Tudayt

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'''Tudayt''' d [[ajjed|ddin]] amezwaru i deg ttamnen yudan belli yella yiǧ n  [[Yillu|Yellu]] 

Isem Rebbi s [[tɛebrit]] d יהוה (YHWH), maca udayen ur zmiren ara ad neṭqen isem-agi, axaṭer ɣur-sen ḥram. Inin nitni אדני ''adonay'' ('agellid-iw') deg tẓallit d השם ''Hacem'' ('Isem' s tmaziɣt) deg wawal.

Rebbi deg tudayt yesɛa lemluk i t-yettɛawanen, yuzen rrusel ɣur medden akken ad ttamnen yi-s. Yahweh yextar agdud : agdud n [[israyil]] akken ad zzuzren awal-is.

Udayen ttganin lmasiḥ,ara ten-iselek d ad yebnu tamurt n Israyil tamqqrant: Erezt Israyil, lmasiḥ-agi ɣur-s tazmert n wessidir wid yemmuten. Udayen ur ttamnen ara belli [[Ɛisa]] d lmasiḥ axaṭer ur yezmir ad yexdem ayen yettwuran deg wedlis-nsen ([[turat]]), ur yebni ara tamurt n israyil tameqqrant, ur ten-yeslik ara seg ifassen n Rruman, tella daɣen yiwet tamacahutt ɣef Ɛisa sɣur imasiḥiyen, mi asen-d-yenna bell netta d lmasiḥ, udayen ṭṭfen-t rnu ddan yid-es ɣer tameqqbert, nnan-as : &quot;ssidir wid yemmuten!&quot;. Udayen n tura ur qbilen ara Ɛisa d lmasiḥ axaṭer deg [[tamasiḥt|tmasiḥt]], Ɛisa d mmi-s n Rebbi, ɣur Udayen, Rebbi ur yesɛi mmi-s.

Mazal ar tura udayen ttganin lmasiḥ. Yuɣ lḥal, udayen xelqen tamurt n Israyil mebla tallalt n lmasiḥ deg 1948, kra n wudayen nnan-d d akken ayen-agi d leḥram, yessefk ad gganin lmasiḥ.

[[Taggayt:Ajjed]]</text>
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  <page>
    <title>Tanzeggit</title>
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'''Tanzeggit''' d tigezmi tameqrant ger igzumen n [[tusnakt]] d win i izerwen [[tawella|tiwellatin]] neɣ Udmawen deg [[Tallunt|tallunin]] s myal [[tasekta]], deg tsekta Tis kraḍ (3) nezmar ad nemmeslay ɣef [[tenzeggit tuklidt]]. Ass-a ur nezmir ad d nesbin tilisa yellan ger tenzeggit akk d [[Asebrurez|wesebrurez]] neɣ d [[aljiber|uljiber]], acku ur nezmir ad nemmeslay ɣef [[Tanzeggit taljibirt|tenzeggit taljibirt]] ma yella ur d-neddim ara kra din kra da.

Tanzeggit diɣen d tafurk n tusnakt i izerrwen talɣiwin, tallunin, imeccaqen, tiɣmar d wassaɣen gar tneqqiḍin d yiḥricen n talɣiwin. Tesɛa azal deg usket n wakal d lebni, maca tuɣal daɣen d taɣult tamatut n tusnakt i yezmer ad tzerrew tallunin ur nezmir ara ad nwali s wallen, neɣ tallunin i yesɛan ugar n kraḍ n tsektiwin.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-16 11-19-35.png|centré|553x553px]]

== 1. Amezruy n tenzeggit ==
Awal agraɣlan géométrie yekka-d seg yigrigiyen i d-yemmalen asket n wakal. Isketen d yisiḍen inzeggane ttwasqedcen deg Maṣer, Mezupuṭamya d tɣermiwin nniḍen uqbel tanzeggit n Yigrigiyen. Ur ilaq ara ad nerṛ tanzeggit meṛṛa d asnulfu n yiwen ugdud kan.
{| class=&quot;wikitable&quot;
|+
!Tallit
!Amhaz agenjdan
|-
|Taglest
|Asket n wakal, lebni, asiḍen n teɣzi, n wanrar d ubleɣ.
|-
|Tasut tis 3 uqbel
tallit-nneɣ
|Aklid deg Iskandariya yesdukkel tizrawin deg &quot;Iferdisen&quot;.
|-
|Tallit talemmast
|Tigawt n yimusnawen deg tmura n Tineslemt, Lehend d Cinwa: asektiɣmer(trigonométrie), asali d
tsenallunt.
|-
|Tasut tis 17
|Descartes d Fermat qqnen talɣiwin ɣer imsidag d tegdiwin.
|-
|Tasut tis 19
|Lobachevsky d Bolyai snernan tanzeggit taknudemt; Gauss d Riemann snernan tazrawt n
tiknit d tallunin.
|-
|1872 d mbeɛd
|Klein yeskan azal n yibeddilen d yigrawen; Hilbert yessegzi lsas s yinagrawen n yigejdan.
|-
|Tasut tis 20–21
|Tanzeggit taljibṛant, taneẓlayt, tukrist, asiḍen s uselkim d uẓeṭṭa n twuriwin gar tfurka.
|}
&quot;'''Iferdisen'''&quot; n Aklid yesseqdac isbaduten d yigejdan iwakken ad yebnu isekkuden. Abrid-a yesɛa tazrirt tameqqrant deg tusnakt. Maca tanzeggit tamirant ur teqqim ara deg yigejdan n Aklid: tazrawt n umṣadaɣ tewwi-d timusniwin ɣef tallunin nniḍen. Tanzeggit tamirant tettawi ula d tallunin yellan deg tfizikt, isefka, tigniwin d yisiḍen. Amezruy-is d anerni n yisental d terrayin, mačči d asemselsi n yiwet n tanzeggit s tayeḍ kan.

== 2. Isbaduten, igejdan d usfukel ==
Asbadu yessegza tamiḍrant s wawalen yettwasnen. Agejdi d tafyirt i neqqbel deg yiwen unagraw war asfukel deg unagraw-nni. Asekkud(tiẓri) d ayen ara d-nsuffeɣ seg yigejdan d yisekkuden yettwasfuklen yakan.

Deg umedya n Aklid, yezmer ad yettwabnu yiɣil n teɣda gar snat n tneqqiḍin, ad yettwasɣezef yiɣil, ad tettwabnu twinest s wammas d waqqar yettwabedren. Yella daɣen agejdi ɣef tɣmar timaɣudin d wayen yeqqnen ɣer umṣadaɣ.

=== Amedya n useɣẓen ===
Deg uɣawas n Aklid, i teneqqiṭ '''P''' i ur nelli ara ɣef taɣda '''d''', tella yiwet kan n teɣda iɛeddan seg '''P''' ur nettmagar ara '''d'''. Talɣa-a n yigejdi n umṣadaɣ tettwassen s yisem n '''Playfair'''; d talɣa tagdazalt i yigejdi wis semmus n Aklid deg lsas n tanzeggit tamagnut.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-18 09-56-11.png|centré]]
&lt;small&gt;Tugna 2. Tiɣmert d wassaɣ n umṣadaɣ. Tigniwin ttɛawanent deg tɣuri n yisekkuden; isfukal ilaq ad d-begnen ayɣer iiṣeḥḥa wassaɣ.&lt;/small&gt;

Deg tugna, tineqqiḍin ttbanent sɛant tehri, izirigen sɛan tuzert, imeccaqen zemren ur ttwaḥerzen ara s tiseddi. Deg tusnakt, taneqqiṭ ur tesɛi ara tehri. Ihi ma tugna teskan-d belli sin n yimeccaqen d igdazalen, ayen-a ur d-yettawi ara asfukel.

== 3. Taneqqiṭ, taɣda d tallunt ==
Taneqqiṭ d amḍiq war tehri; taɣda tettwasɣezef deg sin yinumak war tilisa; iɣil n teɣda yesɛa sin n yixfawen; tazinaɣda tesɛa yiwen n yixef, tettwasɣezef deg yiwen unamek. Aɣawas d tajumma ilweɣ i deg yezmer ad yili wudlif s sin n yimsidag.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-19 12-18-47.png|centré|611x611px]]
&lt;small&gt;Tugna 3. Tisektiwin 0, 1, 2 d 3. Aɣawas n tugna d amur ifuken kan; aɣawas n tusnakt ur yesɛi ara tilisa.&lt;/small&gt;

Tasekta n tallunt tettawi amḍan n yimsidag ilelliyen i ilaqen iwakken ad nesbadu amḍiq. Deg taɣda, yiwen x ikfa; deg uɣawas, nesra (x,y); deg tallunt s kraḍ n tsektiwin, nesra (x,y,z). Tasekta ur tɛelliq ara ɣef wamek ara d-nsuneɣ talɣa: amaḍal s tajumma kan yesɛa snat n tsektiwin, ɣas ma yettwaseknen deg tallunt s kraḍ.

ℝⁿ = {(x₁, x₂, …, xₙ) : xᵢ d imḍanen ilawen}

Tallunin s n &gt; 3 ttwasqedcent deg tusnakt d yisefka. Ma yal amedya n yisefka yesɛa 10 n yimuttiyen ilelliyen, yezmer ad yettwagenses s tneqqiṭ deg ℝ¹⁰. Ayen-a ur d-yemmal ara belli nezmer ad t-nwali s wallen; imsidag d yilugan fkan-d allalen n tazrawt.

=== Tajumma d wanrar ===
Tajumma d talɣa n snat n tsektiwin; anrar d asket-is. S yiwet n tɣawsa, takurt tesɛa daxel-is d ubleɣ, ma amaḍal d tajumma n rrif-is. Asbadu n wayen nzerrew yesɛa azal uqbel yal asiḍen.

== 4. Ikerdisen d usekkud n Pythagore ==
Akerdis yesɛa kraḍ n yidis, kraḍ n tqacucin d kraḍ n tiɣmar. Deg uɣawas n Aklid, timernit n tɣmar-is d 180°. Akerdis agdudisan yesɛa kraḍ n yidis igdazalen; akerdis akendis yesɛa ma drus sin n yidis igdazalen; akerdis amaɣud yesɛa yiwet n tiɣmert n 90°.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-20 11-55-53.png|centré|667x667px]]
&lt;small&gt;Tugna 4. Tama taẓelmaḍt: anrar n umkuẓ ɣef yidis 5 d 25 = 9 + 16. Tama tayeffust: kuẓ n yikerdisen s yidis a d b, d umkuẓ alemmas s yidis c.&lt;/small&gt;

'''a² + b² = c², ma c d alubdis n ukerdis amaɣud''' 

Asfukel n tugna tayeffust: anrar n umkuẓ ameqqran d (a+b)². Kuẓ n yikerdisen sɛan anrar 4 × ab/2 = 2ab. Ayen i d-yeqqimen d c²; ihi c² = (a+b)² − 2ab = a²+b². Ayen-a d aseɣẓen s wanrar, mačči d asket n teɣzi ɣef tugna. Asekkud-a yesɛa daɣen talɣa tamsuɣalt: ma a²+b²=c² deg ukerdis, tiɣmert i d-yezzin i c d 90°. Deg tanzeggit taknudemt neɣ ɣef umaḍal, tanfalit-a ur tettwasemres ara akka war abeddel.

== 5. Tales(Thales) d tarwast ==
Sin n yikerdisen imarwasen sɛan tiɣmar igdazalen d yidis akniwen s yiwen wassaɣ. Ma tasɣent tessenɣas neɣ tessemɣer akk imeccaqen s yiwen umuskir k &gt; 0, tḥerrez tiɣmar d talɣa. D tarwast.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-21 10-35-44.png|centré|676x676px]]
&lt;small&gt;Tugna 5. DE d BC msadaɣen, ihi ikerdisen ADE d ABC d imarwasen. Deg tugna tayeffust, amuskir n teɣzi d 2; win n&lt;/small&gt; &lt;small&gt;wanrar d 4.&lt;/small&gt;

'''AD/AB = AE/AC = DE/BC'''

Deg umedya, A d yiwet n tqacuct n sin yikerdisen; D yella ɣef [AB], E ɣef [AC], yerna DE ∥ BC. Ihi assaɣ n ''Thales'' yessegza ayɣer akk ibḍan-a d igdazalen. Ma nessen kra n teɣziwin, nezmer ad nsiḍen teɣziwin ur nessin ara s useqdec n wassaɣen-a.

'''Teɣzi: × k; anrar: × k²; ableɣ: × k³'''

Ma nsemɣer asrem s umuskir 3, tehri d teɣzi-nni ad nernunt kraḍ n tikal; anrar ad yili 9 n tikal. Ma nsemɣer agasas s 3, ableɣ ad yili 27 n tikal. Ihi amḍan n tsektiwin yesɛa azal deg wamek i yettbeddil usket.

Tagdukta d abeddel iḥerzen imeccaqen; d amedya uslig n tarwast s k = 1. Ur ilaq ara ad nsemmi snat n talɣiwin d igdazalen s wesket ma ttemcabint kan deg talɣa.

== 6. Igeddisen, tiwinas d yiḍebsiyen ==
Ageddis d talɣa n uɣawas iḥerzen yiwen rrif yettwabnan s yiɣallen. I ugeddis afraray, war amager n yidis gar-asen, timernit n tiɣmar n daxel d (n−2) × 180°, anda '''n''' d amḍan n yidis. Abḍu n ugeddis affensu s yiwet n tqacuct yessegza tanfalit-a: ad d-naf n−2 n yikerdisen.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-22 10-56-58.png|centré|595x595px]]
&lt;small&gt;Tugna 6. Tawinest d rrif; aḍebsi yesɛa daxel. Ageddis s semmus n yidisan yettwabḍa ɣef kraḍ n yikerdisen.&lt;/small&gt;

Tawinest s wammas '''O''' d waqqar '''r''' tesdukkel tineqqiḍin '''P''' i yesɛan '''d(O,P)=r'''. Aḍebsi yeɣleq yesdukkel tineqqiḍin i yesɛan d(O,P) ≤ r. Akdu d 2r. Taslayt i twinest deg P tebdd ɣef waqqar OP.

'''Azzikit n twinest: P = 2πr; anrar n uḍebsi: A = πr²'''

Ma '''r''' yettwaskat s yimitren, '''P''' ad yili s yimitren, '''A''' s yimitren imkuẓen. Pi d amḍan agraɣlan π ≈ 3.14159. Ur ilaq ara ad nsexleḍ amḍan n yisekkilen n tamawaẓt d wazal amatu n π.

== 7. Asektiɣmer d radyan ==
Asektiɣmer (trigonométrie) izerrew assaɣ gar tɣmar d teɣziwin. Deg ukerdis amaɣud, '''sin''' '''θ''' d assaɣ n yidis i d-yezzin i θ ɣer ulubdis; '''cos θ''' d assaɣ n yidis n tama-s ɣer ulubdis; '''tan θ''' '''= sin θ / cos θ mi cos θ ≠ 0.'''
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-23 12-24-09.png|centré|612x612px]]
&lt;small&gt;Tugna 7. Tawinest s waqqar 1 tefk amur ilaw cos θ d amur yebdden sin θ. Udlifen n sin d cos sseknen abeddel-nsen d&lt;/small&gt; &lt;small&gt;wallus-nsen.&lt;/small&gt;

'''sin² θ + cos² θ = 1; 180° = π rad'''

Radyan d asket n tɣmert s wassaɣ '''θ = s/r''', anda '''s''' d teɣzi n uḥric n twinest. Ma '''θ = 1''' rad, '''s''' '''= r'''. Tuzzya tummidt d 2π rad, neɣ 360°. Aseqdec n radyan yeshel tigawt n usiḍen aneẓlay d tarrayt n yizellumen.

'''c² = a² + b² − 2ab cos γ'''

Asaḍuf n cosine yessegza assaɣ gar kraḍ n yidis n ukerdis d tɣmert γ i d-yezzin i c. Ma '''γ =''' '''90°''', '''cos γ = 0''', ad d-naf asekkud n Pythagore. Assaɣen-a ttɛawanen deg usket n tiddi n wayen ur nezmir ara ad naweḍ srid d usiḍen n yiberdan.

== 8. Teɣzi, anrar d ubleɣ ==
Teɣzi tettwaskat s tiget n teɣzi, anrar s tiget n teɣzi ɣer sin, ableɣ s tiget n teɣzi ɣer kraḍ. Azzikit d teɣzi n rrif. Tajumma tella d talɣa; anrar d azal n wesket-is. Deg tallunt, ilaq ad nessemgired anrar n rrif d ubleɣ n daxel.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-24 11-26-46.png|centré|716x716px]]
&lt;small&gt;Tugna 8. Tiddi h tebdd ɣef uzadur b. Awlellu d takurt sɛan isketen n ubleɣ; amaḍal d rrif n takurt.&lt;/small&gt;
{| class=&quot;wikitable&quot;
|+
!Talɣa
!Asket
|-
|Asrem s yidis a d b
|A = ab; P = 2(a+b)
|-
|Akerdis s uzadur b d tiddi h
|A = bh/2
|-
|Agasas s yidis a
|V = a³; anrar n rrif = 6a²
|-
|Awlellu s waqqar r d tiddi h
|V = πr²h
|-
|Akaswar s waqqar r d tiddi h
|V = πr²h/3
|-
|Takurt / amaḍal s waqqar r
|V = 4πr³/3; anrar n umaḍal = 4πr²
|}
I talɣiwin ur nesɛi ara tanfalit tafessast, nezmer ad nebḍu talɣa ɣef yiḥricen, ad nessemres aɣred neɣ asiḍen n temawaẓt. Ma yella kra n uḥric i neḥseb snat n tikal, ilaq ad t-nekkes yiwet n tikkelt iwakken ur t-nettḥasab ara snat n tikal.

== 9. Asali s tesɣunt d ukumpas ==
Deg tanzeggit tamensayt, tesɣunt war yizamulen n wesket tettawi-d taɣda iɛeddan seg snat n tneqqiḍin. Akumpas yettawi-d tawinest s wammas d waqqar. Asali d asartu n tigawin s yilugan, mačči d asefru n talɣa s tseddi n tugna kan.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-25 11-13-00.png|centré|645x645px]]
&lt;small&gt;Tugna 9. Sin n yisugnen n twinest sɛan yiwen waqqar, i yugar AB/2. Amager-nsen d P d Q. Taɣda PQ tebdd ɣef AB&lt;/small&gt; &lt;small&gt;deg tlemmast M&lt;/small&gt;

I usali n tabeddayt i yiɣil [AB] deg tlemmast-is, nbennu tawinest s wammas A d tayeḍ s wammas B, s yiwen waqqar i yugar AB/2. Ad mlilent deg P d Q. Acku PA=PB d QA=QB, P d Q bɛaden s yiwen umeccaq seg A d B; taɣda-nsen d tabeddayt n tlemmast n [AB].

Nezmer ad nebnu akerdis agdudisan, talemmast n yiɣil neɣ abḍu n tiɣmert ɣef sin. Maca mačči yal asali yezmer ad yettwaxdem s sin n wallalen-a: amedya, abḍu n yal tiɣmert ɣef kraḍ n yiḥricen igdazalen ur yezmir ara s wudem amatu. Abḍu n kra n tiɣmar usligen yezmer. 

