kampani ya Ŵaswidishi ya East India]] * [[Emden Company|Kampani ya Emden]] * [[Austrian East India Company|Kampani ya Ŵaustiriya ya East India]] * [[Swedish West India Company|Kampani ya Ŵaswidishi ya West India]] * [[Russian-American Company|Kampani ya Russia-America]] {{div end}} * [[10649 VOC]], pulaneti yichoko, asteroid VOC ({{langx|nl|link=no|Vereeniging van de Oostindische Compagnie||Kampani ya East India}}), asteroid ya nambara 10649 kulembeka, ndipo yili mu chigaŵa chikuru cha ma asteroid ==Mazgu ghakulongosora== == Vinyake == {{notelist}} == Ukaboni == {{reflist}} ==Mabuku ghakugwiliskirika ntchito== * {{cite book |last1=De Vries |first1=Jan |author-link1=Jan de Vries (historian) |last2=Van der Woude |first2=Ad |year=1997 |title=Chuma Chakwamba cha Mazuŵa Ghano: Kufiskika, Kuthera na Kulutilira kwa Chuma cha Ŵadachi, 1500–1815 |url=[https://archive.org/details/firstmodernecono0000devr](https://archive.org/details/firstmodernecono0000devr) |url-access=registration |publisher=Cambridge University Press |isbn=0-521-57061-1 }} * {{cite book |editor-last1=Fusaro |editor-first1=Maria |editor-last2=Allaire |editor-first2=Bernard |editor-last3=Blakemore |editor-first3=Richard J. |editor-last4=Vanneste |editor-first4=Tijl |title=Malango, Ntchito na Ufumu: Maghanoghano Ghakuyaniska pa Ŵanthu Ŵakugwira Ntchito pa Sitima, c. 1500–1800 |publisher=Palgrave Macmillan |year=2015 |isbn=978-1-137-44746-3}} * {{cite book |last=Ricklefs |first=M. C. |author-link=M. C. Ricklefs |title=Mbiri ya Indonesia ya Mazuŵa Ghano Kufuma pa c. 1300 |url=[https://archive.org/details/historyofmoderni0000rick\_i0z4](https://archive.org/details/historyofmoderni0000rick_i0z4) |url-access=registration |publisher=MacMillan |year=1993 |location=London |isbn=0-333-57689-6}} * {{cite book |last1=Chaudhuri |first1=K. N. |author-link1=Kirti N. Chaudhuri |last2=Israel |first2=J. I. |author-link2=Jonathan Israel |editor-last1=Israel |editor-first1=J. I. |editor-link=Jonathan Israel |year=1991 |title=Nyengo ya Ŵangerezi na Ŵadachi: Nkhani pa Chiŵukirano Chikuru na Ivyo Chikakhwaskira Charu Chose |url=[https://archive.org/details/anglodutchmoment0000unse](https://archive.org/details/anglodutchmoment0000unse) |url-access=registration |publisher=Cambridge University Press |isbn=0-521-39075-3 }} ==Ukaboni wa kuwali== {{Commons category}} {{Wikisource|nl|Octrooi van de VOC}} * [[http://www.inghist.nl/Onderzoek/Projecten/DAS/voyages](http://www.inghist.nl/Onderzoek/Projecten/DAS/voyages) Maulendo gha sitima za VOC] – nkhokwe ya pa intaneti ya maulendo gha sitima za VOC * [[https://www.atlasofmutualheritage.nl/en/](http://www.atlasofmutualheritage.nl/en/) Atlas of Mutual Heritage] – atlas ya pa intaneti ya malo ghakukhazikikapo ŵanthu na GWC * {{in lang|nl|cap=yew}} [[https://vocopvarenden.nationaalarchief.nl/default.aspx](http://vocopvarenden.nationaalarchief.nl/default.aspx) Nkhokwe ya ŵanthu awo ŵakagwiranga ntchito pa sitima za VOC] {{Webarchive|url=[https://web.archive.org/web/20160322115642/http://vocopvarenden.nationaalarchief.nl/default.aspx](https://web.archive.org/web/20160322115642/http://vocopvarenden.nationaalarchief.nl/default.aspx) |date=22 March 2016}} * [[http://www.vochistory.org.au/](http://www.vochistory.org.au/) Gulu la Mbiri ya VOC] {{Webarchive|url=[https://web.archive.org/web/20200727065844/http://www.vochistory.org.au/](https://web.archive.org/web/20200727065844/http://www.vochistory.org.au/) |date=27 July 2020 }} * [[http://vocwarfare.net](http://vocwarfare.net) Nkhondo za VOC] * [[https://sejarah-nusantara.anri.go.id/foreword/](https://sejarah-nusantara.anri.go.id/foreword/) Nkhokwe ya VOC kufuma ku nkhokwe ya charu cha Indonesia] {{Webarchive|url=[https://web.archive.org/web/20200727065854/https://sejarah-nusantara.anri.go.id/foreword/](https://web.archive.org/web/20200727065854/https://sejarah-nusantara.anri.go.id/foreword/) |date=27 July 2020 }} {{Navboxes|list1= {{Chartered companies}} {{Foreign trade in Imperial China |state=collapsed}} {{Dutch colonies|East India}} {{Dutch Formosa}} {{Governors-general of the Dutch East Indies}} {{Governor of Dutch Mauritius}} {{Governors of the Cape Colony}} {{DutchplacenamesAus}} {{Economic history of the Netherlands}} }} {{Authority control}} [[Category:Kampani ya Ŵadachi ya East India]] [[Category:1602 kukhazikiskika mu Dutch Republic]] [[Category:1800 kumazgika mu Batavian Republic]] [[Category:Makampani ghakupika chilolezo]] [[Category:Makampani gha ku India gha nyengo ya ukoloni]] [[Category:Makampani ghakukhazikika ku Amsterdam]] [[Category:Makampani agho ghakamazgika mu 1800]] [[Category:Makampani agho ghakakhazikiskika mu 1602]] [[Category:Makampani agho pakwamba ghakaŵikika pa Euronext Amsterdam]] [[Category:Makampani gha mitundu yakupambanapambana]] [[Category:Makampani gha Netherlands agho ghalije]] [[Category:Ma monopoly ghakale]] [[Category:Mbiri ya Ufumu wa Ŵadachi]] [[Category:Ubwezi pakati pa India na Netherlands]] [[Category:Mbiri ya panyanja ya Dutch Republic]] [[Category:Mbiri ya nkhondo ya Ufumu wa Ŵadachi]] [[Category:Makampani gha mitundu yinandi agho ghali na likuru ku Netherlands]] [[Category:Makampani ghakunyamura vinthu gha Dutch Republic]] [[Category:Malonda gha ŵazga gha Ŵadachi]] [[Category:Makampani gha malonda agho ghakakhazikiskika mu vyaka vya m'ma 1600]] [[Category:Makampani gha malonda gha Dutch Republic]] [[Category:Ma monopoly gha malonda]] qmtguvnc4jf5aap99rmkdj6u7c559nv 10 48728 121842 121795 2026-09-08T21:07:47Z Tumbuka Arch 6863 code need upating 121842 wikitext text/x-wiki <!-- ⚠️ SERIOUS WARNING — DO NOT EDIT THIS TEMPLATE WITHOUT PRIOR DISCUSSION. 