Tanzeggit tagellamt tessemres tigriyin iwakken ad d-tessekna talɣiwin n kraḍ n tsektiwin deg uɣawas. D lsas i tesneḍrit n lebni d kra n terrayin n usunneɣ aṭekniki.

== 10. Imsidag d yimawayen ==
Tanzeggit tusliṭ teqqen talɣa ɣer tegda. S yimsidag n Descartes, taneqqiṭ '''A''' tettwasbadu s '''(x,y)'''; taɣda s '''ax+by+c=0''', anda '''a''' d '''b''' ur llin ara i sin d '''0'''. Tarrayt-a tettawi talɣiwin ɣer yisiḍen(leḥsab) n uljibṛ.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-26 11-34-29.png|centré|608x608px]]
&lt;small&gt;Tugna 10. Imeccaqen Δx = 4 d Δy = 3 fkan d = 5. Amaway u+v yettwabna s unadi n v seg yixef n u; amḍiq n tazwara&lt;/small&gt; &lt;small&gt;n umaway ur ibeddel ara talɣa-s.&lt;/small&gt;

'''d(A,B) = √[(x₂−x₁)² + (y₂−y₁)²]'''

Talemmast n [AB] tesɛa imsidag ((x₁+x₂)/2, (y₁+y₂)/2). Deg umedya A(1,1), B(5,4), talemmast d (3,2.5). Tanfalit n umeccaq tekka-d seg Pythagore; tanfalit n tlemmast tekka-d seg wassaɣ n yimawayen.

'''u · v = u₁v₁ + u₂v₂ = ‖u‖ ‖v‖ cos θ'''

Amaway yesɛa teɣzi d tanila. Afaris afesnan n sin yimawayen yezmer ad yessegza tiɣmert gar-asent. Ma u·v = 0 d sin yimawayen ur nelli ara d 0, imawayen-a bedden gar-asen. Tanzeggit tamawayt teshel anerni n yisiḍen-a ar tallunin s waṭas n tsektiwin.

== 11. Ibeddilen d tujjuṛt ==
Tagdukta d abeddel iḥerzen imeccaqen. Tasikelt, tuzzya d tujjuṛt s ugellus d imedyaten deg uɣawas n Aklid. Abeddel yezmer ad yerr talɣa deg umḍiq nniḍen, maca teɣzi, tiɣmar d wanrar ad qqimen d yiwen.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-27 11-43-08.png|centré|661x661px]]
&lt;small&gt;Tugna 11. Talɣa tazegzawt d tin n tazwara. Tasikelt d tuzzya ḥerzent aniri; tujjuṛt s ugellus tbeddel aniri.&lt;/small&gt;

'''Tasikelt: x′ = x + a; y′ = y + b'''

'''Tuzzya: x′ = x cos θ − y sin θ; y′ = x sin θ + y cos θ'''

Tujjuṛt s ugellus y tettawi (x,y) ɣer (−x,y). Tasikelt s umaway v tettawi P ɣer P+v. Taludegt s wammas O d umuskir k tettawi OP ɣer kOP; tessenɣas neɣ tessemɣer imeccaqen s |k|. Ma |k| ≠ 1, mačči d tagdukta.

Timhelt n uḍfar n yibeddilen tesɛa azal: tuzzya deffir tasikelt ur tefk ara dima ayen i d-tefk tasikelt deffir tuzzya. Ibeddilen i yeṭṭafen talɣa meṛṛa ur tettbeddil ara sdukklen agraw n tujjuṛt-is. D allal i tazrawt n yizeṭṭa, lebni d talɣiwin n ugama.

== 12. Igezzumen n ukaswar ==
Igezzumen n ukaswar (coniques) d tiwinas, tiglayin, tikenzirarin d yiknudem. Zemren ad d-ilin s umager n uɣawas d ukaswar asinan; tili n ugzam tettawi talɣa yemgaraden. Deg taenzeggit tusliṭ, d imedyaten n tegdiwin s tfesna 2.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-28 12-03-59.png|centré|636x636px]]
&lt;small&gt;Taglayt tesɛa sin n yidiken. Takenzirart tesɛa adik d teɣda tanilayt. Aknudem yesɛa sin n yifurkan. Ilugan n tigniwin llan deg yizwal-nsent.&lt;/small&gt;

Taglayt tesdukkel tineqqiḍin i yesɛan timernit n yimeccaqen seg sin n yidiken d yiwen wazal. Takenzirart tesdukkel tineqqiḍin i bɛaden s yiwen umeccaq seg udik d teɣda tanilayt. Aknudem yesɛa tameẓla tamagdazt n yimeccaqen seg sin n yidiken d yiwen wazal.

'''Ax² + Bxy + Cy² + Dx + Ey + F = 0'''

I tegda n tfesna 2 war talɣiwin yettwasenɣasen, B²−4AC &lt; 0 yettawi talɣa n teglayt; = 0 talɣa n tkenzirart; &gt; 0 talɣa n uknudem, s tawtilin n tili n talɣa tilawt. Kra n tegdiwin zemrent ad fkent taɣda, snat teɣdiwin, taneqqiṭ neɣ tagrumma tilemt. Ihi ur ilaq ara ad nsemmu talɣa s yiwen umḍan kan.

Talɣiwin-a sɛant aseqdec deg tsenallunt, imeskaren n tafat d usali n kra n yimeslaḍen.

== 13. Tanzeggit talawsant d tseggart ==
Tanzeggit talawsant tḥerrez imeẓla n umsadaɣ d wassaɣen n tneqqiḍin ɣef yiwet n teɣda. Abeddel alawsan yesɛa talɣa x′=Ax+b, anda A d isirew imutti. Yezmer ad yessenɣes yiwen yidis ugar n wayeḍ, ihi tiɣmar d teɣziwin ur ilaq ara ad qqiment d yiwen.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-29 12-34-08.png|centré|526x526px]]
&lt;small&gt;Tugna 13. Tama taẓelmaḍt: amkuẓ yuɣal d talɣa s yidis imsadaɣen. Tama tayeffust: tigri n snat teɣdiwin timsadaɣin tettban tettawi-ten ɣer yiwet n tneqqiṭ.&lt;/small&gt;

Tanzeggit taseggart tzerrew ayen i yeqqimen d yiwen s tigri. Deg uɣawas aseggar, snat teɣdiwin yemgaraden mlilent dima deg yiwet n tneqqiṭ. I taɣdiwin timsadaɣin n uɣawas alawsan, amager-a yettwagenses s tneqqiṭ deg war taggara. 

'''[x : y : z] = [λx : λy : λz], ma λ ≠ 0'''

Deg yimsidag imsariyen, '''z ≠ 0''' yezmer ad yettwarr ɣer z = 1 s ubḍu. Tineqqiḍin s '''z = 0''' d taɣda n war taggara. Snat teɣdiwin timsadaɣin sɛant taneqqiṭ n tanila i ten-yesdukklen. «War taggara» dagi d amur n unagraw n yimsidag, mačči d amḍiq i nettawi s useɣzef n ugdil.

Assaɣ n umager d talɣa n teɣda ttwaḥerzen s tigri, maca umsadaɣ neɣ talemmast ur ilaq ara ad qqimen. Tanzeggit-a tettawi-d allalen i tigniwin n ukamera d tmuɣli n lebni.

== 14. Tanzeggit ur nelli ara n Aklid ==
Tanzeggit taknudemt d tanzeggit n umaḍal sseknayent belli agejdi n umṣsadaɣ ur yelli ara d ayen iwatan i yal tallunt. Deg uɣawas aknudeman, seg P i ur nelli ara ɣef d, llant aṭas n teɣdiwin i ur nettmagar ara d. Ɣef umaḍal, iberdan i yettaken adeg n teɣdiwin d tiwinas timeqqranin.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-30 11-45-25.png|centré|640x640px]]
&lt;small&gt;Tugna 14. Akerdis ɣef umaḍal: seg Ugafa ɣer sin n tneqqiḍin deg usebges i yemgaraden s 90°, timernit d 270°. Deg uḍebsi n Poincaré, yidis n ukerdis d iḥricen n twinas i yebdden ɣef rrif.&lt;/small&gt;

Deg tanzeggit n umaḍal s waqqar '''R''', akerdis s yidis n twinas timeqqranin, deg yiwen umur iwatan, yesɛa timernit n tɣmar tugar '''π'''. Anrar-is d '''R²(α+β+γ−π)''', anda tiɣmar ttwasqedcent s radyan. Deg uɣawas aknudeman s tiknit −1, anrar n ukerdis d '''π−(α+β+γ)'''.

Deg umedya n Poincaré, rrif n uḍebsi ur yelli ara deg tallunt taknudemt: tineqqiḍin ttwaliɣent qqrebent ɣer rrif, maca ameccaq aknudeman yezmer ad yettnerni war tilisa. Ur ilaq ara ad nsket imeccaqen n tallunt-a s tesɣunt ɣef tugna amagnut.

== 15. Tanzeggit taneẓlayt d tiknit ==
Tanzeggit taneẓlayt tessemres izellumen d yiɣraden iwakken ad tzerrew udmawen d tijummiwin. I udem ilweɣ s yiwen uɣewwaṛ t, r(t) = (x(t),y(t)), taslayt teqqen ɣer r′(t). Tiknit tettawi-d asket n ubeddel n tanila mi nettnerni deg teɣzi n ubrid.

'''κ = |x′y″ − y′x″| / (x′² + y′²)^(3/2), ma r′(t) ≠ 0'''
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-31 11-51-15.png|centré|536x536px]]
&lt;small&gt;Tugna 15. Amedya n tiknit n Gauss: tajumma n umaḍal s K &gt; 0, aɣawas s K = 0, d talɣa n ukersi n userdun s K &lt; 0.&lt;/small&gt;

Tawinest s waqqar R tesɛa tiknit 1/R. Taɣda tesɛa tiknit 0. Ɣef tajumma deg tallunt s kraḍ n tsektiwin, llant snat n tikniyin tigejdanin k₁ d k₂; tiknit n Gauss d K = k₁k₂. K tezmer ad tili tugar 0, d 0 neɣ ddaw 0. 

Tiknit n Gauss d taɣara n daxel: yezmer ad tettwasekza seg yisketen deg tajumma, war asket n wamek i tettwabna deg tallunt n berra. D ayen i d-yeskan usekkud n Gauss yettwasnen s Theorema Egregium. Ihi tajumma tettban teɛwej seg berra ur ilaq ara adtesɛu K ≠ 0. Awlellu, amedya, yesɛa K = 0.

== 16. Tanzeggit n Riemann d yiberdan ==
Tanḍa d tallunt i yettemcabin, deg yal amḍiq ameẓẓyan, ɣer ℝⁿ, maca talɣa-is meṛṛa tezmer ad temgarad. Amaḍal d akruri zemren ad ttwabḍun s yikarṭiyen adiganen s sin n yimsidag. Ur ilaq ara yiwen ukarṭi ad yeṭṭef akk tallunt.

Tanzeggit n Riemann ternu asbadu n wesket i yal taneqqiṭ s isirew gᵢⱼ(x) iḍemnen belli teɣzi n yal amaway ur nelli ara d 0 tugar 0. Teɣzi n uḥric ameẓẓyan tettwaru s talɣa-a:

'''ds² = Σᵢⱼ gᵢⱼ(x) dxᵢ dxⱼ'''
[[Tugna:Tuṭṭfa n ugdil seg 2026-11-01 12-24-52.png|centré|700x700px]]
&lt;small&gt;Tugna 16. Awlellu yezmer ad yeldi ɣer uɣawas war abeddel n yimeccaqen adiganen. Taɣda deg tugna tayeffust tettawi abrid yezzin ɣef uwlellu.&lt;/small&gt;

Abrid agejdis (géodésique, asegzi dagi) d abrid iḥerzen tanila s wamek i t-id-tesbadu tallunt. Deg tallunt n Riemann, iberdan-a sɛan taɣara n ubrid ameẓẓyan s teɣzi deg yiḥricen meẓẓiyen iwulmen. Ur ilaq ara yal abrid agejdis ad yili d ameẓẓyan akk gar sin n yixfawen s wudem amatu.

Deg tfizikt n Einstein, tallunt d wakud ttwazerwen s tanzeggit n Lorentz: asket-is ur yesɛi ara yiwen unagraw n yizamulen am Riemann. Ihi «tajumma yeɛwejjen» d asegzi i d-iqerben kan, ur d-yessegzi ara iman-is akk tiẓri n wassaɣ n tallunt d wakud (relativité).

== 17. Tasnidegt d talɣa meṛṛa ==
Tasnidegt tzerrew timitar i ur nettbeddil ara s ubeddel amaɣlal i yesɛan amutti amaɣlal. Zemrent ad ttwazerwent tuqqna, ixjaḍ d wamek i tettwasdukkel tallunt. Teɣzi d tɣmar ur ilaq ara ad ttwaḥerzent. Ihi tasnidegt teqqen ɣer tanzeggit, maca ur telli ara d yiwet n taɣult s sin n yismawen.
[[Tugna:Tuṭṭfa n ugdil seg 2026-11-02 11-11-35.png|centré|636x636px]]
&lt;small&gt;Tugna 17. Amaḍal d ukruri mgaraden deg umḍan n yixjaḍ. amaḍal ur yesɛi ara axjiḍ, a akruri yesɛa yiwen uxjiḍ iɛeddan deg tlemmast-is, Tigniwin-a sseknayent tijummiwin n rrif kan, mačči d talɣiwin yeččuren d axel.&lt;/small&gt;

'''χ = N₀ − N₁ + N₂; i tajumma iɣelqen tusɣilt: χ = 2 − 2g'''

I tajumma yettwabḍan ɣef talɣiwin, N₀ d amḍan n tqacucin, N₁ n yidis d N₂ n wudmawen. χ d taskant n Euler. Ɣef rrif n ugasas, 8−12+6 = 2. Ɣef akruri, χ = 0. Deg tnfalit tis snat, g d amḍan n yixjaḍ s unamek n wanaw(genre), tajumma ilaq ad tili teqqen, teɣleq, tusɣilt d war rrif.

Tazrawt n talɣa meṛṛa tezmer ad d-tefk tilisa i tiknit. Asekkud n Gauss-Bonnet yeqqen aɣred n tiknit n Gauss ɣer χ n tajumma. D amedya ameqqran n tuqqna gar usket adigan d talɣa n tallunt meṛṛa.

== 18. Tanzeggit taljibṛant ==
Tanzeggit taljibṛant tzerrew tegrummiwin n tifrat n tegdiwin n yigetfulen. Ma P(x,y)=0, tineqqiḍin i yettḥeqqiqen tagda-a zemrent ad d-fkent azlig. Tarrayt-a tesdukkel aljibṛ d talɣiwin; tazrawt tamatut tezmer ad tili ɣef yimḍanen ilawen, isemlalen neɣ taɣulin nniḍen.
[[Tugna:Taneqqit tasuft.png|centré|688x688px]]
&lt;small&gt;Tugna 18. Tama taẓelmaḍt: azlig y² = x³ − x + 1 war taneqqiṭ tusligt deg uɣawas ilaw. Tama tayeffust: y² = x³ yesɛa taneqqiṭ tasuft deg (0,0).&lt;/small&gt;

I uzlig P=0, taneqqiṭ tasuft tḥeqqiq P = 0 d akk izellumen imezwura ∂P/∂x = ∂P/∂y = 0. Deg y²−x³=0, ayen-a yettili deg (0,0). Deg y²−x³+x−1=0, ulac taneqqiṭ i yeṭṭfen akk tawtilin-a. Amedya yessekza ayɣer aljibṛ yezmer ad yessegzi tikniyin d yimeẓla n talɣa.

Deg tanzeggit taljibṛant, imḍanen isemlalen zemren ad fken talɣa tummidt n tifrat: ayen yettban d sin n yifurkan deg tugna tilawt yezmer ad yesɛu tuqqniwin nniḍen deg tallunt tasemlalt. Ur ilaq ara tugna tilawt ad tettwaḥsab d tamusni tummidt n talɣa. Tanzeggit taljibṛant tesɛa iseqdacen deg tiẓri n yimḍanen, ladɣa deg tazrawt n tifrat n tegdiwin s yimḍanen ummiden neɣ imeɣẓanen, izligen ilipsiyen d teɣri n tegdiwin. Iwakken ad tili tɣuri n lsas, ilaq aljibṛ imzireg d kra n tiẓri n tegrummiwin.

== 19. Tanzeggit d usiḍen s uselkim ==
Tanzeggit n usiḍen tzerrew ilugan i asiḍen n wassaɣen anzeggane: amager n yiɣallen, taɣlaft taffensut, abḍu n tajumma ɣef ikerdisen d tazrawt n yiberdan. Tanzeggit tafrarayt tzerrew daɣen tegrummiwin n tneqqiḍin d talɣiwin tinzegganin, d wassaɣen gar-asent.
[[Tugna:Tuṭṭfa n ugdil seg 2026-11-04 12-56-10.png|centré|785x785px]]
&lt;small&gt;Tugna 19. Yiwen wamud n 15 n tneqqiḍin: taɣlaft taffensut, abḍu ɣef ikerdisen n Delaunay d taɣulin n Voronoi. Tilisa i yettbanen deg ugdil d tamuɣli n uḥric n uɣawas.&lt;/small&gt;

Tagrumma taffensut teṭṭef iɣil meṛṛa i yeqqnen yal snat n tneqqiḍin-is. Taɣlaft taffensut n wamud d tagrumma taffensut tameẓẓyant i yeṭṭfen akk tineqqiḍin n wamud-nni. Deg wudlif n Voronoi, yal taneqqiṭ n wamud tesɛa taɣult i yesdukklen akk tineqqiḍin i iqerben ɣur-s ugar n tneqqiḍin nniḍen n wamud, neɣ i yebɛaden s yiwen umeccaq ɣur-s d kra seg-sent.

Abḍu n Delaunay d abḍu ɣef ikerdisen, s tawtilt-a: i yal akerdis, ulac taneqqiṭ nniḍen n wamud deg daxel n twinest iɛeddan ɣef kraḍ n tqacucin-is. Deg waddad amatu, abḍu n Delaunay d wudlif n Voronoi qqnen gar-asen akka: snat n tneqqiḍin n wamud ttwaqqnent s yiɣil deg ubḍu n Delaunay ma taɣulin-nsent n Voronoi ccerkent yiwen n yidis. 

Ilaq ad ttwasxedmen yisiḍen s tiseddi: tuccḍa tameẓẓyant tezmer ad d-tefk agmuḍ ur neṣḥiḥ ara mi ara nsenqed ma sin n yiɣallen ttemlilin neɣ ala. Tarrayin-a sɛant azal deg usnulfu n tigniwin s kraḍ n tsektiwin (3D), deg tarubut, deg usnulfu n yikarṭiyen d lebni n yimedyaten n tfizikt.