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magazine|url=https://books.google.com/books?id=1CQEAAAAMBAJ&pg=PT60|title=Dance Trax|magazine=[[Billboard (magazine)|Billboard]]|last=Chin|first=Brian|date=11 May 1985|access-date=3 August 2023|quote= The A-side, produced by the team behind Divine's European successes (also unreleased here), is proof positive that disco is commercial, whether on major or indie label, especially when combined with enough raunch to put it in the "rock" category...}}</ref><ref name="NME">{{Cite web|url=https://www.nme.com/list/100-best-songs-of-the-1980s-1161|title=100 Best Songs Of The 1980s|first=Rebecca|last=Schiller|website=[[NME]] |date=26 March 2017}}</ref><ref name=Burns/><ref name=Waterman/> * [[synth-pop]]<ref>{{cite book|first1= Eric |last1= Weisbard |first2= Craig |last2= Marks |year= 1996 |title= Spin Alternative Record Guide |publisher= [[Vintage Books]] |isbn= 978-0-6797-5574-6 |quote= Stock-Aitken-Waterman, the British schlock-disco maestros who took the trance-like beats of '80s synth-pop to their dancefloor extreme, most famously on Dead or Alive's drag opus "You Spin Me Round (Like A Record)."}}</ref><ref>{{Cite news |last=Beaumont-Thomas |first=Ben |date=1 June 2020 |title=The 100 greatest UK No 1s, No 5: Dead or Alive – You Spin Me Round (Like a Record) |language=en-GB |work=The Guardian |url=https://www.theguardian.com/music/2020/jun/01/the-100-greatest-uk-no-1s-no-5-dead-or-alive-you-spin-me-round-like-a-record |issn=0261-3077}}</ref><ref>{{cite web|first= Tom|last= Owen|title= The top 25 greatest 1980s synthpop songs ever|website= [[Smooth Radio (2014)|Smooth Radio]]|date= 30 April 2024|url= https://www.smoothradio.com/features/best-electronic-synthpop-songs/|accessdate= 27 August 2024}}</ref> * [[hi-NRG]]<ref>{{cite book|first= Lee |last= Barron |year= 2010 |title= Play it Again: Cover Songs in Popular Music |url= https://archive.org/details/playitagaincover0000plas |chapter= Camp Transitions: Genre Adaptation and the Hi-NRG/Dance Cover Version |editor-first= George |editor-last= Plasketes |publisher= [[Ashgate Publishing]] |page= [https://archive.org/details/playitagaincover0000plas/page/214 214] |isbn= 978-0-7546-6809-1}}</ref><ref name="Ankeny">{{cite web|first= Jason |last= Ankeny |title= Dead or Alive – Artist Biography |publisher= [[AllMusic]] |access-date= 24 June 2013 |url= http://www.allmusic.com/artist/dead-or-alive-mn0000226556/biography}}</ref> * [[dance-pop]]<ref>{{Cite web|url=https://music.apple.com/ca/artist/dead-or-alive/544302|title=Dead or Alive|website=Apple Music}}</ref><ref>{{cite web|url=https://www.encyclopedia.com/education/news-wires-white-papers-and-books/dead-or-alive|title= Dead or Alive|website=[[Encyclopedia.com]]|access-date=6 June 2022}}</ref> * [[New wave music|new wave]]<ref>{{Cite web|url=https://www.allmusic.com/album/80s-new-wave-new-wave-dance-mw0000050508|title=80's New Wave: New Wave Dance - Album Reviews, Songs & More &#124; AllMusic|last=Erlewine|first=Stephen Thomas|via=AllMusic}}</ref> | length = * 3:19 (album version) * 3:16 (single version) * 8:01 (Murder mix) * 7:28 (Performance mix) | label = [[Epic Records|Epic]] | writer = * [[Pete Burns]] * Steve Coy * [[Wayne Hussey]] * Tim Lever * Mike Percy | producer = [[Stock Aitken Waterman]] | prev_title = [[That's the Way (I Like It)#Dead or Alive version|That's the Way (I Like It)]] | prev_year = 1984 | next_title = [[Lover Come Back to Me (Dead or Alive song)|Lover Come Back to Me]] | next_year = 1985 | misc = {{External music video|{{youTube|PGNiXGX2nLU|"You Spin Me Round (Like a Record)"}} }}{{Audio sample | type = single | file = You Spin Me Round by Dead or Alive.ogg | description = }} }} "'''You Spin Me Round (Like a Record)'''" ni sumu ya gulu la pop la Chingelezi la Dead or Alive. Iwo ukafumiskika pa 5 Novembala 1984, nga ni sumu yakulongozga kufuma mu chimbale chawo chachiŵiri cha studio, Chindindindi (1985). Nyimbo iyi yikafika pa nambara 1 pa UK Singles Chart mu Malichi 1985, ndipo yikatora masabata 17 kuti yifike ku malo agha. Iyi yikaŵa UK yakwamba nambala 1 iyo yikatimbanizgika na Stock Aitken Waterman wakupanga ŵatatu. Pa US Billboard Hot 100, yikafika pa nambala 11 pa 17 Ogasiti chaka chira, ndipo yikaŵa nyimbo yawo yapachanya chomene kwenekuko. Nyimbo iyi yikafikaso pa nambala 1 ku Ireland na ku Canada, apo ku Australia yikafika pa nambala 3 ndipo yikafika pa nambala 3 mu vyaru vinandi vya ku Europe. Vidiyo yake ya sumu yikalongozgeka na Vaughan Arnell na Anthea Benton. Mu 2003, Q wakaŵika sumu iyi pa nambara 981 pa mndandanda wawo wa "1001 Best Songs Ever", mu 2005 Blender wakayiŵika pa nambara 289 pa mndandanda wake wa "Nyimbo Zikuru Chomene Kufuma apo Mukababikira", ndipo mu 2015 yikavotera na ŵanthu ŵa ku Britain kuŵa nambala19. yumoza mu kafukufuku wa ITV. n0u3uefjoi0fdgohiyahk36u7qrrjfr 0 49559 121831 121829 2026-09-08T12:16:08Z Viyowoyero-vya-Malaŵi 11606 121831 wikitext text/x-wiki {{Databox}} [[Nthowa yakupimira]] ni ndondomeko iyo mikhaliro yakuwoneka (nga ni utali, kulemera, kutentha, na vinyake) yingapimika na manambara. Pakati pa ndondomeko zinandi zakupimira, '''nthowa ya metric''' ([[ChiNgelezi]]: ''metric system'') yikung’anamura chimoza, chilichose chikuŵika pa mlingo seti ya vigaŵa vyakukhazikika na zina ilo likulongosora vigaŵa vikuruvikuru na vichoko chomene mwakugwiliskira ntchito vimanyikwiro vya vigaŵa vyakuchulukizga vyakuthemba pa decimal (nga ni ''[[Kilo-|kilo]] ''na ''[[Milli-|milli]]''). [[International System of Units]] (SI) nchiyelezgero chiwemi, ndipo pali nthowa zinyake izo zikuzomerezgeka chomene (izo zikumanyikwa viŵi yayi kuluska SI) izo zikugwiriskirika nchito chomene mu vigaŵa vinyake, nga ni vigaŵa vya Gaussian vya magesi. Nangauli malango agho ghakulaŵilira nthowa ya metric ghakasintha pakujumpha kwa nyengo, ng’anamuro la mazuŵa ghano mu International System of Units likulongosora vimanyikwiro vya metric na vigaŵa vinkhondi na viŵiri vyakwamba: [[mita]] (m), [[kilogram]] (kg), [[second]] (s), [[ampere]] (A), [[kelvin]] (K), [[mole]] (mol), na [[candela]] (cd).<ref name="SI2019">{{Cite web|url=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf |archive-url=https://web.archive.org/web/20190530124226/https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf |archive-date=2019-05-30 |url-status=live|title=The International System of Units (SI), 9th Edition|date=2019|publisher=Bureau International des Poids et Mesures}}</ref> [[SI yakufumira ku yuniti]] ni zina lakusazgako vigaŵa vyakukhazikika, nga ni [[hertz]] (kuzungulira pa sekondi), [[Newton (yuniti)|newton]] (kg⋅m/s²), na [[tesla (yuniti)|tesla]] (1 kg⋅s⁻²⋅A⁻¹). Pa nkhani ya madigiri [[Celsius]] (°C), ni sikelo yakusinthika iyo yikufuma ku kelvin (273.15 K yikuyana na 0 °C apo nyengo ya 1 K yikuyana waka na nyengo ya 1 °C). Nthowa ya SI yikufuma ku nthowa yakale ya [[mita-kilogram-second]] (MKS) ya vigaŵa, nangauli vilongosolero vya vigaŵa vyakwamba vyasintha pakujumpha kwa nyengo. Lero, vigaŵa vyose vyakukhazikika vikulongosoreka na vinthu vyakuwoneka – na viyezgelero yayi mu kawonekero ka vinthu vyakuwoneka, nga umo vikaŵira kale. Nthowa zinyake zakupambanapambana za metric zikusazgapo nthowa ya centimeter–gram–second ya mayuniti, nthowa ya mita–tani–sekondi ya mayuniti, na nthowa ya gravitational metric. Chilichose chili na mayuniti gha metric ghambura kukolerana, ndipo vinyake mwa ndondomeko izi vikugwiriskirika nchito mu vigaŵa vichoko waka. Mayuniti ghanyake ghambura SI nga ni [[lita]] ghakulutilira kugwiliskirika nchito comene.<ref name="SIbrochure2026">{{Cite web |title=SI-Brochure-9 |url=https://www.bipm.org/en/si-brochure-9 |date=June 2026 |access-date=2026-06-08 |website=BIPM |language=en-US |doi=10.59161/AUEZ1291 |edition=4.01|pages=140–141}}</ref> ==Wonaniso== *[[Kutanthauzira kwa nthowa ya metric]] ==Ukaboni== {{reflist}} ==Malinki gha kuwaro== * {{Wikiversity inline|Using the Metric System}} {{Authority control}} [[Category:Nthowa ya metric| ]] 1cz98bu3sr7w5h5hpn1jpkw7qlaokhn 121836 121831 2026-09-08T12:34:30Z Viyowoyero-vya-Malaŵi 11606 121836 wikitext text/x-wiki {{Databox}} [[Nthowa yakupimira]] ni ndondomeko iyo mikhaliro yakuwoneka (nga ni utali, kulemera, kutentha, na vinyake) yingapimika na manambara. Pakati pa ndondomeko zinandi zakupimira, '''nthowa ya metric''' ([[ChiNgelezi]]: ''metric system''), panji '''ndondomeko ya metric''', yikung’anamura chimoza, chilichose chikuŵika pa mlingo seti ya vigaŵa vyakukhazikika na zina ilo likulongosora vigaŵa vikuruvikuru na vichoko chomene mwakugwiliskira ntchito vimanyikwiro vya vigaŵa vyakuchulukizga vyakuthemba pa decimal (nga ni ''[[Kilo-|kilo]] ''na ''[[Milli-|milli]]''). [[International System of Units]] (SI) nchiyelezgero chiwemi, ndipo pali nthowa zinyake izo zikuzomerezgeka chomene (izo zikumanyikwa viŵi yayi kuluska SI) izo zikugwiriskirika nchito chomene mu vigaŵa vinyake, nga ni vigaŵa vya Gaussian vya magesi. Nangauli malango agho ghakulaŵilira nthowa ya metric ghakasintha pakujumpha kwa nyengo, ng’anamuro la mazuŵa ghano mu International System of Units likulongosora vimanyikwiro vya metric na vigaŵa vinkhondi na viŵiri vyakwamba: [[mita]] (m), [[kilogram]] (kg), [[second]] (s), [[ampere]] (A), [[kelvin]] (K), [[mole]] (mol), na [[candela]] (cd).<ref name="SI2019">{{Cite web|url=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf |archive-url=https://web.archive.org/web/20190530124226/https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf |archive-date=2019-05-30 |url-status=live|title=The International System of Units (SI), 9th Edition|date=2019|publisher=Bureau International des Poids et Mesures}}</ref> [[SI yakufumira ku yuniti]] ni zina lakusazgako vigaŵa vyakukhazikika, nga ni [[hertz]] (kuzungulira pa sekondi), [[Newton (yuniti)|newton]] (kg⋅m/s²), na [[tesla (yuniti)|tesla]] (1 kg⋅s⁻²⋅A⁻¹). Pa nkhani ya madigiri [[Celsius]] (°C), ni sikelo yakusinthika iyo yikufuma ku kelvin (273.15 K yikuyana na 0 °C apo nyengo ya 1 K yikuyana waka na nyengo ya 1 °C). Nthowa ya SI yikufuma ku nthowa yakale ya [[mita-kilogram-second]] (MKS) ya vigaŵa, nangauli vilongosolero vya vigaŵa vyakwamba vyasintha pakujumpha kwa nyengo. Lero, vigaŵa vyose vyakukhazikika vikulongosoreka na vinthu vyakuwoneka – na viyezgelero yayi mu kawonekero ka vinthu vyakuwoneka, nga umo vikaŵira kale. Nthowa zinyake zakupambanapambana za metric zikusazgapo nthowa ya centimeter–gram–second ya mayuniti, nthowa ya mita–tani–sekondi ya mayuniti, na nthowa ya gravitational metric. Chilichose chili na mayuniti gha metric ghambura kukolerana, ndipo vinyake mwa ndondomeko izi vikugwiriskirika nchito mu vigaŵa vichoko waka. Mayuniti ghanyake ghambura SI nga ni [[lita]] ghakulutilira kugwiliskirika nchito comene.<ref name="SIbrochure2026">{{Cite web |title=SI-Brochure-9 |url=https://www.bipm.org/en/si-brochure-9 |date=June 2026 |access-date=2026-06-08 |website=BIPM |language=en-US |doi=10.59161/AUEZ1291 |edition=4.01|pages=140–141}}</ref> ==Wonaniso== *[[Kutanthauzira kwa nthowa ya metric]] ==Ukaboni== {{reflist}} ==Malinki gha kuwaro== * {{Wikiversity inline|Using the Metric System}} {{Authority control}} [[Category:Nthowa ya metric| ]] p99bw4ynvy76oufdgblie0no39ukwc5 121848 121836 2026-09-09T03:59:18Z Viyowoyero-vya-Malaŵi 11606 121848 wikitext text/x-wiki {{Databox}} [[Nthowa yakupimira]] ni ndondomeko iyo mikhaliro yakuwoneka (nga ni utali, kulemera, kutentha, na vinyake) yingapimika na manambara. Pakati pa ndondomeko zinandi zakupimira, '''nthowa ya metric''' ([[ChiNgelezi]]: ''metric system''), panji '''ndondomeko ya metric''', yikung’anamura chimoza, chilichose chikuŵika pa mlingo seti ya vigaŵa vyakukhazikika na zina ilo likulongosora vigaŵa vikuruvikuru na vichoko chomene mwakugwiliskira ntchito vimanyikwiro vya vigaŵa vyakuchulukizga vyakuthemba pa decimal (nga ni ''[[Kilo-|kilo]] ''na ''[[Milli-|milli]]''). [[International System of Units]] (SI) nchiyelezgero chiwemi, ndipo pali nthowa zinyake izo zikuzomerezgeka chomene (izo zikumanyikwa viŵi yayi kuluska SI) izo zikugwiriskirika nchito chomene mu vigaŵa vinyake, nga ni vigaŵa vya Gaussian vya magesi. Nangauli malango agho ghakulaŵilira nthowa ya metric ghakasintha pakujumpha kwa nyengo, ng’anamuro la mazuŵa ghano mu International System of Units likulongosora vimanyikwiro vya metric na vigaŵa vinkhondi na viŵiri vyakwamba: [[mita]] (m), [[kilogram]] (kg), [[second]] (s), [[ampere]] (A), [[kelvin]] (K), [[mole]] (mol), na [[candela]] (cd).