==Imuren imeqranen n tenzeggit ==

* [[Tanzeggit tuklidit]] 

* [[Tanzeggit artuklidit]] 

* [[Tanzeggit tummit]]

* [[Tanzeggit tigriwt]]

* [[Tanzeggit taljibirt]]

* [[Tanzeggit tanebrurzant]] 

* [[Aljiber imzireg]]

== Amezruy n tenzeggit ==


[[Taggayt:Tusnakt]]</text>
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'''Tanzeggit''' d tigezmi tameqrant ger igzumen n [[tusnakt]] d win i izerwen [[tawella|tiwellatin]] neɣ Udmawen deg [[Tallunt|tallunin]] s myal [[tasekta]], deg tsekta Tis kraḍ (3) nezmar ad nemmeslay ɣef [[tenzeggit tuklidt]]. Ass-a ur nezmir ad d nesbin tilisa yellan ger tenzeggit akk d [[Asebrurez|wesebrurez]] neɣ d [[aljiber|uljiber]], acku ur nezmir ad nemmeslay ɣef [[Tanzeggit taljibirt|tenzeggit taljibirt]] ma yella ur d-neddim ara kra din kra da.

Tanzeggit diɣen d tafurk n tusnakt i izerrwen talɣiwin, tallunin, imeccaqen, tiɣmar d wassaɣen gar tneqqiḍin d yiḥricen n talɣiwin. Tesɛa azal deg usket n wakal d lebni, maca tuɣal daɣen d taɣult tamatut n tusnakt i yezmer ad tzerrew tallunin ur nezmir ara ad nwali s wallen, neɣ tallunin i yesɛan ugar n kraḍ n tsektiwin.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-16 11-19-35.png|centré|553x553px]]

== 1. Amezruy n tenzeggit ==
Awal agraɣlan géométrie yekka-d seg yigrigiyen i d-yemmalen asket n wakal. Isketen d yisiḍen inzeggane ttwasqedcen deg Maṣer, Mezupuṭamya d tɣermiwin nniḍen uqbel tanzeggit n Yigrigiyen. Ur ilaq ara ad nerṛ tanzeggit meṛṛa d asnulfu n yiwen ugdud kan.
{| class=&quot;wikitable&quot;
|+
!Tallit
!Amhaz agenjdan
|-
|Taglest
|Asket n wakal, lebni, asiḍen n teɣzi, n wanrar d ubleɣ.
|-
|Tasut tis 3 uqbel
tallit-nneɣ
|Aklid deg Iskandariya yesdukkel tizrawin deg &quot;Iferdisen&quot;.
|-
|Tallit talemmast
|Tigawt n yimusnawen deg tmura n Tineslemt, Lehend d Cinwa: asektiɣmer(trigonométrie), asali d
tsenallunt.
|-
|Tasut tis 17
|Descartes d Fermat qqnen talɣiwin ɣer imsidag d tegdiwin.
|-
|Tasut tis 19
|Lobachevsky d Bolyai snernan tanzeggit taknudemt; Gauss d Riemann snernan tazrawt n
tiknit d tallunin.
|-
|1872 d mbeɛd
|Klein yeskan azal n yibeddilen d yigrawen; Hilbert yessegzi lsas s yinagrawen n yigejdan.
|-
|Tasut tis 20–21
|Tanzeggit taljibṛant, taneẓlayt, tukrist, asiḍen s uselkim d uẓeṭṭa n twuriwin gar tfurka.
|}
&quot;'''Iferdisen'''&quot; n Aklid yesseqdac isbaduten d yigejdan iwakken ad yebnu isekkuden. Abrid-a yesɛa tazrirt tameqqrant deg tusnakt. Maca tanzeggit tamirant ur teqqim ara deg yigejdan n Aklid: tazrawt n umṣadaɣ tewwi-d timusniwin ɣef tallunin nniḍen. Tanzeggit tamirant tettawi ula d tallunin yellan deg tfizikt, isefka, tigniwin d yisiḍen. Amezruy-is d anerni n yisental d terrayin, mačči d asemselsi n yiwet n tanzeggit s tayeḍ kan.

== 2. Isbaduten, igejdan d usfukel ==
Asbadu yessegza tamiḍrant s wawalen yettwasnen. Agejdi d tafyirt i neqqbel deg yiwen unagraw war asfukel deg unagraw-nni. Asekkud(tiẓri) d ayen ara d-nsuffeɣ seg yigejdan d yisekkuden yettwasfuklen yakan.

Deg umedya n Aklid, yezmer ad yettwabnu yiɣil n teɣda gar snat n tneqqiḍin, ad yettwasɣezef yiɣil, ad tettwabnu twinest s wammas d waqqar yettwabedren. Yella daɣen agejdi ɣef tɣmar timaɣudin d wayen yeqqnen ɣer umṣadaɣ.

=== Amedya n useɣẓen ===
Deg uɣawas n Aklid, i teneqqiṭ '''P''' i ur nelli ara ɣef taɣda '''d''', tella yiwet kan n teɣda iɛeddan seg '''P''' ur nettmagar ara '''d'''. Talɣa-a n yigejdi n umṣadaɣ tettwassen s yisem n '''Playfair'''; d talɣa tagdazalt i yigejdi wis semmus n Aklid deg lsas n tanzeggit tamagnut.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-18 09-56-11.png|centré]]
&lt;small&gt;Tugna 2. Tiɣmert d wassaɣ n umṣadaɣ. Tigniwin ttɛawanent deg tɣuri n yisekkuden; isfukal ilaq ad d-begnen ayɣer iiṣeḥḥa wassaɣ.&lt;/small&gt;

Deg tugna, tineqqiḍin ttbanent sɛant tehri, izirigen sɛan tuzert, imeccaqen zemren ur ttwaḥerzen ara s tiseddi. Deg tusnakt, taneqqiṭ ur tesɛi ara tehri. Ihi ma tugna teskan-d belli sin n yimeccaqen d igdazalen, ayen-a ur d-yettawi ara asfukel.

== 3. Taneqqiṭ, taɣda d tallunt ==
Taneqqiṭ d amḍiq war tehri; taɣda tettwasɣezef deg sin yinumak war tilisa; iɣil n teɣda yesɛa sin n yixfawen; tazinaɣda tesɛa yiwen n yixef, tettwasɣezef deg yiwen unamek. Aɣawas d tajumma ilweɣ i deg yezmer ad yili wudlif s sin n yimsidag.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-19 12-18-47.png|centré|611x611px]]
&lt;small&gt;Tugna 3. Tisektiwin 0, 1, 2 d 3. Aɣawas n tugna d amur ifuken kan; aɣawas n tusnakt ur yesɛi ara tilisa.&lt;/small&gt;

Tasekta n tallunt tettawi amḍan n yimsidag ilelliyen i ilaqen iwakken ad nesbadu amḍiq. Deg taɣda, yiwen x ikfa; deg uɣawas, nesra (x,y); deg tallunt s kraḍ n tsektiwin, nesra (x,y,z). Tasekta ur tɛelliq ara ɣef wamek ara d-nsuneɣ talɣa: amaḍal s tajumma kan yesɛa snat n tsektiwin, ɣas ma yettwaseknen deg tallunt s kraḍ.

ℝⁿ = {(x₁, x₂, …, xₙ) : xᵢ d imḍanen ilawen}

Tallunin s n &gt; 3 ttwasqedcent deg tusnakt d yisefka. Ma yal amedya n yisefka yesɛa 10 n yimuttiyen ilelliyen, yezmer ad yettwagenses s tneqqiṭ deg ℝ¹⁰. Ayen-a ur d-yemmal ara belli nezmer ad t-nwali s wallen; imsidag d yilugan fkan-d allalen n tazrawt.

=== Tajumma d wanrar ===
Tajumma d talɣa n snat n tsektiwin; anrar d asket-is. S yiwet n tɣawsa, takurt tesɛa daxel-is d ubleɣ, ma amaḍal d tajumma n rrif-is. Asbadu n wayen nzerrew yesɛa azal uqbel yal asiḍen.

== 4. Ikerdisen d usekkud n Pythagore ==
Akerdis yesɛa kraḍ n yidis, kraḍ n tqacucin d kraḍ n tiɣmar. Deg uɣawas n Aklid, timernit n tɣmar-is d 180°. Akerdis agdudisan yesɛa kraḍ n yidis igdazalen; akerdis akendis yesɛa ma drus sin n yidis igdazalen; akerdis amaɣud yesɛa yiwet n tiɣmert n 90°.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-20 11-55-53.png|centré|667x667px]]
&lt;small&gt;Tugna 4. Tama taẓelmaḍt: anrar n umkuẓ ɣef yidis 5 d 25 = 9 + 16. Tama tayeffust: kuẓ n yikerdisen s yidis a d b, d umkuẓ alemmas s yidis c.&lt;/small&gt;

'''a² + b² = c², ma c d alubdis n ukerdis amaɣud''' 

Asfukel n tugna tayeffust: anrar n umkuẓ ameqqran d (a+b)². Kuẓ n yikerdisen sɛan anrar 4 × ab/2 = 2ab. Ayen i d-yeqqimen d c²; ihi c² = (a+b)² − 2ab = a²+b². Ayen-a d aseɣẓen s wanrar, mačči d asket n teɣzi ɣef tugna. Asekkud-a yesɛa daɣen talɣa tamsuɣalt: ma a²+b²=c² deg ukerdis, tiɣmert i d-yezzin i c d 90°. Deg tanzeggit taknudemt neɣ ɣef umaḍal, tanfalit-a ur tettwasemres ara akka war abeddel.

== 5. Tales(Thales) d tarwast ==
Sin n yikerdisen imarwasen sɛan tiɣmar igdazalen d yidis akniwen s yiwen wassaɣ. Ma tasɣent tessenɣas neɣ tessemɣer akk imeccaqen s yiwen umuskir k &gt; 0, tḥerrez tiɣmar d talɣa. D tarwast.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-21 10-35-44.png|centré|676x676px]]
&lt;small&gt;Tugna 5. DE d BC msadaɣen, ihi ikerdisen ADE d ABC d imarwasen. Deg tugna tayeffust, amuskir n teɣzi d 2; win n&lt;/small&gt; &lt;small&gt;wanrar d 4.&lt;/small&gt;

'''AD/AB = AE/AC = DE/BC'''

Deg umedya, A d yiwet n tqacuct n sin yikerdisen; D yella ɣef [AB], E ɣef [AC], yerna DE ∥ BC. Ihi assaɣ n ''Thales'' yessegza ayɣer akk ibḍan-a d igdazalen. Ma nessen kra n teɣziwin, nezmer ad nsiḍen teɣziwin ur nessin ara s useqdec n wassaɣen-a.

'''Teɣzi: × k; anrar: × k²; ableɣ: × k³'''

Ma nsemɣer asrem s umuskir 3, tehri d teɣzi-nni ad nernunt kraḍ n tikal; anrar ad yili 9 n tikal. Ma nsemɣer agasas s 3, ableɣ ad yili 27 n tikal. Ihi amḍan n tsektiwin yesɛa azal deg wamek i yettbeddil usket.

Tagdukta d abeddel iḥerzen imeccaqen; d amedya uslig n tarwast s k = 1. Ur ilaq ara ad nsemmi snat n talɣiwin d igdazalen s wesket ma ttemcabint kan deg talɣa.

== 6. Igeddisen, tiwinas d yiḍebsiyen ==
Ageddis d talɣa n uɣawas iḥerzen yiwen rrif yettwabnan s yiɣallen. I ugeddis afraray, war amager n yidis gar-asen, timernit n tiɣmar n daxel d (n−2) × 180°, anda '''n''' d amḍan n yidis. Abḍu n ugeddis affensu s yiwet n tqacuct yessegza tanfalit-a: ad d-naf n−2 n yikerdisen.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-22 10-56-58.png|centré|595x595px]]
&lt;small&gt;Tugna 6. Tawinest d rrif; aḍebsi yesɛa daxel. Ageddis s semmus n yidisan yettwabḍa ɣef kraḍ n yikerdisen.&lt;/small&gt;

Tawinest s wammas '''O''' d waqqar '''r''' tesdukkel tineqqiḍin '''P''' i yesɛan '''d(O,P)=r'''. Aḍebsi yeɣleq yesdukkel tineqqiḍin i yesɛan d(O,P) ≤ r. Akdu d 2r. Taslayt i twinest deg P tebdd ɣef waqqar OP.

'''Azzikit n twinest: P = 2πr; anrar n uḍebsi: A = πr²'''

Ma '''r''' yettwaskat s yimitren, '''P''' ad yili s yimitren, '''A''' s yimitren imkuẓen. Pi d amḍan agraɣlan π ≈ 3.14159. Ur ilaq ara ad nsexleḍ amḍan n yisekkilen n tamawaẓt d wazal amatu n π.

== 7. Asektiɣmer d radyan ==
Asektiɣmer (trigonométrie) izerrew assaɣ gar tɣmar d teɣziwin. Deg ukerdis amaɣud, '''sin''' '''θ''' d assaɣ n yidis i d-yezzin i θ ɣer ulubdis; '''cos θ''' d assaɣ n yidis n tama-s ɣer ulubdis; '''tan θ''' '''= sin θ / cos θ mi cos θ ≠ 0.'''
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-23 12-24-09.png|centré|612x612px]]
&lt;small&gt;Tugna 7. Tawinest s waqqar 1 tefk amur ilaw cos θ d amur yebdden sin θ. Udlifen n sin d cos sseknen abeddel-nsen d&lt;/small&gt; &lt;small&gt;wallus-nsen.&lt;/small&gt;

'''sin² θ + cos² θ = 1; 180° = π rad'''

Radyan d asket n tɣmert s wassaɣ '''θ = s/r''', anda '''s''' d teɣzi n uḥric n twinest. Ma '''θ = 1''' rad, '''s''' '''= r'''. Tuzzya tummidt d 2π rad, neɣ 360°. Aseqdec n radyan yeshel tigawt n usiḍen aneẓlay d tarrayt n yizellumen.

'''c² = a² + b² − 2ab cos γ'''

Asaḍuf n cosine yessegza assaɣ gar kraḍ n yidis n ukerdis d tɣmert γ i d-yezzin i c. Ma '''γ =''' '''90°''', '''cos γ = 0''', ad d-naf asekkud n Pythagore. Assaɣen-a ttɛawanen deg usket n tiddi n wayen ur nezmir ara ad naweḍ srid d usiḍen n yiberdan.

== 8. Teɣzi, anrar d ubleɣ ==
Teɣzi tettwaskat s tiget n teɣzi, anrar s tiget n teɣzi ɣer sin, ableɣ s tiget n teɣzi ɣer kraḍ. Azzikit d teɣzi n rrif. Tajumma tella d talɣa; anrar d azal n wesket-is. Deg tallunt, ilaq ad nessemgired anrar n rrif d ubleɣ n daxel.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-24 11-26-46.png|centré|716x716px]]
&lt;small&gt;Tugna 8. Tiddi h tebdd ɣef uzadur b. Awlellu d takurt sɛan isketen n ubleɣ; amaḍal d rrif n takurt.&lt;/small&gt;
{| class=&quot;wikitable&quot;
|+
!Talɣa
!Asket
|-
|Asrem s yidis a d b
|A = ab; P = 2(a+b)
|-
|Akerdis s uzadur b d tiddi h
|A = bh/2
|-
|Agasas s yidis a
|V = a³; anrar n rrif = 6a²
|-
|Awlellu s waqqar r d tiddi h
|V = πr²h
|-
|Akaswar s waqqar r d tiddi h
|V = πr²h/3
|-
|Takurt / amaḍal s waqqar r
|V = 4πr³/3; anrar n umaḍal = 4πr²
|}
I talɣiwin ur nesɛi ara tanfalit tafessast, nezmer ad nebḍu talɣa ɣef yiḥricen, ad nessemres aɣred neɣ asiḍen n temawaẓt. Ma yella kra n uḥric i neḥseb snat n tikal, ilaq ad t-nekkes yiwet n tikkelt iwakken ur t-nettḥasab ara snat n tikal.

== 9. Asali s tesɣunt d ukumpas ==
Deg tanzeggit tamensayt, tesɣunt war yizamulen n wesket tettawi-d taɣda iɛeddan seg snat n tneqqiḍin. Akumpas yettawi-d tawinest s wammas d waqqar. Asali d asartu n tigawin s yilugan, mačči d asefru n talɣa s tseddi n tugna kan.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-25 11-13-00.png|centré|645x645px]]
&lt;small&gt;Tugna 9. Sin n yisugnen n twinest sɛan yiwen waqqar, i yugar AB/2. Amager-nsen d P d Q. Taɣda PQ tebdd ɣef AB&lt;/small&gt; &lt;small&gt;deg tlemmast M&lt;/small&gt;

I usali n tabeddayt i yiɣil [AB] deg tlemmast-is, nbennu tawinest s wammas A d tayeḍ s wammas B, s yiwen waqqar i yugar AB/2. Ad mlilent deg P d Q. Acku PA=PB d QA=QB, P d Q bɛaden s yiwen umeccaq seg A d B; taɣda-nsen d tabeddayt n tlemmast n [AB].

Nezmer ad nebnu akerdis agdudisan, talemmast n yiɣil neɣ abḍu n tiɣmert ɣef sin. Maca mačči yal asali yezmer ad yettwaxdem s sin n wallalen-a: amedya, abḍu n yal tiɣmert ɣef kraḍ n yiḥricen igdazalen ur yezmir ara s wudem amatu. Abḍu n kra n tiɣmar usligen yezmer. 

Tanzeggit tagellamt tessemres tigriyin iwakken ad d-tessekna talɣiwin n kraḍ n tsektiwin deg uɣawas. D lsas i tesneḍrit n lebni d kra n terrayin n usunneɣ aṭekniki.

== 10. Imsidag d yimawayen ==
Tanzeggit tusliṭ teqqen talɣa ɣer tegda. S yimsidag n Descartes, taneqqiṭ '''A''' tettwasbadu s '''(x,y)'''; taɣda s '''ax+by+c=0''', anda '''a''' d '''b''' ur llin ara i sin d '''0'''. Tarrayt-a tettawi talɣiwin ɣer yisiḍen(leḥsab) n uljibṛ.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-26 11-34-29.png|centré|608x608px]]
&lt;small&gt;Tugna 10. Imeccaqen Δx = 4 d Δy = 3 fkan d = 5. Amaway u+v yettwabna s unadi n v seg yixef n u; amḍiq n tazwara&lt;/small&gt; &lt;small&gt;n umaway ur ibeddel ara talɣa-s.&lt;/small&gt;

'''d(A,B) = √[(x₂−x₁)² + (y₂−y₁)²]'''

Talemmast n [AB] tesɛa imsidag ((x₁+x₂)/2, (y₁+y₂)/2). Deg umedya A(1,1), B(5,4), talemmast d (3,2.5). Tanfalit n umeccaq tekka-d seg Pythagore; tanfalit n tlemmast tekka-d seg wassaɣ n yimawayen.

'''u · v = u₁v₁ + u₂v₂ = ‖u‖ ‖v‖ cos θ'''

Amaway yesɛa teɣzi d tanila. Afaris afesnan n sin yimawayen yezmer ad yessegza tiɣmert gar-asent. Ma u·v = 0 d sin yimawayen ur nelli ara d 0, imawayen-a bedden gar-asen. Tanzeggit tamawayt teshel anerni n yisiḍen-a ar tallunin s waṭas n tsektiwin.