<ref name="SI2019">{{Cite web|url=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf |archive-url=https://web.archive.org/web/20190530124226/https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf |archive-date=2019-05-30 |url-status=live|title=The International System of Units (SI), 9th Edition|date=2019|publisher=Bureau International des Poids et Mesures}}</ref> [[SI yakufumira ku yuniti]] ni zina lakusazgako vigaŵa vyakukhazikika, nga ni [[hertz]] (kuzungulira pa sekondi), [[Newton (yuniti)|newton]] (kg⋅m/s²), na [[tesla (yuniti)|tesla]] (1 kg⋅s⁻²⋅A⁻¹). Pa nkhani ya madigiri [[Celsius]] (°C), ni sikelo yakusinthika iyo yikufuma ku kelvin (273.15 K yikuyana na 0 °C apo nyengo ya 1 K yikuyana waka na nyengo ya 1 °C). Nthowa ya SI yikufuma ku nthowa yakale ya [[mita-kilogram-second]] (MKS) ya vigaŵa, nangauli vilongosolero vya vigaŵa vyakwamba vyasintha pakujumpha kwa nyengo. Lero, vigaŵa vyose vyakukhazikika vikulongosoreka na vinthu vyakuwoneka – na viyezgelero yayi mu kawonekero ka vinthu vyakuwoneka, nga umo vikaŵira kale. Nthowa zinyake zakupambanapambana za metric zikusazgapo nthowa ya centimeter–gram–second ya mayuniti, nthowa ya mita–tani–sekondi ya mayuniti, na nthowa ya gravitational metric. Chilichose chili na mayuniti gha metric ghambura kukolerana, ndipo vinyake mwa ndondomeko izi vikugwiriskirika nchito mu vigaŵa vichoko waka. Mayuniti ghanyake ghambura SI nga ni [[lita]] ghakulutilira kugwiliskirika nchito comene.<ref name="SIbrochure2026">{{Cite web |title=SI-Brochure-9 |url=https://www.bipm.org/en/si-brochure-9 |date=June 2026 |access-date=2026-06-08 |website=BIPM |language=en-US |doi=10.59161/AUEZ1291 |edition=4.01|pages=140–141}}</ref> ==Wonaniso== *[[Kutanthauzira kwa nthowa ya metric]] *[[Metrication]] ==Ukaboni== {{reflist}} ==Malinki gha kuwaro== * {{Wikiversity inline|Using the Metric System}} {{Authority control}} [[Category:Nthowa ya metric| ]] kl2mgur7b8hxn4ef5s9o700r9qc6q47 0 49561 121832 121828 2026-09-08T12:20:43Z Viyowoyero-vya-Malaŵi 11606 /* Metrication magulu na ŵamazaza */ 121832 wikitext text/x-wiki {{Revision}} Kutanthauzira yakulondezgapo yikupelekeka nga ni ndondomeko ya nthowa ya metric: '''[[Nthowa ya metric]]''' – [[Nthowa yakupimira|nthowa zakupimira]] zakupambanapambana zakukhwaskana mwakufwatuka izo zikulongosora umo zikambira ku ndondomeko ya kupimira ya decimal iyo yikayambiskika ku [[France]] pa nyengo ya [[French Revolution]]. == Mtundu wa nthowa ya metric == === Fundo yikuru ya nthowa ya metric === === Filosofe yakubisika === == Mayuniti ghakupimira == == Mbiri ya nthowa ya metric == === Mndandanda wa nyengo mbiri ya nthowa ya metric === === Mbiri ya metrication === === Kusintha kwa nthowa ya metric ya mbiri yakale === === Mbiri ya mayuniti vya metric === == Ndale za nthowa ya metric == == Munthazi mwa nthowa ya metric == == Metrication magulu na ŵamazaza == * [[US Metric Association]] (USA, 1916–sono) * [[Metric Commission]] (Canada, 1971–1985) * [[Metrication Board]] (Ufumu Ubanyi, 1969–1981) == Mabuku gha nthowa ya metric == * ''[[:en:Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States|Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States]]'' [https://web.archive.org/web/20160819195416/http://www.yale.edu/lawweb/avalon/jeffplan.htm malemba] ([[Thomas Jefferson]] 1790) == Ŵanthu awo ŵakuwovwira mu nthowa ya metric == * [[Simon Stevin]] (1548–1620) * [[Gabriel Mouton]] (1618–1694) * [[Marquis de Condorcet]] (1743–1794) * [[Pierre Méchain]] (1744–1804) * [[Pierre-Simon Laplace]] (1749–1827) * [[Jean Baptiste Joseph Delambre]] (1749–1822) * [[Adrien-Marie Legendre]] (1753–1834) * [[James Clerk Maxwell]] (1831–1879) * [[William Thomson, 1st Baron Kelvin]] (1824–1907) * [[Giovanni Giorgi]] (1871–1950) == Malinki gha kuwaro == {{Sister project links|Metric system}} * [https://www.metric-conversions.org/ Metric conversions] {{Outline footer}} [[Category:Nthowa ya metric]] 83wnpjxv9utzpk08ge64ekm4gavjrzk 121833 121832 2026-09-08T12:23:25Z Viyowoyero-vya-Malaŵi 11606 /* Filosofe yakubisika */ 121833 wikitext text/x-wiki {{Revision}} Kutanthauzira yakulondezgapo yikupelekeka nga ni ndondomeko ya nthowa ya metric: '''[[Nthowa ya metric]]''' – [[Nthowa yakupimira|nthowa zakupimira]] zakupambanapambana zakukhwaskana mwakufwatuka izo zikulongosora umo zikambira ku ndondomeko ya kupimira ya decimal iyo yikayambiskika ku [[France]] pa nyengo ya [[French Revolution]]. == Mtundu wa nthowa ya metric == === Fundo yikuru ya nthowa ya metric === === Filosofe yakubisika === Kudumbiskana kwa fundo zakuzirwa za nthowa ya metric (na ndondomeko zinyake zakupimira) kukusazgapo: *[[Coherence (mayuniti ghakupimira)]] *[[Realisation (metrology)]] == Mayuniti ghakupimira == == Mbiri ya nthowa ya metric == === Mndandanda wa nyengo mbiri ya nthowa ya metric === === Mbiri ya metrication === === Kusintha kwa nthowa ya metric ya mbiri yakale === === Mbiri ya mayuniti vya metric === == Ndale za nthowa ya metric == == Munthazi mwa nthowa ya metric == == Metrication magulu na ŵamazaza == * [[US Metric Association]] (USA, 1916–sono) * [[Metric Commission]] (Canada, 1971–1985) * [[Metrication Board]] (Ufumu Ubanyi, 1969–1981) == Mabuku gha nthowa ya metric == * ''[[:en:Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States|Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States]]'' [https://web.archive.org/web/20160819195416/http://www.yale.edu/lawweb/avalon/jeffplan.htm malemba] ([[Thomas Jefferson]] 1790) == Ŵanthu awo ŵakuwovwira mu nthowa ya metric == * [[Simon Stevin]] (1548–1620) * [[Gabriel Mouton]] (1618–1694) * [[Marquis de Condorcet]] (1743–1794) * [[Pierre Méchain]] (1744–1804) * [[Pierre-Simon Laplace]] (1749–1827) * [[Jean Baptiste Joseph Delambre]] (1749–1822) * [[Adrien-Marie Legendre]] (1753–1834) * [[James Clerk Maxwell]] (1831–1879) * [[William Thomson, 1st Baron Kelvin]] (1824–1907) * [[Giovanni Giorgi]] (1871–1950) == Malinki gha kuwaro == {{Sister project links|Metric system}} * [https://www.metric-conversions.org/ Metric conversions] {{Outline footer}} [[Category:Nthowa ya metric]] e9i0y1t4xuwzan7ywvj5c3y8caw6w65 121835 121833 2026-09-08T12:33:00Z Viyowoyero-vya-Malaŵi 11606 /* Mbiri ya nthowa ya metric */ 121835 wikitext text/x-wiki {{Revision}} Kutanthauzira yakulondezgapo yikupelekeka nga ni ndondomeko ya nthowa ya metric: '''[[Nthowa ya metric]]''' – [[Nthowa yakupimira|nthowa zakupimira]] zakupambanapambana zakukhwaskana mwakufwatuka izo zikulongosora umo zikambira ku ndondomeko ya kupimira ya decimal iyo yikayambiskika ku [[France]] pa nyengo ya [[French Revolution]]. == Mtundu wa nthowa ya metric == === Fundo yikuru ya nthowa ya metric === === Filosofe yakubisika === Kudumbiskana kwa fundo zakuzirwa za nthowa ya metric (na ndondomeko zinyake zakupimira) kukusazgapo: *[[Coherence (mayuniti ghakupimira)]] *[[Realisation (metrology)]] == Mayuniti ghakupimira == == Mbiri ya nthowa ya metric == [[Mbiri ya nthowa ya metric]] – nthowa ya metric yikapangika kufuma ku ndondomeko ya desimali ya kuyezga iyo yikazomerezgeka na France pamanyuma pa French Revolution. === Mndandanda wa nyengo mbiri ya nthowa ya metric === === Mbiri ya metrication === [[File:Metric and imperial systems (2019).svg|thumb|upright=1.3|Vyalo ivyo vikugwiriskira nchito nthowa ya [[Nthowa ya metric|metric]], [[Nthowa ya Imperial|imperial]] na [[Nthowa ya Chikhalidwe cha US|chikhalidwe cha US]] kufuma mu 2019.]] === Kusintha kwa nthowa ya metric ya mbiri yakale === === Mbiri ya mayuniti vya metric === == Ndale za nthowa ya metric == == Munthazi mwa nthowa ya metric == == Metrication magulu na ŵamazaza == * [[US Metric Association]] (USA, 1916–sono) * [[Metric Commission]] (Canada, 1971–1985) * [[Metrication Board]] (Ufumu Ubanyi, 1969–1981) == Mabuku gha nthowa ya metric == * ''[[:en:Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States|Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States]]'' [https://web.archive.org/web/20160819195416/http://www.yale.edu/lawweb/avalon/jeffplan.htm malemba] ([[Thomas Jefferson]] 1790) == Ŵanthu awo ŵakuwovwira mu nthowa ya metric == * [[Simon Stevin]] (1548–1620) * [[Gabriel Mouton]] (1618–1694) * [[Marquis de Condorcet]] (1743–1794) * [[Pierre Méchain]] (1744–1804) * [[Pierre-Simon Laplace]] (1749–1827) * [[Jean Baptiste Joseph Delambre]] (1749–1822) * [[Adrien-Marie Legendre]] (1753–1834) * [[James Clerk Maxwell]] (1831–1879) * [[William Thomson, 1st Baron Kelvin]] (1824–1907) * [[Giovanni Giorgi]] (1871–1950) == Malinki gha kuwaro == {{Sister project links|Metric system}} * [https://www.metric-conversions.org/ Metric conversions] {{Outline footer}} [[Category:Nthowa ya metric]] dfk20zme20oyqo19yvs8b8ca4o8z7ac 121852 121835 2026-09-09T05:24:59Z Viyowoyero-vya-Malaŵi 11606 121852 wikitext text/x-wiki {{Revision}} Kutanthauzira yakulondezgapo yikupelekeka nga ni ndondomeko ya nthowa ya metric: '''[[Nthowa ya metric]]''' – [[Nthowa yakupimira|nthowa zakupimira]] zakupambanapambana zakukhwaskana mwakufwatuka izo zikulongosora umo zikambira ku ndondomeko ya kupimira ya decimal iyo yikayambiskika ku [[France]] pa nyengo ya [[French Revolution]]. == Mtundu wa nthowa ya metric == === Fundo yikuru ya nthowa ya metric === === Filosofe yakubisika === Kudumbiskana kwa fundo zakuzirwa za nthowa ya metric (na ndondomeko zinyake zakupimira) kukusazgapo: *[[Coherence (mayuniti ghakupimira)]] *[[Realisation (metrology)]] == Mayuniti ghakupimira == == Mbiri ya nthowa ya metric == [[Mbiri ya nthowa ya metric]] – nthowa ya metric yikapangika kufuma ku ndondomeko ya desimali ya kuyezga iyo yikazomerezgeka na France pamanyuma pa French Revolution. === Mndandanda wa nyengo mbiri ya nthowa ya metric === === Mbiri ya metrication === [[File:Metric and imperial systems (2019).svg|thumb|upright=1.3|Vyalo ivyo vikugwiriskira nchito nthowa ya [[Nthowa ya metric|metric]], [[Nthowa ya imperial|imperial]] na [[Nthowa ya chikhalidwe cha US|chikhalidwe cha US]] kufuma mu 2019.]] === Kusintha kwa nthowa ya metric ya mbiri yakale === === Mbiri ya mayuniti vya metric === == Ndale za nthowa ya metric == == Munthazi mwa nthowa ya metric == == Metrication magulu na ŵamazaza == * [[US Metric Association]] (USA, 1916–sono) * [[Metric Commission]] (Canada, 1971–1985) * [[Metrication Board]] (Ufumu Ubanyi, 1969–1981) == Mabuku gha nthowa ya metric == * ''[[:en:Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States|Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States]]'' [https://web.archive.org/web/20160819195416/http://www.yale.edu/lawweb/avalon/jeffplan.htm malemba] ([[Thomas Jefferson]] 1790) == Ŵanthu awo ŵakuwovwira mu nthowa ya metric == * [[Simon Stevin]] (1548–1620) * [[Gabriel Mouton]] (1618–1694) * [[Marquis de Condorcet]] (1743–1794) * [[Pierre Méchain]] (1744–1804) * [[Pierre-Simon Laplace]] (1749–1827) * [[Jean Baptiste Joseph Delambre]] (1749–1822) * [[Adrien-Marie Legendre]] (1753–1834) * [[James Clerk Maxwell]] (1831–1879) * [[William Thomson, 1st Baron Kelvin]] (1824–1907) * [[Giovanni Giorgi]] (1871–1950) == Malinki gha kuwaro == {{Sister project links|Metric system}} * [https://www.metric-conversions.org/ Metric conversions] {{Outline footer}} [[Category:Nthowa ya metric]] 0xcalgokeq1zuq20zunxw8wnv7y0kwo 14 49563 121830 2026-09-08T12:15:03Z Viyowoyero-vya-Malaŵi 11606 Created page with "[[{{PAGENAME}}]]" 121830 wikitext text/x-wiki [[{{PAGENAME}}]] ewjikusk4kvxxflz6s1v2f1pd62lyq4 121856 121830 2026-09-09T05:36:59Z Viyowoyero-vya-Malaŵi 11606 121856 wikitext text/x-wiki [[{{PAGENAME}}]] [[Category:Nthowa yakupimira]] ljsl2g3p5mlt5d0yk1cdmcjkuvytep9 0 49564 121834 2026-09-08T12:26:59Z Viyowoyero-vya-Malaŵi 11606 Redirecting until proper article is created 121834 wikitext text/x-wiki #REDIRECT [[Kutanthauzira kwa nthowa ya metric#Mbiri ya nthowa ya metric]] ljzix6e56fanxsn6hc8domda02pijvz 0 49565 121844 2026-09-09T03:56:14Z Viyowoyero-vya-Malaŵi 11606 Created page with "[[File:Metrication by year map.svg|thumb|upright=1.35|World map, colour-coded to show the years the countries started the process of official conversion to the metric system. Using data from PhD thesis by Hector Vera and NIST.]] '''Metrication''' panji '''metrification''' ni nchito panji ndondomeko ya kusinthira ku [[nthowa ya metric]] ya kuyezga.<ref>https://www.oed.com/search/dictionary/?q=Metrication</ref> Pa charu chose, vyaru vyasintha kufuma ku vipimilo vya ku malo..." 121844 wikitext text/x-wiki [[File:Metrication by year map.svg|thumb|upright=1.35|World map, colour-coded to show the years the countries started the process of official conversion to the metric system. Using data from PhD thesis by Hector Vera and NIST.]] '''Metrication''' panji '''metrification''' ni nchito panji ndondomeko ya kusinthira ku [[nthowa ya metric]] ya kuyezga.<ref>https://www.oed.com/search/dictionary/?q=Metrication</ref> Pa charu chose, vyaru vyasintha kufuma ku vipimilo vya ku malo na vya chikhalidwe kuya ku nthowa ya metric. Nthowa iyi yikamba ku [[France]] mu vilimika vya m’ma 1790 ndipo yalutilira kwa vyaka vyakujumpha 200. Kufuma mu 2011, pafupifupi 95% ya ŵanthu ŵa pa charu chose ŵakakhalanga mu vyaru ivyo nthowa ya metric ndiyo yikaŵa nthowa yimoza pera yakupimira.<ref name=":9">{{cite thesis |id={{ProQuest|924487292}} |last1=Vera |first1=Hector |date=2012 |title=The Social Life of Measures Metrication in the United States and Mexico, 1789–2004 |at= p. 49, ch 2}}</ref> Nangauli vili nthena, vyaru vinyake na vigaŵa vinyake vikusintha panji vyasankha kuleka kuzomerezga ndondomeko ya metric. ==Ukaboni== {{reflist}} [[Category:Metrication| ]] t0pybm2g7qtd7wtnnky5eb9odknm4nl 121846 121844 2026-09-09T03:57:17Z Viyowoyero-vya-Malaŵi 11606 121846 wikitext text/x-wiki [[File:Metrication by year map.svg|thumb|upright=1.35|Mapu ya charu chose, yakulembeka na mitundu yakupambanapambana kuti yilongore vyaka ivyo vyaru ivi vikambira kusintha kwakuzomerezgeka ku nthowa ya metric. Kugwiriskira ncito data kufuma ku PhD ya Hector Vera na NIST.]] '''Metrication''' panji '''metrification''' ni nchito panji ndondomeko ya kusinthira ku [[nthowa ya metric]] ya kuyezga.<ref>https://www.oed.com/search/dictionary/?q=Metrication</ref> Pa charu chose, vyaru vyasintha kufuma ku vipimilo vya ku malo na vya chikhalidwe kuya ku nthowa ya metric. Nthowa iyi yikamba ku [[France]] mu vilimika vya m’ma 1790 ndipo yalutilira kwa vyaka vyakujumpha 200. Kufuma mu 2011, pafupifupi 95% ya ŵanthu ŵa pa charu chose ŵakakhalanga mu vyaru ivyo nthowa ya metric ndiyo yikaŵa nthowa yimoza pera yakupimira.<ref name=":9">{{cite thesis |id={{ProQuest|924487292}} |last1=Vera |first1=Hector |date=2012 |title=The Social Life of Measures Metrication in the United States and Mexico, 1789–2004 |at= p. 49, ch 2}}</ref> Nangauli vili nthena, vyaru vinyake na vigaŵa vinyake vikusintha panji vyasankha kuleka kuzomerezga ndondomeko ya metric. ==Ukaboni== {{reflist}} [[Category:Metrication| ]] gf232p3ggdl21wt22580ywzhs2e4ykn 121851 121846 2026-09-09T04:06:34Z Viyowoyero-vya-Malaŵi 11606 121851 wikitext text/x-wiki [[File:Metrication by year map.svg|thumb|upright=1.35|Mapu ya charu chose, yakulembeka na mitundu yakupambanapambana kuti yilongore vyaka ivyo vyaru ivi vikambira kusintha kwakuzomerezgeka ku nthowa ya metric. Kugwiriskira ncito data kufuma ku PhD ya Hector Vera na NIST.]] '''Metrication''' panji '''metrification''' ni nchito panji ndondomeko ya kusinthira ku [[nthowa ya metric]] ya kuyezga.<ref>https://www.oed.com/search/dictionary/?q=Metrication</ref> Pa charu chose, vyaru vyasintha kufuma ku vipimilo vya ku malo na vya chikhalidwe kuya ku nthowa ya metric. Nthowa iyi yikamba ku [[France]] mu vilimika vya m’ma 1790 ndipo yalutilira kwa vyaka vyakujumpha 200. Kufuma mu 2011, pafupifupi 95% ya ŵanthu ŵa pa charu chose ŵakakhalanga mu vyaru ivyo nthowa ya metric ndiyo yikaŵa nthowa yimoza pera yakupimira.<ref name=":9">{{cite thesis |id={{ProQuest|924487292}} |last1=Vera |first1=Hector |date=2012 |title=The Social Life of Measures Metrication in the United States and Mexico, 1789–2004 |at= p. 49, ch 2}}</ref> Nangauli vili nthena, vyaru vinyake na vigaŵa vinyake vikusintha panji vyasankha kuleka kuzomerezga nthowa ya metric. ==Ukaboni== {{reflist}} [[Category:Metrication| ]] 7pcm0cmg65mt870ddc9ysl8gk15ri4n 1 49566 121845 2026-09-09T03:56:32Z Viyowoyero-vya-Malaŵi 11606 Created page with "{{talk header}}" 121845 wikitext text/x-wiki {{talk header}} frwy0ondkbaajki04xjgq9mnxpg47li 14 49567 121847 2026-09-09T03:58:29Z Viyowoyero-vya-Malaŵi 11606 Created page with "[[{{PAGENAME}}]] [[Category:Nthowa ya metric]]" 121847 wikitext text/x-wiki [[{{PAGENAME}}]] [[Category:Nthowa ya metric]] 51gi8wrfla7t3kinls59bdb3t92894y 0 49568 121849 2026-09-09T04:02:06Z Viyowoyero-vya-Malaŵi 11606 Redirected page to [[Metrication]] 121849 wikitext text/x-wiki #REDIRECT [[Metrication]] klbxnk2bsqqdwifuwil91gux0jmhlmg 0 49569 121850 2026-09-09T04:02:43Z Viyowoyero-vya-Malaŵi 11606 Redirected page to [[Nthowa ya metric]] 121850 wikitext text/x-wiki #REDIRECT [[Nthowa ya metric]] n2o789ewuvg5s0nh2ooiyahwdj6aqxc 0 49570 121853 2026-09-09T05:35:41Z Viyowoyero-vya-Malaŵi 11606 Created page with "{{Databox}} '''Nthowa ya imperial''' (ChiNgelezi: ''imperial system'') ni [[nthowa yakupimira]] iyo yikalongosoreka pakwamba mu dango la [[Ufumu Ubanyi]] [[Weights and Measures Act 1824]] ndipo ilo likalutilira kupangika kwizira mu malango ghanandi gha Weights and Measures Act na kusintha kwake. Nthowa ya imperial yikanjira mu malo gha [[Muyeso wa Winchester|Winchester Standards]], iyo yikaŵa kuti yikugwira ntchito kufuma mu 1588 m'paka 1825.