== 11. Ibeddilen d tujjuṛt ==
Tagdukta d abeddel iḥerzen imeccaqen. Tasikelt, tuzzya d tujjuṛt s ugellus d imedyaten deg uɣawas n Aklid. Abeddel yezmer ad yerr talɣa deg umḍiq nniḍen, maca teɣzi, tiɣmar d wanrar ad qqimen d yiwen.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-27 11-43-08.png|centré|661x661px]]
&lt;small&gt;Tugna 11. Talɣa tazegzawt d tin n tazwara. Tasikelt d tuzzya ḥerzent aniri; tujjuṛt s ugellus tbeddel aniri.&lt;/small&gt;

'''Tasikelt: x′ = x + a; y′ = y + b'''

'''Tuzzya: x′ = x cos θ − y sin θ; y′ = x sin θ + y cos θ'''

Tujjuṛt s ugellus y tettawi (x,y) ɣer (−x,y). Tasikelt s umaway v tettawi P ɣer P+v. Taludegt s wammas O d umuskir k tettawi OP ɣer kOP; tessenɣas neɣ tessemɣer imeccaqen s |k|. Ma |k| ≠ 1, mačči d tagdukta.

Timhelt n uḍfar n yibeddilen tesɛa azal: tuzzya deffir tasikelt ur tefk ara dima ayen i d-tefk tasikelt deffir tuzzya. Ibeddilen i yeṭṭafen talɣa meṛṛa ur tettbeddil ara sdukklen agraw n tujjuṛt-is. D allal i tazrawt n yizeṭṭa, lebni d talɣiwin n ugama.

== 12. Igezzumen n ukaswar ==
Igezzumen n ukaswar (coniques) d tiwinas, tiglayin, tikenzirarin d yiknudem. Zemren ad d-ilin s umager n uɣawas d ukaswar asinan; tili n ugzam tettawi talɣa yemgaraden. Deg taenzeggit tusliṭ, d imedyaten n tegdiwin s tfesna 2.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-28 12-03-59.png|centré|636x636px]]
&lt;small&gt;Taglayt tesɛa sin n yidiken. Takenzirart tesɛa adik d teɣda tanilayt. Aknudem yesɛa sin n yifurkan. Ilugan n tigniwin llan deg yizwal-nsent.&lt;/small&gt;

Taglayt tesdukkel tineqqiḍin i yesɛan timernit n yimeccaqen seg sin n yidiken d yiwen wazal. Takenzirart tesdukkel tineqqiḍin i bɛaden s yiwen umeccaq seg udik d teɣda tanilayt. Aknudem yesɛa tameẓla tamagdazt n yimeccaqen seg sin n yidiken d yiwen wazal.

'''Ax² + Bxy + Cy² + Dx + Ey + F = 0'''

I tegda n tfesna 2 war talɣiwin yettwasenɣasen, B²−4AC &lt; 0 yettawi talɣa n teglayt; = 0 talɣa n tkenzirart; &gt; 0 talɣa n uknudem, s tawtilin n tili n talɣa tilawt. Kra n tegdiwin zemrent ad fkent taɣda, snat teɣdiwin, taneqqiṭ neɣ tagrumma tilemt. Ihi ur ilaq ara ad nsemmu talɣa s yiwen umḍan kan.

Talɣiwin-a sɛant aseqdec deg tsenallunt, imeskaren n tafat d usali n kra n yimeslaḍen.

== 13. Tanzeggit talawsant d tseggart ==
Tanzeggit talawsant tḥerrez imeẓla n umsadaɣ d wassaɣen n tneqqiḍin ɣef yiwet n teɣda. Abeddel alawsan yesɛa talɣa x′=Ax+b, anda A d isirew imutti. Yezmer ad yessenɣes yiwen yidis ugar n wayeḍ, ihi tiɣmar d teɣziwin ur ilaq ara ad qqiment d yiwen.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-29 12-34-08.png|centré|526x526px]]
&lt;small&gt;Tugna 13. Tama taẓelmaḍt: amkuẓ yuɣal d talɣa s yidis imsadaɣen. Tama tayeffust: tigri n snat teɣdiwin timsadaɣin tettban tettawi-ten ɣer yiwet n tneqqiṭ.&lt;/small&gt;

Tanzeggit taseggart tzerrew ayen i yeqqimen d yiwen s tigri. Deg uɣawas aseggar, snat teɣdiwin yemgaraden mlilent dima deg yiwet n tneqqiṭ. I taɣdiwin timsadaɣin n uɣawas alawsan, amager-a yettwagenses s tneqqiṭ deg war taggara. 

'''[x : y : z] = [λx : λy : λz], ma λ ≠ 0'''

Deg yimsidag imsariyen, '''z ≠ 0''' yezmer ad yettwarr ɣer z = 1 s ubḍu. Tineqqiḍin s '''z = 0''' d taɣda n war taggara. Snat teɣdiwin timsadaɣin sɛant taneqqiṭ n tanila i ten-yesdukklen. «War taggara» dagi d amur n unagraw n yimsidag, mačči d amḍiq i nettawi s useɣzef n ugdil.

Assaɣ n umager d talɣa n teɣda ttwaḥerzen s tigri, maca umsadaɣ neɣ talemmast ur ilaq ara ad qqimen. Tanzeggit-a tettawi-d allalen i tigniwin n ukamera d tmuɣli n lebni.

== 14. Tanzeggit ur nelli ara n Aklid ==
Tanzeggit taknudemt d tanzeggit n umaḍal sseknayent belli agejdi n umṣsadaɣ ur yelli ara d ayen iwatan i yal tallunt. Deg uɣawas aknudeman, seg P i ur nelli ara ɣef d, llant aṭas n teɣdiwin i ur nettmagar ara d. Ɣef umaḍal, iberdan i yettaken adeg n teɣdiwin d tiwinas timeqqranin.
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-30 11-45-25.png|centré|640x640px]]
&lt;small&gt;Tugna 14. Akerdis ɣef umaḍal: seg Ugafa ɣer sin n tneqqiḍin deg usebges i yemgaraden s 90°, timernit d 270°. Deg uḍebsi n Poincaré, yidis n ukerdis d iḥricen n twinas i yebdden ɣef rrif.&lt;/small&gt;

Deg tanzeggit n umaḍal s waqqar '''R''', akerdis s yidis n twinas timeqqranin, deg yiwen umur iwatan, yesɛa timernit n tɣmar tugar '''π'''. Anrar-is d '''R²(α+β+γ−π)''', anda tiɣmar ttwasqedcent s radyan. Deg uɣawas aknudeman s tiknit −1, anrar n ukerdis d '''π−(α+β+γ)'''.

Deg umedya n Poincaré, rrif n uḍebsi ur yelli ara deg tallunt taknudemt: tineqqiḍin ttwaliɣent qqrebent ɣer rrif, maca ameccaq aknudeman yezmer ad yettnerni war tilisa. Ur ilaq ara ad nsket imeccaqen n tallunt-a s tesɣunt ɣef tugna amagnut.

== 15. Tanzeggit taneẓlayt d tiknit ==
Tanzeggit taneẓlayt tessemres izellumen d yiɣraden iwakken ad tzerrew udmawen d tijummiwin. I udem ilweɣ s yiwen uɣewwaṛ t, r(t) = (x(t),y(t)), taslayt teqqen ɣer r′(t). Tiknit tettawi-d asket n ubeddel n tanila mi nettnerni deg teɣzi n ubrid.

'''κ = |x′y″ − y′x″| / (x′² + y′²)^(3/2), ma r′(t) ≠ 0'''
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-31 11-51-15.png|centré|536x536px]]
&lt;small&gt;Tugna 15. Amedya n tiknit n Gauss: tajumma n umaḍal s K &gt; 0, aɣawas s K = 0, d talɣa n ukersi n userdun s K &lt; 0.&lt;/small&gt;

Tawinest s waqqar R tesɛa tiknit 1/R. Taɣda tesɛa tiknit 0. Ɣef tajumma deg tallunt s kraḍ n tsektiwin, llant snat n tikniyin tigejdanin k₁ d k₂; tiknit n Gauss d K = k₁k₂. K tezmer ad tili tugar 0, d 0 neɣ ddaw 0. 

Tiknit n Gauss d taɣara n daxel: yezmer ad tettwasekza seg yisketen deg tajumma, war asket n wamek i tettwabna deg tallunt n berra. D ayen i d-yeskan usekkud n Gauss yettwasnen s Theorema Egregium. Ihi tajumma tettban teɛwej seg berra ur ilaq ara adtesɛu K ≠ 0. Awlellu, amedya, yesɛa K = 0.

== 16. Tanzeggit n Riemann d yiberdan ==
Tanḍa d tallunt i yettemcabin, deg yal amḍiq ameẓẓyan, ɣer ℝⁿ, maca talɣa-is meṛṛa tezmer ad temgarad. Amaḍal d akruri zemren ad ttwabḍun s yikarṭiyen adiganen s sin n yimsidag. Ur ilaq ara yiwen ukarṭi ad yeṭṭef akk tallunt.

Tanzeggit n Riemann ternu asbadu n wesket i yal taneqqiṭ s isirew gᵢⱼ(x) iḍemnen belli teɣzi n yal amaway ur nelli ara d 0 tugar 0. Teɣzi n uḥric ameẓẓyan tettwaru s talɣa-a:

'''ds² = Σᵢⱼ gᵢⱼ(x) dxᵢ dxⱼ'''
[[Tugna:Tuṭṭfa n ugdil seg 2026-11-01 12-24-52.png|centré|700x700px]]
&lt;small&gt;Tugna 16. Awlellu yezmer ad yeldi ɣer uɣawas war abeddel n yimeccaqen adiganen. Taɣda deg tugna tayeffust tettawi abrid yezzin ɣef uwlellu.&lt;/small&gt;

Abrid agejdis (géodésique, asegzi dagi) d abrid iḥerzen tanila s wamek i t-id-tesbadu tallunt. Deg tallunt n Riemann, iberdan-a sɛan taɣara n ubrid ameẓẓyan s teɣzi deg yiḥricen meẓẓiyen iwulmen. Ur ilaq ara yal abrid agejdis ad yili d ameẓẓyan akk gar sin n yixfawen s wudem amatu.

Deg tfizikt n Einstein, tallunt d wakud ttwazerwen s tanzeggit n Lorentz: asket-is ur yesɛi ara yiwen unagraw n yizamulen am Riemann. Ihi «tajumma yeɛwejjen» d asegzi i d-iqerben kan, ur d-yessegzi ara iman-is akk tiẓri n wassaɣ n tallunt d wakud (relativité).

== 17. Tasnidegt d talɣa meṛṛa ==
Tasnidegt tzerrew timitar i ur nettbeddil ara s ubeddel amaɣlal i yesɛan amutti amaɣlal. Zemrent ad ttwazerwent tuqqna, ixjaḍ d wamek i tettwasdukkel tallunt. Teɣzi d tɣmar ur ilaq ara ad ttwaḥerzent. Ihi tasnidegt teqqen ɣer tanzeggit, maca ur telli ara d yiwet n taɣult s sin n yismawen.
[[Tugna:Tuṭṭfa n ugdil seg 2026-11-02 11-11-35.png|centré|636x636px]]
&lt;small&gt;Tugna 17. Amaḍal d ukruri mgaraden deg umḍan n yixjaḍ. amaḍal ur yesɛi ara axjiḍ, a akruri yesɛa yiwen uxjiḍ iɛeddan deg tlemmast-is, Tigniwin-a sseknayent tijummiwin n rrif kan, mačči d talɣiwin yeččuren d axel.&lt;/small&gt;

'''χ = N₀ − N₁ + N₂; i tajumma iɣelqen tusɣilt: χ = 2 − 2g'''

I tajumma yettwabḍan ɣef talɣiwin, N₀ d amḍan n tqacucin, N₁ n yidis d N₂ n wudmawen. χ d taskant n Euler. Ɣef rrif n ugasas, 8−12+6 = 2. Ɣef akruri, χ = 0. Deg tnfalit tis snat, g d amḍan n yixjaḍ s unamek n wanaw(genre), tajumma ilaq ad tili teqqen, teɣleq, tusɣilt d war rrif.

Tazrawt n talɣa meṛṛa tezmer ad d-tefk tilisa i tiknit. Asekkud n Gauss-Bonnet yeqqen aɣred n tiknit n Gauss ɣer χ n tajumma. D amedya ameqqran n tuqqna gar usket adigan d talɣa n tallunt meṛṛa.

== 18. Tanzeggit taljibṛant ==
Tanzeggit taljibṛant tzerrew tegrummiwin n tifrat n tegdiwin n yigetfulen. Ma P(x,y)=0, tineqqiḍin i yettḥeqqiqen tagda-a zemrent ad d-fkent azlig. Tarrayt-a tesdukkel aljibṛ d talɣiwin; tazrawt tamatut tezmer ad tili ɣef yimḍanen ilawen, isemlalen neɣ taɣulin nniḍen.
[[Tugna:Taneqqit tasuft.png|centré|688x688px]]
&lt;small&gt;Tugna 18. Tama taẓelmaḍt: azlig y² = x³ − x + 1 war taneqqiṭ tusligt deg uɣawas ilaw. Tama tayeffust: y² = x³ yesɛa taneqqiṭ tasuft deg (0,0).&lt;/small&gt;

I uzlig P=0, taneqqiṭ tasuft tḥeqqiq P = 0 d akk izellumen imezwura ∂P/∂x = ∂P/∂y = 0. Deg y²−x³=0, ayen-a yettili deg (0,0). Deg y²−x³+x−1=0, ulac taneqqiṭ i yeṭṭfen akk tawtilin-a. Amedya yessekza ayɣer aljibṛ yezmer ad yessegzi tikniyin d yimeẓla n talɣa.

Deg tanzeggit taljibṛant, imḍanen isemlalen zemren ad fken talɣa tummidt n tifrat: ayen yettban d sin n yifurkan deg tugna tilawt yezmer ad yesɛu tuqqniwin nniḍen deg tallunt tasemlalt. Ur ilaq ara tugna tilawt ad tettwaḥsab d tamusni tummidt n talɣa. Tanzeggit taljibṛant tesɛa iseqdacen deg tiẓri n yimḍanen, ladɣa deg tazrawt n tifrat n tegdiwin s yimḍanen ummiden neɣ imeɣẓanen, izligen ilipsiyen d teɣri n tegdiwin. Iwakken ad tili tɣuri n lsas, ilaq aljibṛ imzireg d kra n tiẓri n tegrummiwin.

== 19. Tanzeggit d usiḍen s uselkim ==
Tanzeggit n usiḍen tzerrew ilugan i asiḍen n wassaɣen anzeggane: amager n yiɣallen, taɣlaft taffensut, abḍu n tajumma ɣef ikerdisen d tazrawt n yiberdan. Tanzeggit tafrarayt tzerrew daɣen tegrummiwin n tneqqiḍin d talɣiwin tinzegganin, d wassaɣen gar-asent.
[[Tugna:Tuṭṭfa n ugdil seg 2026-11-04 12-56-10.png|centré|785x785px]]
&lt;small&gt;Tugna 19. Yiwen wamud n 15 n tneqqiḍin: taɣlaft taffensut, abḍu ɣef ikerdisen n Delaunay d taɣulin n Voronoi. Tilisa i yettbanen deg ugdil d tamuɣli n uḥric n uɣawas.&lt;/small&gt;

Tagrumma taffensut teṭṭef iɣil meṛṛa i yeqqnen yal snat n tneqqiḍin-is. Taɣlaft taffensut n wamud d tagrumma taffensut tameẓẓyant i yeṭṭfen akk tineqqiḍin n wamud-nni. Deg wudlif n Voronoi, yal taneqqiṭ n wamud tesɛa taɣult i yesdukklen akk tineqqiḍin i iqerben ɣur-s ugar n tneqqiḍin nniḍen n wamud, neɣ i yebɛaden s yiwen umeccaq ɣur-s d kra seg-sent.

Abḍu n Delaunay d abḍu ɣef ikerdisen, s tawtilt-a: i yal akerdis, ulac taneqqiṭ nniḍen n wamud deg daxel n twinest iɛeddan ɣef kraḍ n tqacucin-is. Deg waddad amatu, abḍu n Delaunay d wudlif n Voronoi qqnen gar-asen akka: snat n tneqqiḍin n wamud ttwaqqnent s yiɣil deg ubḍu n Delaunay ma taɣulin-nsent n Voronoi ccerkent yiwen n yidis. 

Ilaq ad ttwasxedmen yisiḍen s tiseddi: tuccḍa tameẓẓyant tezmer ad d-tefk agmuḍ ur neṣḥiḥ ara mi ara nsenqed ma sin n yiɣallen ttemlilin neɣ ala. Tarrayin-a sɛant azal deg usnulfu n tigniwin s kraḍ n tsektiwin (3D), deg tarubut, deg usnulfu n yikarṭiyen d lebni n yimedyaten n tfizikt.

== 20. Tarrayt n wesket n umeccaq ==
Tallunt timizrirt d tagrumma X akked tesɣent d i d-yettaken ameccaq gar yal snat n tneqqiḍin. Ilaq '''d(x,y) ≥ 0; d(x,y)=0 ma x=y''' kan; '''d(x,y)=d(y,x); d(x,z) ≤ d(x,y)+d(y,z)'''. 

Tawtilt taneggarut d targadda n ukerdis: abrid usrid ur yugar ara abrid iɛeddan seg yiwet n tneqqiṭ nniḍen.
[[Tugna:Tuṭṭfa n ugdil seg 2026-11-05 12-06-14.png|centré|608x608px]]
&lt;small&gt;Tugna 20. Kraḍ n terrayin n umeccaq. Yal talɣa tesdukkel tineqqiḍin i bɛaden s umeccaq ≤ 1 seg (0,0); rrif-is yesɛa ameccaq = 1.&lt;/small&gt;

'''d₂ = √(Δx² + Δy²); d₁ = |Δx| + |Δy|'''

'''d∞ = max(|Δx|, |Δy|)'''

Deg umedya A(0,0), B(3,4), ameccaq n Aklid d 5, win n Manhattan d 7, win n Chebyshev d 4. Manhattan yettemcabi ɣer ubrid deg uẓeṭṭa n yiberdan ibedden: nezmer ad neddu kan s sin n yidis n uẓeṭṭa. Ihi «aqrab» yeqqen ɣer tarrayt n wesket, mačči ɣer tugna kan.

Tarrayt n umeccaq ur teqqin ara kan ɣer tallunt i nettwali. Nezmer ad nesbadu ameccaq gar tesɣunin, imḍan n yibeddilen gar sin n yiḍrisen, neɣ amgired gar talɣiwin. Maca yal tanfalit i nsemmi «ameccaq» ilaq ad tettasenqed ma tḥerrez akk tawtilin n tallunt timizrirt.

Asekkud n Pythagore yesɛa azal deg umeccaq n Aklid. Ma nbeddel tarrayt n wesket, tanfalit n twinest d ubrid ameẓẓyan ad tbeddel. Tigniwin-a sseknayent umgired gar uẓeṭṭa n yimsidag d wesket i yettwafernen deg-s.

==Imuren imeqranen n tenzeggit ==

* [[Tanzeggit tuklidit]] 

* [[Tanzeggit artuklidit]] 

* [[Tanzeggit tummit]]

* [[Tanzeggit tigriwt]]

* [[Tanzeggit taljibirt]]

* [[Tanzeggit tanebrurzant]] 

* [[Aljiber imzireg]]

== Amezruy n tenzeggit ==


[[Taggayt:Tusnakt]]</text>
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'''Dawed''' ([[Tutlayt taɛebrit|taɜebrit]]: דוד ''Dawid)'' d agellid wis sin n tgelda n [[Israyil]]   tamzikit, yuder deg uwines wis mraw send talalit n [[Ɛisa]].
Deg ajjed n [[Islam|tineslemt]], d nnbi seg 25 inbiyen yuran di [[Leqran]].

== Tudert-is ==
D ameksa n udrum n [[Yahuda]], d mmis amaẓuz n [[Yasa]] , [[Ḍalut]] agellid n imir nni yusem fellas acku yebɣa ad as yekkes tagelda mi i yenɣa [[Ǧalut]] ameqran.
Asmi yemmut [[Ḍalut]] yuɣal Dawed d agellid yeẓaz tilisa n [[tgelda n israyil]] alama d [[Maṣer]] akked [[Furat]] imi yemmut dawed ixelf t id [[Sliman]] mmis ɣef uqerru n tgelda.

{{Inabiyen}}

[[Category:Tameddurt]][[Category:Ajjed]]</text>
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      <comment>arniɣ ayen ilaqen</comment>
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      <text bytes="1039" sha1="is53n8ekft8qd4krizz8qpa6vnmozxv" xml:space="preserve">{{Databox}}
'''''{{lang|en|Microsoft Corporation}}''''' d taṛmist n tsenselkimt d tamikṛusenselkimt agettaɣlant [[Iwunak idduklen n Marikan|tamarikanit]], tettwassebded sɣur [[Bill Gates]] d [[Paul Allen]]. Armud ines amezzwaru d taneflit d ussenzi n [[Anagraw n wammud|inagrawen n wammud]] akkw d [[aseɣẓan|iseɣẓanen]].

Tettwassen s waṭas n yifarisen-is am Windows, Microsoft 365, Azure, Xbox, GitHub, LinkedIn akked Microsoft Copilot.

Tarmiṣt-a tettwasebded deg 4 Yebrir 1975 sɣur Bill Gates akked Paul Allen deg Marikan. Deg tazwara, leqdic-is yella ɣef yiznanen n usihel n yiselkimen, maca deg yiseggasen i d-iteddun, tuɣal d yiwet seg teṛmisin i yesɛan tazrirt tameqqrant ɣef wamek i seqdacen yimdanen iselkimen deg tudert n yal ass.

Microsoft ur teqqim ara kan deg usufeɣ n Windows. Tura, leqdic-is yebḍa ɣef waṭas n taɣulin: iseɣẓanen n tɣellist, aselkim n usigna, tigzi taragmawant, aselmed umḍin, tasenselkimt n teṛmisin, akked wuraren uvidyu.
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    <title>Isusiyen</title>
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      <text bytes="1476" sha1="k6cjzjmra213aano94a8vxpm8x9j0q7" xml:space="preserve">{{Infobox ethnic group
&lt;!-- [[WP:NOETHNICGALLERIES]] --&gt;
|group=Icelḥiyen, Isusiyen
|population=~5.1 imelyan&lt;ref name=&quot;Comm&quot;&gt;{{cite web|last1=Haut commissariat au Plan, Moroccan Kingdom|first1=Haut commissariat au Plan|title=Recensement général de la Maroc|url=http://rgphentableaux.hcp.ma/Default1/|website=HCP|publisher=Haut commissariat du Plan|accessdate=16 August 2016|language=fr|archive-date=20 April 2024|archive-url=https://web.archive.org/web/20240420192516/http://rgphentableaux.hcp.ma/Default1/|url-status=dead}}&lt;/ref&gt; (14.2% n lmerruk)
|popplace={{flagcountry|Morocco}}-[[Idurar n waṭlas]], [[Sus]]
|langs=[[Tacelḥit]]
|rels=Amur ameqqren d [[Islam|Inselmen]] 
|related=[[Imaziɣen]] nniḍen
|flag=
|native_name=ⵉⵛⵍⵃⵉⵢⵏ (''Icelḥiyen'')|native_name_lang=}}
[[Tugna:COLLECTIE TROPENMUSEUM Berbervrouw in feestkledij uit Tafraoute Zuid-Marokko TMnr 60033850.jpg|vignette]]
'''Isusiyen''' neɣ '''Ayt Sus''' (s [[tifinaɣ]]: ⵉⵙⵓⵙⵉⵢⵏ) d [[aɣref]] [[imaziɣen|amaziɣ]] yettidiren deg unẓul n [[Ameṛṛuk|tgelda n Umeṛṛuk]], deg tmennaṭ n [[Sus]] ilan (yesɛan) [[Agadir]] d tamdint tamenrut. D nutni i d agraw meqqren akk gar yegrawen Imaziɣen deg [[Tamazɣa|tmazɣa]] imi ahat wwḍen 12 imelyan. Tutlayt i d ttmeslayen, d [[Tutlayt Tasusit|tasusit]] igan d yiwet gar waṭas n [[tutlayin timaziɣin]].

==Tiwelhiwin==
{{refs}}
[[Taggayt:iɣerfan]]
[[Taggayt:Iɣerfan iẓaranen n tferka n ugafa]]
[[Category:Agdud]]</text>
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  <page>
    <title>OpenAI</title>
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      <text bytes="10773" sha1="h3jk09z1gwi1rhyhjq2rd93qbqu810y" xml:space="preserve">{{Infobox company
| name = OpenAI
| official_name = OpenAI
| type = Taṛmist Tatiknulujit
| founded = 2015
| founder = Sam Altman, Elon Musk, Greg Brockman, Ilya Sutskever, Wojciech Zaremba, John Schulman
| headquarters = San Francisco
| country = Iwunak Yedduklen
| industry = Tigzi taragmawant
| products = ChatGPT, DALL·E, Sora
| website = https://openai.com
| image = [[File:1515 Third Street.jpg|300px]]
| image_caption = Tasɣimt n OpenAI deg San Francisco.
| logo = [[File:OpenAI Logo.svg|200px]]
| logo_caption = Alugu n OpenAI
| wikidata_operating_income = yes
| wikidata_net_income = yes
| wikidata_revenue = yes
}}

'''OpenAI''' d taṛmist n unadi d usnas deg '''[[Tigzi Taragmawant|tigzi taragmawant]]''' (AI) i d-yennulfan deg useggas 2015 deg Marikan, d tuddsa ur nettnadi ara ɣef tedrimt. Iswi agejdan i d-teskanay OpenAI d ad teḍmen belli tigzi taragmawant tamatut (AGI) ad d-tawi abaɣur i yimdanen merra. Ass-a, OpenAI tettwassen s waṭas s yifarisen d yinagrawen am ChatGPT, imudam GPT, Codex, akked wallalen i yesseqdacen imsihal seg API.

== 1. Talalit n OpenAI ==
OpenAI tettwasnulfa-d sɣur [[Sam Altman]] d [[Elon Musk]] d wiyaḍ deg 2015 am tuddsa ur nettnadi ara ɣef tedrimt (nonprofit). Seg tazwara, tuddsa-a tefka iman-is yiwen n yiswi ɣezzifen: asnerni n tigzi taragmawant s wudem ara d-yawin abaɣur i yimdanen merra, ladɣa ma tewweḍ tetiknulujit-a ɣer uswir n '''tigzi taragmawant tamatut'''.

Tamiḍrant-a tettak azal i wugur ameqqran: ma yella inagrawen n tigzi taragmawant uɣalen sɛan tazmert meqqren, ilaq tazmert-nsen ur tettwakerrez ara kan deg ufus n kra n yimdanen, n tiṛmisin neɣ n tmura, maca ad tettwaseqdac i lfayda tamatut.

Deg 2019, OpenAI tesnulfa-d aferdis n tedrimt iwakken ad tessiweḍ ad d-tawi idrimen, imdanen d tazmert n usiḍen i ilaqen i usnerni n yimudam imeqqranen. Aferdis-a yella ddaw n leḥkem n tuddsa ur nettnadi ara ɣef tedrimt.

== 2. D acu-tt tigzi taragmawant? ==
Tigzi taragmawant d taɣult n tussna d tetiknulujit i yesnernayen inagrawen n tmacint i izemren ad xedmen tiwuriwin i yeḥwaǧǧen s umata kra n tzemmar n tigzi: tegzi n tutlayt, tifrat n wuguren, asuddes n yisefka, tira n yiḍrisen, asnulfu n tugniwin, asihel, neɣ tuddma n kra n yimektayen seg yisefka.

Ur ilaq ara, ad nefhem awal tigzi dagi amzun tamacint tesɛa iman, iḥulfan neɣ tamuɣli n umaḍal am umdan. Imudam n tura d inagrawen n uiḍen i yettwaselmaden ɣef yisefka yerna xeddmen s yimenzayen n tussna n uselmed n tmacint.

OpenAI tettadi ladɣa deg yimudam imuqqranen(frontier), asuddes d tifrat n wuguren, inagrawen i izemren ad gzun ugar n yiwen n wanaw n yisefka (multimodal systems), akked wamek ara yettwaseqdec AI s tɣellist.

== 3. Tigzi taragmawant tamatut — AGI ==
Iswi ɣezzifen n OpenAI yeqqen ɣer wayen i semman ''Artificial General Intelligence (AGI)'', i nezmer ad d-nini s teqbaylit tigzi taragmawant tamatut.

OpenAI tesbadut AGI am inagrawen s timmad-nsen i izemren ad ɣelben imdanen deg tuget n twuriwin yesɛan azal adamsan.

Tamiḍrant n tamatut d tagejdant. Anagraw n tigzi taragmawant yezmer ad yili igerraz deg yiwet n twuri kan; AGI, ma tewweḍ tetiknulujit ɣer din, ilaq ad tesɛu tazmert wessiɛen: ad tegzu uguren yemgaraden, ad tesdukkel tamusni seg waṭas n taɣulin, ad tesseqdec ayen telmed deg tegnatin timaynutin, yerna ad tefru uguren ur nettwaselmed ara fell-asen s talɣa tusridt.

OpenAI tettwali AGI am iswi n wakud ɣezzifen, maca akud ilaqen akken ad naweḍ ɣer AGI mazal ur yettwassen ara.

== 4. Imudam GPT ==
Gar yisenfaren i d-yerran OpenAI tettwassen deg umaḍal llan imudam GPT — ''Generative Pre-trained Transformer''.

Imudam-a d inagrawen n tigzi taragmawant i yettwaselmaden ɣef yisefka imeqqranen. S uselmed-a, zemren ad gzun asiḍen n tutlayt, ad d-snulfun iḍrisen, ad d-rren ɣef yisteqsiyen, ad frun uguren, ad ɛiwnen deg usihel, yerna imudam imaynuten zemren ad xedmen akked yiḍrisen, tugniwin d wanawen-nniḍen n yisefka. OpenAI teskanay tawacult GPT am inagrawen i izemren ad gzun asiḍen, ad d-snulfun agbur yerna ad xedmen tifrat n wuguren deg waṭas n yimeslayen n yisefka.

Anamek n azarsileɣ(pre-trained) d akken amudam yettwaselmad uqbel ad yettwaseqdec deg udiwenni. Turriwt(Generative), ma d nettat, temmal-d tazmert-is n usnulfu n ugemmuḍ am yiḍrisen neɣ tangalt n useɣẓan.

== 5. ChatGPT ==
[[ChatGPT]] d afaris agejdan n OpenAI i yiseqdacen. D agrudem n udiwenni i yettaǧǧan amdan ad yesseqdec imudam n tigzi taragmawant s tutlayt tagamant. OpenAI tessegza ChatGPT am ufaris-is agejdan i yiseqdacen.

Aseqdac yezmer ad yesteqsi, ad yessuter asegzi, ad yaru neɣ ad iseɣti aḍris, ad yesseqdec tasleḍt, ad yelmed tamiḍrant n tussna, ad yessuter tallelt deg usihel, neɣ ad ixdem ɣef yisefka d yisemliyen.

Azal n ChatGPT deg umezruy n tigzi taragmawant d ameqqran acku yessekcem imudam n tutlayt ɣer useqdec n yal ass. Deg umḍiq anda tigzi taragmawant tella tettwassen ladɣa deg tesdawiyin, tanaremt d tkebbaniyin n tetiknulujit, agrudem n udiwenni yerra-tt d allal i yezmer ad yesseqdec umdan s tutlayt-is.

== 6. Codex d usihel ==
Taɣult-nniḍen i deg tesseqdac OpenAI tigzi taragmawant s waṭas d asihel.

'''Codex''' d anagraw n tigzi taragmawant i yellan i uxeddim ɣef tengalt d yisenfaren n useɣẓan. Yezmer ad yegzu tangalt yellan, ad yesseɣti tuccḍiwin, ad ibeddel taneɣruft n usenfar, ad yernu timahilin timaynutin, yerna ad ixdem tiwuriwin n usihel seg tazwara ar taggara.

Anect-a yeskanay abeddel meqqren deg useqdec n tigzi taragmawant: seg unagraw i d-yettarra kan ɣef yisteqsiyen ɣer umeggi n tigzi taragmawant (AI agent) i izemren ad yesseqdec allalen, ad ixdem ddeqs n yimahilen yerna ad ikemmel ɣer yiswi i as-yettunefken.

== 7. Anadi deg OpenAI ==
OpenAI mačči d taṛmist n yifarisen kan. Anadi yezga d yiwen seg yiḥricen-is igejdanen.

Taṛmist txeddem ɣef usnerni n yimudam n tigzi taragmawant, tifrat n wuguren, inagrawen wagutaskaran(multimodal), tɣellist, akked useqdec n yimudam s wudem ara yilin d abaɣur i yimdanen.

Yiwet seg tmuɣliwin timeqqranin d aseqdec n tigzi taragmawant deg unadi ussnan. Deg tiɣula am tusnakt, tussna, asihel d tesleḍt n yisefka, anagraw yezmer ad yuɣal d allal ara iɛiwnen imnadiyen deg usnulfu n turdiwin, tifrat n wuguren d useɣiwel n unadi.

== 8. Taɣellist d umṣada ==
Mi ara tettnerni tazmert n tigzi taragmawant, yettnerni daɣen wazal n tɣellist.

Anagraw yesɛan tazmert meqqren yezmer ad d-yawi abaɣur, maca yezmer daɣen ad d-yawi uguren ma yella ixdem tuccḍiwin, ma yettwaseqdec i wayen n diri, neɣ ma yella tikli-s ur temṣada ara akked wayen i yebɣa umdan.

Ɣef waya, OpenAI tessemras tamiḍrant n &quot;''alignment&quot;'', i d-yemmalen s umata amṣada n tikli n unagraw n tigzi taragmawant akked yiswan d tɣellist i d-yefka umdan.

'''''OpenAI Charter''''' yesseḥbibber ɣef sin yimenzayen meqqren: ad yettwabḍu ubaɣur n AGI s wudem wessiɛen, yerna ad yettwaseḥbiber ɣef tɣellist n wakud ɣezzifen.

== 9. Taneɣruft n OpenAI ==
Taneɣruft n OpenAI tbeddel s wakud.

OpenAI tebda deg 2015 d tuddsa ur nettnadi ara ɣef tedrimt. Deg 2019, tesnulfa-d aferdis n tedrimt iwakken ad tesnerni anadi d usnas-is.

Deg 28 Tubber 2025, tettwasekna-d taneɣruft tamaynut:

tuddsa ur nettnadi ara ɣef tedrimt tuɣal tettusemma ''OpenAI Foundation'';

aferdis n tedrimt yuɣal d ''OpenAI Group PBC'', anamek-is d ''Public Benefit Corporation'';

''OpenAI Foundation'' teqqim tettḥekkim deg ''OpenAI Group''.

OpenAI Foundation tesɛa 26% n iḥricen deg ''OpenAI Group''. Microsoft, deg tallit n useggem n taneɣruft, tesɛa azal n 27%, ma d 47% i d-yeqqimen sɛan-t ixeddamen n tura d wid yezrin akked yimendaden-nniḍen.

Taneɣruft-a tebɣa ad tesdukkel iswi n OpenAI akked tezmert-is ad d-tawi idrimen imeqqranen i yeḥwaǧǧ unadi n tigzi taragmawant.

== 10. Tazmert n usiḍen ==
Aselmed n yimudam imeqqranen n tigzi taragmawant yeḥwaǧǧ ddeqs n tezmert n usiḍen.

Anect-a yesɛa azal acku asnerni n yimudam ur yeqqin ara kan ɣer tarrayin n uselmed. Yeḥwaǧǧ daɣen iselkimen s tezmert tameqqrant n usiḍen, tiḥerci n yisefka, tazmert n trisiti, iẓeḍwan, isefka d tedrimt.

Ɣef waya, tigzi taragmawant n uswir unnig tuɣal d taɣult anda anadi ussnan, tiḥerci n usiḍen d tdamsa qqnen gar-asen.

== 11. OpenAI d Microsoft ==
Microsoft tesɛa assaɣ adamsan d utiknulujan ameqqran akked OpenAI. Deg taneɣruft i yettwasbedden deg 2025, Microsoft tesɛa azal n 27% n OpenAI Group.

Assaɣ-a yesɛa azal ladɣa deg tezmert n usiḍen d usnerni n yifarisen n tigzi taragmawant. Maca, deg taneɣruft n leḥkem n OpenAI, OpenAI Foundation i yeqqimen tettḥekkim deg OpenAI Group, mačči Microsoft.

== 12. OpenAI deg 2026 ==
Deg 2026, OpenAI ur teqqim ara d tanaremt n unadi kan. Tuɣal d taṛmist tameqqrant i yesɛan inagrawen i yiseqdacen, allalen i yimsihel, API i tkebbaniyin, imudam n tigzi taragmawant n uswir unnig, akked yimeggiyen i izemren ad xedmen tiwuriwin ɣezzifen.

ChatGPT d Codex mmalen-d sin n wudmawen n ubeddel-a: ChatGPT d agrudem wessiɛen n tigzi taragmawant i yiseqdacen, ma d Codex yettwabna ugar i uxeddim s tengalt d yisenfaren n useɣẓan.

Anadi n OpenAI yettkemmil daɣen deg tifrat n wuguren, imudam ugetaskaran, tɣellist d usnerni n ubrid ɣer AGI.

== 13. Abaɣur i tmetti ==
Tigzi taragmawant tezmer ad tbeddel aṭas n tiɣula: aselmed, tussna, tadamsa, asihel, aẓeṭṭa, axeddim, tasensegmit, asnulfu d unadi ussnan.

Ma yella inagrawen n tigzi taragmawant zemren ad xedmen ugar n twuriwin i ixeddem umdan ass-a, ad d-ffɣen yisteqsiyen imaynuten:

Amek ara tbeddel tarrayt n uxeddim? Anwi ixeddamen ara d-ilalen? Anwi ara ibeddlen neɣ ara iruḥen? Amek ara ttwasqedcen yimudam-a deg uselmed? Anwa ara yesɛun leḥkem ɣef yiḥricen igejdanen n tetiknulujit-a? Amek ara neḍmen belli abaɣur-is ad ibḍu gar yimdanen?