<ref>{{cite book|author=Cha..." 121853 wikitext text/x-wiki {{Databox}} '''Nthowa ya imperial''' (ChiNgelezi: ''imperial system'') ni [[nthowa yakupimira]] iyo yikalongosoreka pakwamba mu dango la [[Ufumu Ubanyi]] [[Weights and Measures Act 1824]] ndipo ilo likalutilira kupangika kwizira mu malango ghanandi gha Weights and Measures Act na kusintha kwake. Nthowa ya imperial yikanjira mu malo gha [[Muyeso wa Winchester|Winchester Standards]], iyo yikaŵa kuti yikugwira ntchito kufuma mu 1588 m'paka 1825.<ref>{{cite book|author=Chaney, Henry James|title=A Practical Treatise on the Standard Weights and Measures in Use in the British Empire with some account of the metric system|url=https://archive.org/details/ourweightsandme00changoog|access-date=11 September 2016|date=1897|publisher=Eyre and Spottiswoode|page=[https://archive.org/details/ourweightsandme00changoog/page/n11 3]}}</ref> Nthowa iyi yikamba kugwiliskirika ntchito mu Ufumu Ubanyi mu 1826. ==Ukaboni== {{reflist}} ==Malinki gha kuwaro== {{Commons category|British Imperial units}} * [http://bwma.org.uk British Weights And Measures Association] * {{Deprecated archive|url=https://archive.today/20070224102425/http://laws.justice.gc.ca/en/ShowFullDoc/cs/W-6///en|title=Canada Weights and Measures Act 1970-71-72|sec=el}} * [https://web.archive.org/web/20061126120208/http://ts.nist.gov/WeightsAndMeasures/Publications/upload/h4402_appenc.pdf General table of units of measure – NIST – pdf] * [http://www.unc.edu/~rowlett/units/ How Many? A Dictionary of Units of Measurement] {{Webarchive|url=https://web.archive.org/web/20181010153750/http://www.unc.edu/~rowlett/units/ |date=10 October 2018 }} * {{UK SI|year=1995|number=1804|title=Units of Measurement Regulations 1995}} [[Category:Nthowa ya imperial| ]] taavmrwxva6l2a8q1htbd50kicfyui3 121854 121853 2026-09-09T05:35:55Z Viyowoyero-vya-Malaŵi 11606 121854 wikitext text/x-wiki {{Databox}} '''Nthowa ya imperial''' (ChiNgelezi: ''imperial system'') ni [[nthowa yakupimira]] iyo yikalongosoreka pakwamba mu dango la [[Ufumu Ubanyi]] [[Weights and Measures Act 1824]] ndipo ilo likalutilira kupangika kwizira mu malango ghanandi gha Weights and Measures Act na kusintha kwake. Nthowa ya imperial yikanjira mu malo gha [[Muyeso wa Winchester|Winchester Standards]], iyo yikaŵa kuti yikugwira ntchito kufuma mu 1588 m'paka 1825.<ref>{{cite book|author=Chaney, Henry James|title=A Practical Treatise on the Standard Weights and Measures in Use in the British Empire with some account of the metric system|url=https://archive.org/details/ourweightsandme00changoog|access-date=11 September 2016|date=1897|publisher=Eyre and Spottiswoode|page=[https://archive.org/details/ourweightsandme00changoog/page/n11 3]}}</ref> Nthowa iyi yikamba kugwiliskirika ntchito mu Ufumu Ubanyi mu 1826. ==Ukaboni== {{reflist}} ==Malinki gha kuwaro== {{Commons category|British Imperial units}} * [http://bwma.org.uk British Weights And Measures Association] * [https://web.archive.org/web/20061126120208/http://ts.nist.gov/WeightsAndMeasures/Publications/upload/h4402_appenc.pdf General table of units of measure – NIST – pdf] * [http://www.unc.edu/~rowlett/units/ How Many? A Dictionary of Units of Measurement] {{Webarchive|url=https://web.archive.org/web/20181010153750/http://www.unc.edu/~rowlett/units/ |date=10 October 2018 }} [[Category:Nthowa ya imperial| ]] 0vxw7ld11eo8b527jvdbeb3im9urk34 121860 121854 2026-09-09T05:45:36Z Viyowoyero-vya-Malaŵi 11606 121860 wikitext text/x-wiki {{Databox}} '''Nthowa ya imperial''' ([[ChiNgelezi]]: ''imperial system'') ni [[nthowa yakupimira]] iyo yikalongosoreka pakwamba mu dango la [[Ufumu Ubanyi]] [[Weights and Measures Act 1824]] ndipo ilo likalutilira kupangika kwizira mu malango ghanandi gha Weights and Measures Act na kusintha kwake. Nthowa ya imperial yikanjira mu malo gha [[Muyeso wa Winchester|Winchester Standards]], iyo yikaŵa kuti yikugwira ntchito kufuma mu 1588 m'paka 1825.<ref>{{cite book|author=Chaney, Henry James|title=A Practical Treatise on the Standard Weights and Measures in Use in the British Empire with some account of the metric system|url=https://archive.org/details/ourweightsandme00changoog|access-date=11 September 2016|date=1897|publisher=Eyre and Spottiswoode|page=[https://archive.org/details/ourweightsandme00changoog/page/n11 3]}}</ref> Nthowa iyi yikamba kugwiliskirika ntchito mu Ufumu Ubanyi mu 1826. ==Ukaboni== {{reflist}} ==Malinki gha kuwaro== {{Commons category|British Imperial units}} * [http://bwma.org.uk British Weights And Measures Association] * [https://web.archive.org/web/20061126120208/http://ts.nist.gov/WeightsAndMeasures/Publications/upload/h4402_appenc.pdf General table of units of measure – NIST – pdf] * [http://www.unc.edu/~rowlett/units/ How Many? A Dictionary of Units of Measurement] {{Webarchive|url=https://web.archive.org/web/20181010153750/http://www.unc.edu/~rowlett/units/ |date=10 October 2018 }} [[Category:Nthowa ya imperial| ]] d4lmmsx5mkjrs0lr8ykrs4pingxlblv 1 49571 121855 2026-09-09T05:36:09Z Viyowoyero-vya-Malaŵi 11606 Created page with "{{talk header}}" 121855 wikitext text/x-wiki {{talk header}} frwy0ondkbaajki04xjgq9mnxpg47li 14 49572 121857 2026-09-09T05:37:01Z Viyowoyero-vya-Malaŵi 11606 Created page with "[[{{PAGENAME}}]] [[Category:Nthowa yakupimira]]" 121857 wikitext text/x-wiki [[{{PAGENAME}}]] [[Category:Nthowa yakupimira]] ljsl2g3p5mlt5d0yk1cdmcjkuvytep9 14 49573 121858 2026-09-09T05:37:15Z Viyowoyero-vya-Malaŵi 11606 Created page with "{{PAGENAME}}" 121858 wikitext text/x-wiki {{PAGENAME}} ql7em3iplcfeaiu8hvtxv0k9gq9mbec 0 49574 121859 2026-09-09T05:43:40Z Viyowoyero-vya-Malaŵi 11606 Redirected page to [[Nthowa ya imperial]] 121859 wikitext text/x-wiki #REDIRECT [[Nthowa ya imperial]] j8hzudmenntib7gmfftimocsjgtdggt 4 49575 121861 2026-09-09T07:05:12Z Tumbuka Arch 6863 Created page with "'''Mndandanda uwu ngwakukhwaskana na charu cha [[Zambia]]''' <div style="float:left;margin-right:0.9em"> [[File:Flag of Zambia.svg|thumb|left|Mbendela ya [[Zambia]]]] </div> * [[1888]] - Chigaŵa cha sono cha [[Zambia]] chikaŵa pasi pa mazaza gha [[United Kingdom|Britain]] ndipo chikazgoka chigaŵa chakuwusikika na Britain.<br> * [[1911]] - [[Northern Rhodesia]] yikapangika nga ni chigaŵa chakuwusika na [[British South Africa Company]].<br> * [[1924]] - Boma la Br..." 121861 wikitext text/x-wiki '''Mndandanda uwu ngwakukhwaskana na charu cha [[Zambia]]''' <div style="float:left;margin-right:0.9em"> [[File:Flag of Zambia.svg|thumb|left|Mbendela ya [[Zambia]]]] </div> * [[1888]] - Chigaŵa cha sono cha [[Zambia]] chikaŵa pasi pa mazaza gha [[United Kingdom|Britain]] ndipo chikazgoka chigaŵa chakuwusikika na Britain.<br> * [[1911]] - [[Northern Rhodesia]] yikapangika nga ni chigaŵa chakuwusika na [[British South Africa Company]].<br> * [[1924]] - Boma la Britain likatora mazaza gha [[Northern Rhodesia]] kufuma ku British South Africa Company.<br> * [[1948]] - [[Northern Rhodesia Congress]] yikakhazikika, iyo yikazgoka chigaŵa chakuzirwa pa kulimbikira wanangwa wa ŵanthu ŵa mu Africa.<br> * [[1953-08-01|1953]] - [[Northern Rhodesia]] yikamba kuŵa chigaŵa cha [[Federation of Rhodesia and Nyasaland|Federation of Rhodesia na Nyasaland]].<br> * [[1963-12-31|1963]] - [[Federation of Rhodesia and Nyasaland|Federation ya Rhodesia na Nyasaland]] yikamara.<br> * [[1964-10-24|1964]] - [[Zambia]] yikapokera wanangwa kufuma ku [[United Kingdom|Britain]], ndipo [[Kenneth Kaunda]] wakaŵa pulezidenti wakwamba.<br> * [[1991-11-02|1991]] - [[Frederick Chiluba]] wakasankhika kuŵa pulezidenti, ndipo [[Movement for Multi-Party Democracy]] yikathereska [[United National Independence Party]].<br> * [[2011-09-23|2011]] - [[Michael Sata]] wakasankhika kuŵa pulezidenti wa Zambia.<br> * [[2021-08-24|2021]] - [[Hakainde Hichilema]] wakasankhika kuŵa pulezidenti wa Zambia kufuma ku [[United Party for National Development]].<br> <!--HooksEnd--> {{flatlist|class=dyk-footer noprint|style=margin-top:0.5em; text-align:right;}} {{endflatlist}} <noinclude>[[Category:Mndandanda wa nyengo za vyakuchitika mu mwezi wa Ogasiti]]</noinclude> <noinclude>[[Category:Vyakulemba vya pa chikaya cha Chitumbuka]]</noinclude> 9egmmk3y5qy5prgoqq8qw2kwrpbpwnw 4 49576 121862 2026-09-09T07:05:19Z Tumbuka Arch 6863 Created page with "'''Mndandanda uwu ngwakukhwaskana na charu cha [[Zambia]]''' <div style="float:left;margin-right:0.9em"> [[File:Flag of Zambia.svg|thumb|left|Mbendela ya [[Zambia]]]] </div> * [[1888]] - Chigaŵa cha sono cha [[Zambia]] chikaŵa pasi pa mazaza gha [[United Kingdom|Britain]] ndipo chikazgoka chigaŵa chakuwusikika na Britain.<br> * [[1911]] - [[Northern Rhodesia]] yikapangika nga ni chigaŵa chakuwusika na [[British South Africa Company]].<br> * [[1924]] - Boma la Br..." 121862 wikitext text/x-wiki '''Mndandanda uwu ngwakukhwaskana na charu cha [[Zambia]]''' <div style="float:left;margin-right:0.9em"> [[File:Flag of Zambia.svg|thumb|left|Mbendela ya [[Zambia]]]] </div> * [[1888]] - Chigaŵa cha sono cha [[Zambia]] chikaŵa pasi pa mazaza gha [[United Kingdom|Britain]] ndipo chikazgoka chigaŵa chakuwusikika na Britain.<br> * [[1911]] - [[Northern Rhodesia]] yikapangika nga ni chigaŵa chakuwusika na [[British South Africa Company]].<br> * [[1924]] - Boma la Britain likatora mazaza gha [[Northern Rhodesia]] kufuma ku British South Africa Company.<br> * [[1948]] - [[Northern Rhodesia Congress]] yikakhazikika, iyo yikazgoka chigaŵa chakuzirwa pa kulimbikira wanangwa wa ŵanthu ŵa mu Africa.<br> * [[1953-08-01|1953]] - [[Northern Rhodesia]] yikamba kuŵa chigaŵa cha [[Federation of Rhodesia and Nyasaland|Federation of Rhodesia na Nyasaland]].<br> * [[1963-12-31|1963]] - [[Federation of Rhodesia and Nyasaland|Federation ya Rhodesia na Nyasaland]] yikamara.<br> * [[1964-10-24|1964]] - [[Zambia]] yikapokera wanangwa kufuma ku [[United Kingdom|Britain]], ndipo [[Kenneth Kaunda]] wakaŵa pulezidenti wakwamba.<br> * [[1991-11-02|1991]] - [[Frederick Chiluba]] wakasankhika kuŵa pulezidenti, ndipo [[Movement for Multi-Party Democracy]] yikathereska [[United National Independence Party]].<br> * [[2011-09-23|2011]] - [[Michael Sata]] wakasankhika kuŵa pulezidenti wa Zambia.<br> * [[2021-08-24|2021]] - [[Hakainde Hichilema]] wakasankhika kuŵa pulezidenti wa Zambia kufuma ku [[United Party for National Development]].<br> <!--HooksEnd--> {{flatlist|class=dyk-footer noprint|style=margin-top:0.5em; text-align:right;}} {{endflatlist}} <noinclude>[[Category:Mndandanda wa nyengo za vyakuchitika mu mwezi wa Ogasiti]]</noinclude> <noinclude>[[Category:Vyakulemba vya pa chikaya cha Chitumbuka]]</noinclude> 9egmmk3y5qy5prgoqq8qw2kwrpbpwnw 0 49577 121864 2026-09-09T09:14:32Z Anthonymunthali44 5642 Created by translating the page "[[:en:Special:Redirect/revision/1351186760|Agricultural science]]" 121864 wikitext text/x-wiki mukati mwa vyaka vya mu ma 1700, Johann Friedrich Mayer wakayezgayezga kugwiliskira nchito gypsum ( calcium sulfate iyo yili na maji ) kuŵa feteleza . th5u9ayo08m6iqcpymway0ldjnt6hhx