D isteqsiyen-a i yerran asnerni n tigzi taragmawant mačči d tamsalt n tetiknulujit kan, maca d tamsalt tadamsant, tinmettit, tasertant d tasertit n tussna.

== 14. Uguren d umeslay ɣef OpenAI ==
Am yal taṛmist tameqqrant n tetiknulujit, OpenAI tettmagar isteqsiyen d umeslay ɣef tarrayt-is.

Gar temsal tigejdanin llan: aḥraz n yisefka, tanezzut n yimudam, asemres n wayen d-yettwafkan sɣur yimdanen i uselmed n yimudam, tɣellist, leḥkem ɣef tetiknulujit, tasertit n yifarisen, tasertit n uxeddim, akked wamek ara tettbeddil tigzi taragmawant tuddsa n tmetti.

Ɣef waya, OpenAI ur ilaq ara ad tettwafhem kan seg yifarisen-is. Iwakken ad nefhem azal-is, ilaq ad nwali daɣen tamsalt tameqqrant i d-tessufuɣ tetiknulujit i tesnernay: anwa ara yessnernin tigzi taragmawant n uzekka, anwa ara tt-yesqedcen, anwa ara yettḥekkimen deg-s, yerna anwa ara yawin abaɣur seg-s?</text>
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  <page>
    <title>Tiberyus</title>
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    <id>25634</id>
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      <id>117869</id>
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      <timestamp>2026-11-04T19:00:49Z</timestamp>
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        <username>Gurzil90x</username>
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      <comment>arniɣ ayen ilaqen</comment>
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      <text bytes="22589" sha1="jb68vvx9m67okgstmgenx0b7iu8nx3p" xml:space="preserve">{{Infobox biography|item=Q1407|image=[[File:(Venice) Tiberius Portrait of the 'Imperium Maius' type in Museo Archeologico Nazionale.jpg|thumb|(Venice) Tarudemt n Tiberyus s wanaw n 'Imperium Maius' deg usalay n &quot;Archeologico Nazionale&quot;]]|caption=Amenkad Tiberyus.|date of birth=16 Wambeṛ 42|nationality=Tarumanit|date of death=16 Meɣres 37}}

'''Tiberyus''' (s tlaṭinit: Tiberius Caesar Augustus), i d-ilulen ass n 16 Wamber 42 send talalit n Ɛisa (S.T.Ɛ.), i yemmut ass n 16 Meɣres 37 seld talalit n Ɛisa (S.L.Ɛ.), yella d amenkad wis sin n Tmenkda tarumanit. Yeḥkem seg 18 Ɣuct 14 ar 16 Meɣres 37 S.L.Ɛ., deffir n [[Uɣustus]], amenkad amezwaru n Ruma.

Tiberyus yettwaḥsab gar yimenkaden i yesɛan azal ameqqran deg umezruy arumani. Ɣas akken ur yesɛi ara tamanegt n Uɣustus, yella d amseddas n ṭṭrad iǧehden, d anedbal i yessnen amek ara yettwaḥrez wayla n Tmenkda, d win i yesnernan tarrayin n useḥkem i d-yegǧa Uɣustus.

Tallit-is tettwasen s waṭas n tneqqiḍin i yemgaraden: talwit deg waṭas n tmura n Tmenkda, asnerni n wayla n ddula, uguren gar umenkad d Senat, tixidas tisertanin gar yimdanen i iqerrben ɣer umenkad, asnerni n tazmert n yiɛessasen n Pretorya, akked uselḥu n tedbelt seg ugafa n tegzirt n Capri deg yiseggasen-is ineggura.

Tiberyus yella daɣen d amenkad n tallit i deg yedder [[Ɛisa|Ɛisa n Nazaret]](ma neḥsab dakken s tidet [[Ɛisa]] yella s wudem amazray, mačči kan s wudem asɣanen). Ɣef waya, isem-is yettwabder deg yidlisen n tsertit, n umezruy d yidles amasiḥi.

== Aḥric amezwaru — Tudert-is send adabu ==

=== 1. Ruma deg tallit n tlalit n Tiberyus ===
Iwakken ad nefhem tudert n Tiberyus, ilaq ad nẓer tegnit tasertant n Ruma deg useggas 42 S.T.Ɛ.

Deg tallit-nni, Ruma mazal-itt s yisem d tagduda (Res publica Romana), maca tazmert tasertant tebda tettnejmaɛ deg yifassen n kra n yimdanen iǧehden.

Ṭṭrad agensan gar [[Julius Caesar]] d yiɛdawen-is, syin gar [[Uɣustus|Octavianus]] d Mark Untunyus, yessexreb anagraw aqbur n [[Tagduda Taṛumanit|tagduda tarumanit]].

Octavianus, win ara yuɣalen d Uɣustus, yessnerna tazmert-is armi yuɣal d amdan i yesɛan tazmert tameqqrant deg Ruma.

Tiberyus, i d-ilulen deg tegnit-a, ad yedder akk ibeddilen imeqqranen i d-yewwin asnulfu n [[Tamnekda Tarumanit|Tmenkda tarumanit]].

=== 2. Tallit n temẓi ===
Tiberyus ilul ass n 16 Wamber 42 S.T.Ɛ., deg Ruma. Baba-s, Tiberiyus Claudius Nero, yella d amdan n tawacult Claudii, yiwet seg twaculin timeqqranin n Ruma.

Yemma-s, Livia Drusilla, tella d tameṭṭut i yesɛan azal ameqqran deg tsertit tarumanit.

Deg yiseggasen imezwura n tudert-is, tawacult-is tella deg tegnit taɛekkamt, acku baba-s yella deg tama n yiɛdawen n Octavianus.

Tawacult teḥwaǧ ad tarewel seg Ruma, uqbel ad d-tuɣal mi terkad tegnit tasertant.

==== 2.1. Livia d Uɣust ====
Deg 39 S.T.Ɛ., Livia tefraq d urgaz-is amezwaru, syin tuɣ Octavianus deg 38 S.T.Ɛ.

S wakka, Tiberyus yuɣal d mmi-s n tmeṭṭut n Octavianus, syin d mmi-s s tedbelt(s usmemmi) n [[Uɣustus]].

Aya yeldi-as abrid ɣer tsertit tameqqrant n Ruma. Maca ur yelli ara d amezwaru i yebɣa Uɣustus ad t-yeḍfer deg useḥkem.

=== 3. Taɣuri d uselmed n Tiberyus ===
Tiberyus yekker deg twennaḍt n yimdanen i yesɛan azal deg Ruma.

Yelmed:

- Tlaṭinit d tegrigit.

- Amezruy n Ruma d win n Yigrigiyen.

- Tamsislit d tarrayin n umeslay deg ugraw.

- Tasertit d yilugan n tagduda.

- Tarrayin n useḥkem n yiserdasen.

- Tifelsafit d yidles agrigi.

Tiberyus yella d amdan i yettwaḥesben d win i yettxemmimen aṭas, ur yettmeslay ara s waṭas, maca yettɛassa s leḥder ayen i d-yettḍerrun.

Tiberyus yebda tudert-is tasertant deg tlemmast n yIbeddilen n Uɣustus.

=== 4. Tiberyus d amseddas n ṭṭrad ===
Send ad yuɣal d amenkad, Tiberyus yella d yiwen seg yimseddasen n ṭṭrad iǧehden n Ruma.

Yettwasekcem deg waṭas n yimennuɣen iserdasen deg tmura yemgaraden.

==== 4.1. Ṭṭrad deg Hispania ====
Deg yiseggasen 20 S.T.Ɛ., Tiberyus yebda ad yettekki deg yimennuɣen iserdasen n Uɣustus.

Yettwasekcem deg kra n yimennuɣen deg Hispania, anda Ruma tella tettḥarab iwakken ad tesnerni tazmert-is ɣef waṭas n tmura.

==== 4.2. Aɣelluy n tgelda n Parthia deg tsertit tarumanit ====
Deg 20 S.T.Ɛ., Tiberyus yella d yiwen seg yimdanen i yesɛan tawuri deg uselḥu n tmeslayt tasertant gar Ruma d Parthia.

Ayen i d-yellan ur yelli ara d ṭṭrad ameqran, maca d anerni tasertant i Ruma.

Ayen i d-yettwafken i Ruma yella d tiririt n yizamulen iserdasen i tesseṛṛeḥ deg ṭṭradat yezrin.

Aya yella d asmekti n tamanegt n Ruma, acku izamulen iserdasen sɛan azal ameqqran deg tmetti tarumanit.

==== 4.3. Ṭṭrad deg Alpes ====
Deg 15 S.T.Ɛ., Tiberyus d gma-s Drusus msefhamen iwakken ad snernin tazmert n Ruma deg tmura n Alpes.

Ɣelben kra n yigrawen n yimdanen i yellan deg temnaḍt.

Aya yessnerna tazmert n Ruma deg ugafa n ṭṭelyan, yerna yesseǧhed iberdan n tnezzut d usiweḍ n yiserdasen.

==== 4.4. Ṭṭrad deg Pannonia ====
Tiberyus yesɛa tawuri tameqqrant deg uselḥu n ṭṭrad deg Pannonia, temnaḍt i d-yezgan deg tama n Danube.

Deg 12–9 S.T.Ɛ., yesɛa tawuri deg yimennuɣen i d-yewwin asnerni n tazmert tarumanit deg temnaḍt.

Deg 6–9 S.L.Ɛ., yesseḥbes yiwen n umennuɣ ameqqran n yimdanen n Illyricum i yellan mgal Ruma.

Amennuɣ-a yettwassen deg umezruy s yisem Bellum Batonianum.

Yella d yiwen seg yimennuɣen iɛekkmen i tmenkda deg tallit n [[Uɣustus]].

==== 4.5.Ǧermaniya ====
Tiberyus yella daɣen deg yimennuɣen n Ruma deg Ǧermaniya.

Deffir tawaɣit n ṭṭrad n Teutoburg deg 9 S.L.Ɛ., anda Ruma tesṛuḥ kraḍ n yeḥricen seg tredsa-s, Tiberyus yesseǧhed taɣellist n tilisa n Ruma.

Ur yelli ara d win i d-yewwin aɣelluy n Ǧermaniya meṛṛa, maca yessaweḍ ad yesseḥrez kra n temnaḍin d yiserdasen n Ruma.

==== 4.6. Azal-is deg ṭṭrad ====
Tiberyus yettwassen s kra n tulmisin:

1. Aheggi n ṭṭrad uqbel amennuɣ.

2. Aḥraz n yiserdasen d usiweḍ n wuččî(lmakla).

3. Aseḥbes n yimennuɣen ur nesɛi ara lfayda.

4. Aseqdec n tsertit d umeslay send ṭṭrad.

5. Aḥraz n tilisa deg umkan n usnerni war tilas.

Tarrayt-is temgarad ɣef tin n kra n yimseddasen i yettnadin kan ɣef tamanegt deg ṭṭrad.

Tiberyus yettḥadar aṭas asṛuḥ n yiserdasen.

Aḥric wis sin — Tawacult d ubrid ɣer useḥkem

=== 6. Tiberyus d Vipsania Agrippina ===
Tiberyus yuɣ Vipsania Agrippina deg 19 S.T.Ɛ. Vipsania tella d yell-is n ''Marcus Vipsanius Agrippa'', yiwen seg yimdukal d yimeɛiwnen imeqqranen n [[Uɣustus]]. Tiberyus d Vipsania sɛan yiwen n mmi-tsen, Drusus Julius Caesar.

Tizdit-nsen tettwasegza deg waṭas n yiɣbula d tin i deg tella tayri. Maca Uɣustus yebɣa ad yesseǧhed assaɣen gar twaculin timeqqranin.

Ɣef waya, Tiberyus yuḥwaǧ ad yebru d Vipsania deg 12 neɣ 11 S.T.Ɛ.

=== 7. Tizdit d Julia ===
Uɣustus yuɣ Julia, yell-is, i Tiberyus. Tizdit-a tella d tin n tsertit ugar n tin n tayri. Assaɣ gar Tiberyus d Julia ur yelli ara d win iǧehden.

Deg 2 S.T.Ɛ., Julia tettwaḥkem ɣef unejli s sebba n tardayt n tuzzuft beṛṛa n zzwaǧ d yisumar nniḍen. Aya yessexreb ugar assaɣen n Tiberyus d tawacult n Uɣustus.

=== 8. Tiberyus deg Rodos ===
Deg 6 S.T.Ɛ., Tiberyus yeǧǧa Ruma, iruḥ ɣer tegzirt n Rodos. Iɣbula iqburen ur msefhamen ara meṛṛa ɣef sebba n uɛzal-is.

Kra n yimezrayen ttwalin d akken:

- Yella yettḥulfu s leḥqer deg tawacult n Uɣustus.

- Yebɣa ad yebɛed ɣef Julia.

- Ur yebɣi ara ad yili deg tsertit n useḍfer n Uɣustus.

- Yella yettnadi ɣef tudert i yesɛan ugar n talwit.

Deg Rodos, Tiberyus yeqqim azal n 8 n yiseggasen.

Yettwasen d amdan i iḥemmlen idles agrigi, tifelsafit d tɣuri.

=== 9. Aseḍfer n Uɣustus ===
Uɣustus yella yebɣa ad t-yeḍfer yiwen seg yimeẓẓyanen n twacult-is. Maca aṭas n yimdanen i yellan d imezwura deg ubrid n useḍfer mmuten send-as.

Gar-asen:

- Marcellus, mmi-s n weltma-s n Uɣustus.

- Gaius Caesar, mmi-s n Julia.

- Lucius Caesar, gma-s n Gaius.

Deg useggas wis 4 S.L.Ɛ., Uɣustus yeṭṭef Tiberyus d mmi-s s yilugan n tadbelt tarumanit(s usmemmi).

Deg wass-nni, Tiberyus yesseḍfer Germanicus, mmi-s n gma-s Drusus, s tarrayt n usettem s yilugan.

Tiberyus yuɣal d amdan i yellan deg ubrid agejdan ɣer udabu.

Deg 13 S.L.Ɛ., tazmert-is tasertant tettwasnerna armi yuɣal yesɛa kra n tezmert i yesɛa Uɣustus deg tmura n Tmenkda.

== Aḥric wis kraḍ — Tiberyus d amenkad ==

=== 10. Tamettant n Uɣustus ===
Uɣustus yemmut ass n 19 Ɣuct 14 S.L.Ɛ., deg Nola, deg ṭṭelyan.

Tiberyus, i yesɛan azal n 55 n yiseggasen, yella d win i yellan deg ubrid ɣer udabu. Maca abeddel n tazmert ur yelli ara d win i d-yellan s yiwet n tikkelt.

Senat arumani yesɛa mazal tawuri deg tsertit n Ruma.

Tiberyus yesken-d leḥder deg uqbal n tazmert n umenkad.

Kra n yiɣbula qqaren d akken yella yebɣa ad yesseḥrez tugna n tagduda, ma d wiyaḍ ttwalin d akken yella yettɛemmid ad yessexdem leḥder iwakken ad yesɛu ugar n tazmert.

Deg 18 Ɣuct 14 S.L.Ɛ., Senat yeqbel tazmert-is, Tiberyus yuɣal d amenkad wis sin n Tmenkda tarumanit.

=== 11. Anagraw n udabu ===
Tiberyus ur yebni ara anagraw amaynut seg yilem. Yekcem deg unagraw i d-yesnulfa Uɣustus, i yettwasnen s yisem n Principatus.

Deg unagraw-a, amenkad yesɛa tazmert tameqqrant, maca kra n yizamulen d yilugan n tagduda mazal-iten.

==== 11.1. Tazmert n umenkad ====
Tiberyus yesɛa:

'''''Imperium proconsulare''''': tazmert tameqqrant ɣef yiserdasen d kra n tmura n Tmenkda.

'''''Tribunicia potestas''''': tazmert tasertant i t-yeǧǧan ad yesseḥbes kra n leqrarat, ad yesseḥrez kra n yilugan, ad yesseqdec izerfan n tribuns n ugdud.

'''''Auctoritas''''': azal d tazmert i yesɛa umdan deg tmetti d tsertit, ur nettwasbadu ara kan s yilugan.

==== 11.2. Tiberyus d Senat ====
Tiberyus yebɣa, deg tazwara, ad yesseǧhed tawuri n Senat. Yessekcem kra n leqrarat ɣer Senat, yerna yettɛemmid ad yesseḥrez izerfan n yiɛeggalen-is. Maca assaɣen gar-asen beddlen s wakud. Kra n yiɛeggalen n Senat ttwalin Tiberyus d amdan i yettḥellilen aṭas.

Tiberyus, s tama-s, yebda yettḥadar aṭas ɣef kra n yimdanen n Senat. Aya yessnerna uguren n tsertit deg Ruma.

=== 12. Tadbelt n Tmenkda ===
Tiberyus yesseḍfer tarrayt n Uɣustus deg tadbelt.

Yebɣa ad yesseḥrez anagraw yellan deg umkan n usnulfu n waṭas n yibeddilen.

==== 12.1. Timura n Tmenkda ====
Tamenkda tarumanit tella tesɛa timura deg:

- Tefriqt n ugafa.

- Iberia.

- Gallia.

- Germania n wadda.

- Balkans.

- Yunan.

- Anatolia.

- Surya.

- Miṣr.

Tiberyus yebɣa ad yesseḥrez tilisa n tmura-a. Ur yelli ara yettnadi ad yesseǧhed tamenkda s ṭṭrad deg yal tama.

==== 12.2. Imeḍbren n tmura ====
Tiberyus yessexdem aṭas n yimeḍbrenn idiganen i yeqqimen deg twuri-nsen i waṭas n yiseggasen. Aya yezmer ad yesseǧhed tadbelt, acku imeḍbren ssnen timura i ḥekkmen.

Maca yezmer daɣen ad d-yawi uguren mi ara yeqqim yiwen n umeḍber deg yiwet n temnaḍt i waṭas n wakud.

==== 12.3. Aḥraz n yilugan ====
Tiberyus yebɣa ad yesseḥrez anagraw n yilugan n Ruma. Maca deg tallit-is, ilugan i yerzan maiestas, neɣ tuccḍa mgal tazmert d wazal n ddula, ttwaseqdecen s wudem i d-yewwin aṭas n tneqqiḍin.

Kra n yimdanen ttwaḥekmen s sebba n wawalen neɣ n yisumar i yettwaḥesben d senɣes n wazal n umenkad. Aya yessexreb talwit tasertant deg Ruma.

== Aḥric wis kuẓ — Tadamsa d wayla n Tmenkda ==

=== 13. Tasertit n yidrimen ===
Tiberyus yettwassen s tarrayt-is n leḥder deg useqdec n yidrimen n ddula.

Ur yelli ara yettxeṣṣir aṭas n yidrimen ɣef yibniyat imeqqranen neɣ ɣef yisebdaden n tamanegt. Yebɣa ad yesseḥrez wyla n tmenkda.

==== 13.1. Akufi n tmenkda ====
Iɣbula iqburen qqaren d akken Tiberyus yeǧǧa akufi ameqqran n yidrimen mi yemmut.

Suetonius yebder azal n 2,7 n milliard n sesterces, maca amḍan-a ilaq ad yettwaḥsab d ayen i d-yettwabedren deg uɣbalu aqbur, mačči d amḍan i nettwassen s lǧehd s usekyed amḍan. Aya yeskan-d belli tasertit-is tella tettḥadar aṭas axessar.

==== 13.2. Tiberyus d tiwsiwin ====
Ur yelli ara d amenkad i yesnernan tiwsitin s waṭas deg yal tamnaḍt. Yettwaḥsab d win i yebɣan ad yesseḥrez tiwsitin yellan, ad yesseḥbes aɛekkem ɣef yimezdaɣ n tmura.

Yettwabder deg kra n yiɣbula s yisem n umdan i yebɣan ad yesseḥrez tadamsa n tmura i yettwaḥekmen.

==== 13.3. Ugur n yidrimen deg 33 S.L.Ɛ. ====
Deg 33 S.L.Ɛ., Ruma tekcem deg yiwet n tegnit taɛekkamt n yidrimen d usellef. Tella tuffɣa n yidrimen seg tnezzut, akked uɛekkem deg usellef. Tiberyus yessekcem azal n 100 n milyun n sesterces deg unagraw n usellef iwakken ad yesseḥbes ugur. Aya yettwaḥsab d yiwen seg yimeḍqan imeqqranen n tsertit tadamsant n tallit-is.

= Aḥric wis semmus — Ṭṭrad d tlisa n Tmenkda =

=== 14. Tasertit n tlisa ===
Tiberyus yebɣa ad yesseḥrez tilisa n Tmenkda ugar n usnerni-nsent. Deg tallit-is, Ruma tella d tamenkda tameqqrant i yesɛan aṭas n tmura. Maca aḥraz n tilisa-a yella yettawi aṭas n yidrimen d yiserdasen. Tiberyus yettḥadar aṭas asnerni n ṭṭradat ur nesɛi ara lfayda.

=== 15. Germanicus d Germania ===
''Germanicus'', mmi-s n gma-s n Tiberyus, yella d amseddas n ṭṭrad i yesɛan tamanegt deg Ruma. Deg 14–16 S.L.Ɛ., Germanicus yessekcem iserdasen ɣer Germania. Yebɣa ad yerr tazmert n Ruma deffir tawaɣit n Teutoburg.

Germanicus yewwi-d kra n tirniwin, maca ur yessaweḍ ara ad yesseḥkem Germania meṛṛa. Tiberyus yesseḥbes aṭas n yimenɣiyen, yerna yesseḥrez tilisa ɣef Yill n Rhine.

Aya yessebgen-d amgired gar-asen deg tarrayt n ṭṭrad. Germanicus yebɣa ad yesseǧhed tamanegt n Ruma s ṭṭrad, ma d Tiberyus yebɣa ad yesseḥrez ayen i yellan.

=== 16. Tamettant n Germanicus ===
Germanicus yemmut deg 19 S.L.Ɛ., deg Antiochia, deg Surya. Tamettant-is teǧǧa aṭas n yimdanen deg Ruma deg lḥif.

Kra n yimdanen ttwalin belli Germanicus yettwasemmem, maca ur yelli ara usekyed aḥeqqani i d-yessbegginen belli Tiberyus yesseḍfer asenqed n tmettant-is.

Gnaeus Calpurnius Piso, ameḥkam arumani, yettwatbaɛ s waṭas n tirdayin. Tamettant n Germanicus tesnerna ccek gar tawacult n Germanicus d Tiberyus.

= Aḥric wis sḍis — Sejanus d yiɛessasen n Pretorya =
[[Tugna:Relief of Soldiers of the Praetorian Guard 04 (51220287572).jpg|centré|vignette|550x550px|Tasreɣta ɣef Iɛessasen umenkad.]]

=== 17. Aɛessas n Pretorya ===
Iɛessasen n Pretorya (''Iɛessasen n umenkad'') llan d agraw n yiserdasen i yettɛassan amenkad d tazmert-is. Deg tallit n Tiberyus, agraw-a yesnerna azal-is deg tsertit.

=== 18. Sejanus ===
Lucius Aelius Sejanus yella d amseddas n yiɛessasen n Pretorya. Deg tallit n Tiberyus, Sejanus yuɣal d amdan i yesɛan tazmert tameqqrant. Yessaweḍ ad yesseǧhed tazmert n yiɛessasen, yerna yesseǧmeɛ-iten deg yiwen n umkan deg Ruma. Aya yesseǧhed tawuri n Pretorya deg tsertit tarumanit.

==== 18.1. Tamettant n Drusus ====
Drusus Julius Caesar, mmi-s n Tiberyus, yemmut deg 23 S.L.Ɛ. Iɣbula iqburen, ladɣa Tacitus, qqaren d akken Sejanus d Livilla llan deg uheggi n tmettant-is s ssem. Maca isallen-a ur ttwasekyaden ara s yilugan n umezruy atrar. Tamettant n Drusus teldi abrid i Sejanus iwakken ad yesnerni tazmert-is.

==== 18.2. Aɛzal n Tiberyus ====
Deg 26–27 S.L.Ɛ., Tiberyus yebda yettɛizil iman-is deg tegzirt n Capri. Sejanus yuɣal yettḥekkim deg waṭas n yimennuɣen n Ruma s yisem n umenkad. Aya yesseǧhed tazmert-is.

=== 19. Aɣelluy n Sejanus ===
Deg 31 S.L.Ɛ., Tiberyus yesseḥbes tazmert n Sejanus. Senat yeḥkem fell-as, Sejanus yettwanɣa. Deffir tmettant-is, aṭas n yimdanen i yellan deg tama-s ttwaḥekmen. Aya yewwi-d tallit n leḥder d ccek deg Ruma.

Tiberyus yuɣal yettḥadar ɣef waṭas yimdanen i t-iqerrben.

= Aḥric wis sa — Capri d yiseggasen ineggura =
[[Tugna:Capri island - Campania - Italy - July 12th 2013 - 21.jpg|centré|vignette|550x550px|Tigzirt n Capri deg ṭṭelyan.]]

=== 20. Tiberyus deg Capri ===
Deg 26–27 S.L.Ɛ., Tiberyus yebda yettidir aṭas n wakud deg tegzirt n Capri, deg yilel n Tirranit. Capri tella d adeg i yesɛan talwit, d tugniwin n yilel, d yidurar. Tiberyus yebna neɣ yesseqdec kra n yixxamen imeqqranen deg tegzirt-a.

Gar-asen, ''Villa Jovis'', yiwen seg yibniyen i yettwassnen deg umezruy n Capri.

=== 20.1. Ayɣer iruḥ ɣer Capri? ===
Iɣbula iqburen ur msefhamen ara ɣef sebba n uɛzal-is. Kra n yimezrayen ttwalin d akken:

* Yebɣa ad yebɛed ɣef ccwal n Senat.
* Yebɣa ad yidir deg talwit.
* Yella yettḥadar aṭas ɣef kra n yiɛdawen-is.
* Yebɣa ad yesseḥkem s tarrayt i t-yeǧǧan ad yili beṛṛa n Ruma.

=== 20.2. Aseḥkem seg lebɛid ===
Ɣas akken yella deg Capri, Tiberyus mazal-it d amenkad. Yettazen tibṛatin d leqrarat ɣer Senat d yimeḥkamen.

Aya yeskan-d belli tazmert n umenkad ur teqqin ara kan ɣer Ruma d usqamu-is. Maca aɛzal-is yesseǧhed daɣen tazmert n yimdanen i yettḥekkmen s yisem-is.

== 21. Tirdayin ɣef tudert-is deg Capri ==
Suetonius d Cassius Dio uran aṭas n yisallen ɣef tudert n Tiberyus deg Capri. Bḍan-d kra n teḥkayt i yerzan aɛekkem, lḥif d yisumar n yimeɣriyen. Maca imezrayen n wass-a ttḥadaren aṭas isallen-a.

Aṭas seg teḥkayt-a zemrent ad ilint d asnerni n tirdayin tisartinin neɣ d tirawt n yiɛdawen n Tiberyus.

Ɣef waya, ilaq ad nefrez gar:

'''Ayen i nettwassen s yiɣbula yemgaraden:''' Tiberyus yella deg Capri, yesseḥkem seg lebɛid, yerna tella tazmert tameqqrant n yimeɛiwnen-is.

'''Ayen i yellan d tirdayin:''' kra n teḥkayt ɣef tudert-is tudmawant, i ur nezmir ara ad tent-nessekyed s lǧehd.

= Aḥric wis tam — Tiberyus d tmetti tarumanit =

=== 22. Tameṭṭut, tawacult d yizerfan n yimdanen ===
Deg tallit n Tiberyus, tella temgarda tameqqrant gar yimdanen n tmetti tarumanit, ladɣa deg wayla, tazmert d yizerfan

Timetti tarumanit tella tebḍa ɣef waṭas n yigran:

* '''Patricii:''' tawaculin tiqburin i yesɛan azal ameqqran deg tsertit.
* '''Plebeii:''' agraw ameqqran n yimezdaɣ ilelliyen.
* '''Equites:''' imdanen i yesɛan azal deg tnezzut, tedbelt d yiserdasen.
* '''Liberti:''' imdanen i yellan d aklan, syin uɣalen d ilelliyen.
* '''Servi:''' aklan i ur nesɛi ara izerfan n yimdanen ilelliyen.

Deg tallit n Tiberyus, anagraw n waklan mazal-it d aḥric agejdan n tdamsa tarumanit. Aklan xeddmen deg tfellaḥt, deg yixxamen, deg yibniyen, deg tnezzut d waṭas n twuriwin nniḍen. Tiberyus ur yesseḥbes ara anagraw-a.

=== 22.1. Tameṭṭut deg Ruma ===
Tilawin tirumanin sɛant kra n yizerfan deg wayla, tizdit(neɣ tisulya) d twacult, maca ur sɛint ara izerfan isertanen am wid n yirgazen.

Ur zmirent ara ad ilint d tiɛeggalin n Senat neɣ ad sɛunt tawuri tameqqrant deg tadbelt tasertant. Maca kra n tlawin n twaculin timeqqranin sɛant tazrirt deg tsertit. Livia Drusilla, yemma-s n Tiberyus, tella d yiwet seg tlawin i yesɛan tazrirt tameqqrant deg tawacult n umenkad. Assaɣ gar Tiberyus d yemma-s yella d win iɛekkmen, ladɣa deg yiseggasen ineggura n tudert n Livia.

== 23. Asɣan deg tallit n Tiberyus ==
Asɣan arumani aqbur yella dasɣan n waṭas n yirebbite.

Deg tallit n Tiberyus, Irumanen ttɛebbiden i waṭas n yirebbiten d tirebbatin, gar-asen:
{| class=&quot;wikitable&quot;
!Arebbi neɣ tarebbit
!Tawuri
|-
|Jupiter
|Arebbi agejdan n igenni d tazmert
|-
|Juno
|Tarebbit n tizdit d tawacult
|-
|Mars
|Arebbi n ṭṭrad
|-
|Minerva
|Tarebbit n tmusni d tṣenɛat
|-
|Venus
|Tarebbit n tayri
|-
|Neptune
|Arebbi n yilel
|-
|Apollo
|Arebbi i yeqqnen ɣer usɣan, asefru d usseɣti
|-
|Diana
|Tarebbit n ṣṣyada d waggur
|}

=== 23.1. Aɛbad n umenkad ===
[[Uɣustus]] yella yettwaḥsab d amdan i yesɛan azal ameqran deg tsertit d usɣan. Deffir tmettant-is, yettwasekcem deg yigraw n ṛṛebbitan n ddula tarumanit. Tiberyus yesseḍfer kra n tarrayin n usɣan n Uɣustus. Maca yella yettḥadar aṭas aɛbad n yiman-is mi yella mazal-it yedder. Deg kra n tmura n Tmenkda, ladɣa deg usamar, aɛbad n umenkad yella d aḥric seg usɣan d tsertit.

== 24. Tiberyus d tazwara n tmasiḥit ==
Tiberyus yesɛa azal deg umezruy n [[Tamasiḥit|tmasiḥit]], acku deg tallit n useḥkem-is i d-yellan kra n tedyanin i d-yettwabedren deg Yinjilen.

Deg Unejil n Luqa (3:1), yettwabder useggas wis 15 n useḥkem n Tiberyus, deg usatal n tazwara n ubeccer n Yeḥya Ameɣṭas.

Ɣef waya, imezrayen qqnen aṭas n tedyanin n tudert n Ɛisa n Nazaret ɣer tallit n Tiberyus.

=== 24.1. Pontius Pilatus ===
Pontius Pilatus yella d ameḥkam(neɣ amasay) arumani n Yahudiya, seg azal n 26 ar 36 S.L.Ɛ. Yella d amdan i yesɛan tawuri deg tedyanin n useḥkem ɣef [[Ɛisa]], akken i d-ttmeslayen Yinjilen.

Maca ilaq ad nefrez gar tedyanin i d-yettwabedren deg yiɣbula n usɣan d wayen i nezmer ad nessekyed s tarrayt n umezruy.

=== 24.2. Tiberyus yessen Ɛisa? ===
Ur yelli ara uɣbalu aḥeqqani i d-yessbegginen belli Tiberyus yemlal Ɛisa neɣ yessen s timmad-is ayen i d-yellan deg Yahudiya.

Tiberyus yella d amenkad n Ruma deg tallit-nni, maca ur d-yettwabder ara s wudem usrid deg tedyanin n useḥkem ɣef Ɛisa.

Ihi, '''assaɣ gar Tiberyus d Ɛisa yella d assaɣ n tallit d tazmert tasertant, mačči d assaɣ udmawan i yettwasekyeden.'''
----

= Aḥric wis tẓa — Tafelsafit, idles d tudert n Tiberyus =

=== 25. Tiberyus d tfelsafit ===
Tiberyus yella d amdan i yesɛan aselmed agrigi d arumani. Iɣbula iqburen bedren belli yella iḥemmel taɣuri, tifelsafit d tmusni n yitran. Maca ur yelli ara d afilusuf i d-yeǧǧan idlisen n tfelsafit. Ur nezmir ara ad nini belli yella d amseddas n yiwet n tɣuri tafelsafit s lǧehd.

=== 25.1. Tiberyus d leḥder ===
Deg tsertit-is, Tiberyus yessexdem aṭas n leḥder.

Yella yettḥadar ṭṭradat ur nesɛi ara lfayda, axessar n yidrimen d yibeddilen imeqqranen. Aya yezmer ad yettwafhem d tarrayt n umdan i yesɛan tikti n wazal n tɣawsa d wayen ara d-yawi deg yimal. Maca leḥder-a yuɣal deg kra n tegnatin d ccek ameqqran ɣef yimdanen i t-iqerrben.

=== 25.2. Tarrayt-is n tudert ===
Tiberyus ur yelli ara d amdan i yettnadin aṭas ɣef tamanegt deg yimenɣiyen. Yettwasegza deg yiɣbula d win iḥemmlen tudert n uɛzal, taɣuri d umeslay akked yimdanen i yesɛan tamusni. Maca tugna-a ur telli ara d tin i d-ttakken akk yiɣbula s yiwen n wudem. Kra n yimaru iqburen fkan-as tugna n umdan aḥerci, iǧehden, maca yettḥadaren aṭas wiyaḍ. Wiyaḍ fkan-as tugna n umenkad i yessnernan ccek d tugdi deg Ruma.</text>
      <sha1>jb68vvx9m67okgstmgenx0b7iu8nx3p</sha1>
    </revision>
  </page>
  <page>
    <title>Huratyus</title>
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      <timestamp>2026-11-05T11:02:06Z</timestamp>
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        <username>Gurzil90x</username>
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      <comment>arniɣ ayen ilaqen</comment>
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      <text bytes="11951" sha1="ipmwb16ecpbfuvvq1xn7ty3wyaf8864" xml:space="preserve">{{Infobox biography|item=Q6197|image=[[File:Quintus Horatius Flaccus.jpg|thumb|Quintus Horatius Flaccus]]|caption=Huratyus|date of birth=8 Duǧember 65 send talalit n Ɛisa|date of death=27 Wamber 8 send talalit n Ɛisa|nationality=Tarumanit}}

'''Huratyus''', s yisem-is ummid '''Quintus Horatius Flaccus''', d yiwen seg yimedyazen irumanen imeqqranen n tallit taɣustit. Ilul ass n 8 Duǧember 65 send talalit n Ɛisa, di Venusia, di ṭṭelyan, yemmut ass n 27 Wamber 8 send talalit n Ɛisa, di Ruma.

Yettwassen ladɣa s yedlisen-is '''Sermones (Satires)''', '''Epodi''', '''Carmina (Odes)''', '''Epistulae''' akked '''Ars Poetica'''. Deg yisefra-s, Huratyus yesseqdec isental n tudert, tayri, timdukal, tafelsafit, tasertit, agama, talwit n wul d wakud i yettɛeddin.

Yedder deg yiwet n tallit i yesɛan azal ameqqran deg umezruy n Ruma: taggara n Tagduda Trumanit, ṭṭrad n daxel, asali n [[Uɣustus|Octavianus]] ɣer leḥkem, d tazwara n tmenkda n [[Uɣustus]].

Maca Huratyus yemgarad ɣef [[Virgil]] d [[Ovid]]. Ur yesseqdec ara timucuha timeqqranin kan iwakken ad yessefhem umezruy n Ruma. Yella yettmeslay s waṭas ɣef tudert n yal ass, ɣef wayen i yezmer umdan ad yeg iwakken ad yidir s talwit, d wamek ara yesseqdec akud-is s wudem yelhan.

Yiwet seg tektiwin-is yettwassnen d ''carpe diem'', i yezmer ad yettwasuqqel s teqbaylit: «Awi-d ayen yelhan seg wass-a», neɣ, s unamek alqayan, «Seqdec ass-a, ur tettuɣal ara kan ɣer usirem n uzekka».

== 2. Talalit d twacult-is ==

=== 2.1. Venusia, tamdint n Huratyus ===
[[Tugna:Venosa.jpg|centré|vignette|550x550px|Tamdint n Venusia deg ṭṭelyan.]]


Huratyus ilul di Venusia, tamdint tarumanit i yellan deg unẓul n [[ṭṭelyan]], deg temnaḍt i d-yettuɣalen ass-a d Basilicata.

Venusia tella d tamdint i d-yessbedden Yirumanen deg useggas 291 send Ɛisa, deg tallit n usnerni n tezmert n Tagduda Trumanit deg ṭṭelyan.

Deg tallit n Huratyus, tamdint-a tella deg temnaḍt n tfellaḥt, anda i zedɣen yifellaḥen, imdanen n tenzut d yiserdasen.

Tudert deg temnaḍt-a tella temgarad ɣef tin n Ruma. Deg Ruma, yella leḥkem, tazmert d tedbelt, ma deg Venusia, tudert tella tettɛeddi s waṭas deg yigran d tuddar.

=== 2.2. Baba-s n Huratyus ===
Baba-s n Huratyus yella d amdan i d-yettwaslellin seg waddad n wakli. Deg yiɣbula iqburen, yettwabder belli yella d wakli i yettwaserḥen, i yuɣalen yesɛa tilelli.

Yella ixeddem deg taɣult n tedbelt n yidrimen, ladɣa deg uleqqaḍ n tewsitin n tnezzut d yisuter n yidrimen.

Ɣas akken ur yelli ara d amdan n twacult tameqqrant, baba-s yesɛa idrimen iwakken ad yesseɣri mmi-s.

Deg yisefra-s, Huratyus yessefk-d s waṭas n tikkal azal n baba-s. Yettmeslay fell-as s leqder, imi baba-s yebɣa ad yili mmi-s d amdan i yesɛan tamusni d wazalen.

Deg ''Satires 1.6'', Huratyus yessefhem belli baba-s ur t-yeǧǧa ara ad yili kan d amdan i yessnen tira, maca yesselm-ed-as daɣen amek ara yefrez gar wayen yelhan d wayen n diri.

=== 2.3. Tazrirt n baba-s ===
Huratyus yella d amdan i yesɛan tazrirt tameqqrant seg uselmed n baba-s.

Deg yisefra-s, yettmeslay ɣef wayen i as-yenna baba-s, d wamek i t-yesselm-ed ad yili d amdan i yesɛan leqder, aḥraz n yiman-is d tmuɣli ɣer tmetti.

D aya i d-yettbanen deg yisefra-s n deffir, anda i yesseqdec kra n yimedyaten seg tudert n yal ass iwakken ad yessefhem tiktiwin tifelsafiyin.

== 3. Aselmed n Huratyus ==

=== 3.1. Azraw di Ruma ===
Mi yella d ameẓẓyan, baba-s yewwi-t ɣer Ruma iwakken ad yelmed deg yiɣerbazen yelhan. Deg Ruma, Huratyus yelmed talaṭinit, tasnukyest , asefru d tsekla tagrigit. Yella daɣen yessen imyura iqburen, ladɣa Homer, Archilochus d kra n yimesfrayen n Yunan.

Deg tallit-nni, aselmed n tutlayt tagrigit yella d aḥric ameqqran n uselmed n yimdanen i yebɣan ad ilin deg tedbelt neɣ deg tsekla.

=== 3.2. Azraw deg Athenes ===
Huratyus iruḥ daɣen ɣer Athenes, tamdint tagrigit i yellan d yiwen seg yidigan imeqqranen n tfelsafit. Deg Athenes, yelmed tafelsafit, tasekla d tseknawt n wawal. Deg tallit-nni, Athenes tella mazal d amkan n uselmed n tfelsafit n [[Flaṭun|Plato]], [[Aristot|Aristote]], [[Epikur|Epicurus]] d yifelsafiyen-nniḍen.

Huratyus yella yettwajbed ɣer tfelsafit n Epicurus, maca ur yelli ara d amdan i yesseqdec yiwet n tfelsafit kan deg yisefra-s.

Yesseqdec kra n tiktiwin n yifelsafiyen yemgaraden, ladɣa deg usentel n talwit n wul d useqdec n wakud.

== 4. Huratyus deg ṭṭrad n daxel n Ruma ==

=== 4.1. Tamettant n Julius Caesar ===
Deg useggas 44 send Ɛisa, [[Julius Caesar]] yettwanɣa deg Ruma. Tamettant-is teǧǧa Tagduda Trumanit deg tazɣent tasertant tameqqrant. Gar yimdanen i yebɣan ad ḥerzen Tagduda Trumanit, yella Marcus Junius Brutus, yiwen seg wid i yenɣan Caesar.

Huratyus yella deg Athenes deg tallit-a.

=== 4.2. Huratyus d Brutus ===
Brutus yessdukel taserdast iwakken ad yemennuɣ mgal [[Uɣustus|Octavianus]] d Mark Untunyus.

Huratyus yekcem deg tsedrast n Brutus, yettwafk-as waddad n tribunus militum, anamek-is d ameqran aserdasi i yesɛan kra n tzemmar n leḥkem ɣef yiserdasen.

D taɣawsa i yesɛan azal ameqqran, imi Huratyus ur yekki ara deg ṭṭrad am uselway n tsekla, maca am amdan i yesɛan tuɣdaḍt taserdasit.

=== 4.3. Ṭṭrad n Filippi ===
Deg useggas 42 send Ɛisa, taserdast n Brutus d Cassius temmenɣ akked tsedrast n Octavianus d Mark Untunyus deg Filippi, deg temnaḍt n Macedonia. Brutus d Cassius xesren ṭṭrad, syin mmuten.

Huratyus yeslek iman-is, yuɣal ɣer ṭṭalyan. Deg yiwen n yisefra-s, yettmeslay s leḥzen ɣef wayen i yeḍran deg Philippi, am wakken yeǧǧa aglim-is deg umkan n ṭṭrad, i d-yettwasfahmen s waṭas n tikkal d tarrayt n usqerdec ɣef tarewla-s.

Maca ur ilaq ara ad neḥseb tafyirt-a d aḍris amezruyan usrid i d-yettalesen akk ayen i yeḍran.

=== 4.4. Tuɣalin ɣer Ruma ===
Mi yuɣal Huratyus ɣer Ruma, yufa belli kra n wayla n twacult-is yettwakkes. Yella yesɛa tagnit ad yexdem deg tedbelt, deg leqdic n scriba quaestorius, amaru n tedbelt i yellan yettawi isallen n yidrimen d tɣawsiwin n leḥkem.

Leqdic-a yefka-as tazmert ad yidir, d wakud iwakken ad yaru isefra.

== 5. Huratyus d Maecenas ==
[[Tugna:Maecenas Coole Park.JPG|centré|vignette|Asebdad n uqeṛṛu n  Maecenas.]]


Yiwet seg tɣawsiwin i d-yebnan tudert n Huratyus d assaɣ-is akked Maecenas.

Gaius Cilnius Maecenas yella d amdan i yesɛan tazmert deg Ruma, d amdukal n [[Uɣustus|Octavianus]], d win i yettɛawanen imyura d yinaẓuren.

Deg useggas 38 send Ɛisa, [[Virgil]] d Varius ssnen Huratyus i Maecenas. Maecenas yefka-as tagnit ad yekcem deg ugraw n yimyura i yellan deg tmetti n Ruma.

=== 5.1. Taduklil d uɛiwen ===
Huratyus yuɣal d amdukal n Maecenas. Assaɣ-nsen ur yelli ara kan d win n umdan i yesɛan idrimen d umedyaz i yettwarzen fell-as. Yella daɣen d assaɣ n yimdukal, leqder d tmuɣli ɣer tsekla.

Maecenas yesseɛwan Huratyus s yidrimen d wakal. Deg kra n yiɣbula, yettwabder belli yefka-as tamurt tameẓẓyant deg yidurar n Sabina, qrib ɣer Ruma. Tamurt-a teǧǧa Huratyus ad yidir deg talwit, beɛden ɣef lḥir n temdint.

=== 5.2. Tamurt n Sabina ===
Huratyus yettmeslay s waṭas ɣef tudert-is deg tmurt n Sabina. Dinna, yella yezmer ad yesseqdec akud-is deg tira, aselmed n yiman-is d tmuɣli ɣer ugama.

Deg yisefra-s, tamurt-a tettban d amkan n talwit d tilelli. Maca ur ilaq ara ad neḥseb belli Huratyus yebɣa ad yeǧǧ Ruma i lebda. Yella yettidir gar Ruma d tmurt-is, yettɛeddi seg tmetti n temdint ɣer tudert taḥerfit n yigran.

== 6. Sermones — Satires ==
Sermones, i yettwasemman daɣen Satires, d ammud n yisefra i yura Huratyus deg tallit tamezwarut n tudert-is aseklant.

Yebḍa ɣef sin n yedlisen: amezwaru yettwasuffeɣ azal n useggas 35 send Ɛisa, wis sin azal n useggas 30 send Ɛisa.

=== 6.1. Aɣanib n Satires ===
Deg Satires, Huratyus yesseqdec asefru iwakken ad yesseqdec azɣan n tmetti. Yettmeslay ɣef yidrimen, tayri, leqder, tazmert, timdukal d wayen i d-yettawin imdanen ɣer tuccḍa.

Maca azɣan-is ur yelli ara s wudem n cceḥna kan. Yesseqdec tahuski d usqerdec iwakken ad yessefhem tikti-s.

=== 6.2. Amedya: amdan i ur nettqenniɛ ara ===
Huratyus yettmeslay ɣef yimdanen i yebɣan yal tikelt ayen i ur sɛin ara. Afellaḥ yezmer ad yebɣu tudert n umdan n ttjara.

Amdan n ttjara yezmer ad yebɣu tudert n ufellaḥ.

Amdan i yesɛan idrimen yezmer ad yebɣu ugar, war ma yettḥulfu s talwit.

Huratyus yesseqdec imedyaten-a iwakken ad yessefhem belli talwit ur tettwabna ara kan ɣef yidrimen d tzemmar.

=== 6.3. Amedya: tudert taḥerfit ===
Deg kra n yisefra-s, Huratyus yessefhem belli amdan yezmer ad yidir s talwit mi yesɛa ayen i t-yettɛawanen deg tudert, war ma yebɣa yal tikelt ad yili d ameqran neɣ d amdan yesɛan idrimen meqqren.

Tamuɣli-a tesɛa assaɣ d tfelsafit n Epicurus, maca Huratyus yesseqdec-it s wudem aseklan, s thuski d yimedyaten n tudert n yal ass.

== 7. Epodi — Isefrayen n uzɣan d tissas ==
Epodi d ammud n 17 n yisefra i d-yessuffeɣ Huratyus azal n useggas 30 send Ɛisa.

Deg-s, yesseqdec isental n ṭṭrad, tayri, tasertit, lḥif d tmetti. Kra n yisefra-a sɛan aɣanib aqesḥan, s uzɣan i yimdanen d tɣawsiwin i t-yesḥeznen.

=== 7.1. Ṭṭrad agensan(n daxel) ===
Deg kra n yisefra n Epodi, Huratyus yessefhem lḥif i d-yettawi ṭṭrad n daxel. Yettmeslay ɣef Ruma am tmurt i yellan tettnaɣ iman-is.

D tikti i yesɛan azal ameqqran, imi ṭṭrad n daxel ur yelli ara d ṭṭrad mgal aɣerfan azɣaray, maca gar Yirumanen s timmad-nsen.

=== 7.2. Tayri d usqerdec ===
Deg kra n yisefra-nniḍen, Huratyus yesseqdec tayri d wassaɣen n yimdanen am usentel n thuski. Yettmeslay ɣef tissmin, tissas, usirem d wayen i d-yettawi wassaɣ ur nelhi ara.

Deg waya, yella kra n wassaɣ gar Huratyus d [[Ovid]], maca Huratyus yesseqdec tayri s wudem yemgaraden: yettawi-tt deg usqerdec d tfelsafit n tudert, ma d Ovid yesseqdec-itt am usentel agejdan n tsekla-s.

== 8. Carmina — Odes ==
Carmina, i yettwasemman Odes, d ammud n yisefra i yesɛan azal ameqqran deg tsekla talaṭinit. Kraḍ n yedlisen imezwura ttwassuffɣen deg useggas 23 send Ɛisa, ma d wis kuẓ deg useggas 13 send Ɛisa.

Deg yisefra-a, Huratyus yesseqdec isental n tayri, imdukal, tafelsafit, tasertit, tamettant d wakud.

=== 8.1. Carpe diem ===
Yiwet seg tektiwin yettwassnen n Huratyus d carpe diem. Tafyirt-a tella deg Odes 1.11, anda i yettmeslay i Leuconoe.

Deg usefru-a, Huratyus yessefhem belli ur nezmir ara ad nissin ayen ara d-yeḍrun azekka. Ɣef waya, ilaq ad nesseqdec ass-a s wudem yelhan, war ma nerr akk asirem-nneɣ ɣer yimal.

Carpe diem ur d-yemmal ara belli ilaq ad nexdem yal ayen i nebɣa war tilisa. Deg uḍris n Huratyus, tikti-a tesɛa assaɣ d usenqes n tugdi n yimal, d uḥraz n wakud i aɣ-d-yettunefken.

=== 8.2. Aurea mediocritas — Talemmast n wureɣ(ddheb) ===
Deg Odes 2.10, Huratyus yesseqdec tikti n ''aurea mediocritas''. Anamk-is yezmer ad yettwafhem d «talemmast n ddheb», neɣ «tarrayt talemmast i yelhan».

Huratyus yessefhem belli amdan ilaq ad yesseqdec tarrayt talemmast deg tudert-is.

Ur ilaq ara ad yili d amdan i yebɣan yal tikelt ayen i ur yesɛi ara, maca ur ilaq ara daɣen ad yili d amdan i yessawḍen iman-is ɣer lḥif s ufran n wayen i ur nelhi ara. Tiktii-a tesɛa assaɣ d tfelsafit n talemmast n [[Aristot|Aristote]], maca Huratyus yesseqdec-itt s wudem aseklan.

=== 8.3. Non omnis moriar — Ur tmettat ara meṛṛa ===
Deg Odes 3.30, Huratyus yesseqdec tikti n tazmert n tsekla ɣef wakud. Yessefhem belli yesnulfa-d aḍris i yezmer ad yeqqim deffir tmettant-is.

Deg-s, tella tafyirt talaṭinit:

«Non omnis moriar».

Anamk-is s teqbaylit:

«Ur tmettat ara meṛṛa.»

Ayen i yebɣa ad yini dakken amdan yezmer ad yemmet s tfekka-s, maca isem-is d wayen i d-yura zemren ad qqimen deg tmetti.

Deg waya, Huratyus yesseqdec tasekla am ubrid n uḥraz n yisem n umdan deffir tmettant-is.</text>
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  <page>
    <title>Milton Friedman</title>
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      <text bytes="6877" sha1="ej7mg05s9u7g4addjtgvip21vuvu72z" xml:space="preserve">{{Infobox biography|item=Q47426|image=[[File:Portrait Of Milton Friedman (cropped).jpg|thumb|Portrait Of Milton Friedman (cropped)]]|caption=Milton Friedman.|date of birth=31 Yulyu 1912.|nationality=Tamarikanit.|date of death=16 Wambeṛ 2006}}

'''Milton Friedman''' d yiwen seg yimussnawen n tdamsa i yesɛan tazrirt tameqqrant ɣef tikti tadamsant deg tasut tis 20. Yettwassen s unadi-ines ɣef yidrimen, asadur, annerni n wazalen, iɣimi war axeddim, akked wamek i tezmer tdamsa ad teddu s tlelli n ulzuz, war ma yessekcam uwanek iman-is deg yal armud.

Friedman yella gar wid i d-yessuffɣen tiktiwin n tdamsa n tallit-nni seg yiberdan i tent-ttwalin s John Maynard Keynes, ɣer tarrayt-nniḍen i d-yettakken azal ameqqran i yidrimen, tamsizzelt deg ulzuz, d tlelli n umdan deg tiferniwin-is tidamsanin.

Tiẓriyin-is ur qqiment ara deg tesdawit. Uɣalent d aḥric n umeslay asartan d udamsan deg Marikan, Britanya, Cili, akked waṭas n tmura-nniḍen.

Maca ur yelli ara d amussnaw iɣef mtafan akk imazzagen. Kra n tiktiwin-is ttwasqeblent deg tussna n tdamsa tatrart, ma d kra nniḍen mazal fell-asent umeslay d uzɣan, ladɣa ayen yeɛnan tamlilt n uwanek, taɣdemt tamettit, tawziɛt n tbuɣar d tsertiyin tidamsanin.

Deg useggas 1976, yewwi-d Arraz n Nobel n tussniwin tidamsanin ɣef leqdic-is deg tesleḍt n usadur, amezruy d teẓri n yidrimen, akked usegzi n wuguren n tsertit n usezdi n tdamsa.

== 1. Tudert-is d umezruy-is ==
Deg temẓi-s, Friedman yesɛa leḥmala tameqqrant i tusnakt. Tazwara n ubrid-is asdawan tella deg tussniwin-a, uqbel ad yettwelleh ɣer tdamsa.

=== 1.2. Aɣerbaz d tesdawit ===
Timliliyin tigejdanin deg ubrid-is:

* 1932: yemmug d anelmad i d-yeffɣen seg tesdawit n Rutgers, s ugerruj n tmusniwin deg tusnakt d tdamsa.
* 1933: yewwi-d agerdas n Master deg tesdawit n Chicago.
* 1933–1934: ikemmel tizrawin-is deg tesdawit n Columbia.
* 1937: yebda assaɣ-is aɣezzfan d NBER, tasudut n unadi adamsan deg Marikan.
* 1938: yuɣ '''''Rose Director''''', i d-yuɣalen d tameṭṭut-is, tamdakkelt-is deg unadi d tira.
* 1946: yewwi-d agerdas n dukṭura deg Columbia, yerna yebda aselmed n tdamsa deg tesdawit n Chicago.
* 1977: yemmed uḥric-is agejdan n uselmed deg Chicago, yernu yebda leqdic deg Hoover Institution ɣer Stanford.
* 16 Nwanbir 2006: yemmut deg San Francisco, deg leɛmer n 94 n yiseggasen.

=== 1.3. Rose Friedman d twuri-ines deg tudert-is ===
''Rose Director Friedman'' ur telli ara kan d tameṭṭut-is. Tella d tamassant n tdamsa, tecerek yid-s deg waṭas n yimahilen.

Yid-s i d-yura Free to Choose deg 1980, akked Two Lucky People deg 1998. Sin-a sdukklen tiktiyin tidamsanin d tifelsafiyin ɣef tlelli n umdan. Rose tettɛawan daɣen deg usegzi n tmiḍranin tidamsanin yuɛren i tegzi, akken ad tent-fehmen ula d yimdanen ur nelli ara d imazzagen deg tdamsa.

== 2. Tallit n Friedman: tamurt d umaḍal deg ubeddel ==
Iwakken ad negzu tiktiwin n Friedman, ilaq ad nissin amek tella tdamsa n umaḍal deg tasut tis 20.

=== 3.1. Tazɣent tameqqrant n 1929 ===
Deg 1929, tebda yiwet seg tezɣanin tidamsanin timeqqranin i yeẓra umezruy amaynut. Tazɣent-a tḥuza Marikan, syin tekcem ɣer waṭas n tmura.

Tiṛmisin uɣalent ɣellqent, iɣimi war axeddim yugar ayen yellan uqbel, aṭas n yibankiyen rẓen, azal n yifarisen yuder.

Deg tallit-a, aṭas n yimussnawen n tdamsa bdan ttwalin belli ulzuz s yiman-is ur yezmir ara yal tikkelt ad d-yerr tadamsa ɣer waddad-is amagnu.

=== 3.2. Tazrirt n John Maynard Keynes ===
John Maynard Keynes yella gar yimussnawen i d-yefkan tifratin tatrarin i tezɣanin tidamsanin.

Ɣur-s, mi ara yili usadur d yisuter n yifarisen s ddaw n wayen i yezmer ad d-yefk ufares, anerni n yirmad n uwanek yezmer ad yesseḥyu tadamsa.

Amedya: ma ulac axeddim, awanek yezmer ad yesnerni lebni n yiberdan, isedduyen n waman d yiɣerbazen. S waya, ad d-yili uxeddim, ad nernun yidrimen i d-yettawin yimdanen, ad yernu usadur.

Friedman ur yugi ara akk timlilt n uwanek, maca yella yesseḥsab belli aṭas n tsertiyin-a zemrent ad d-glunt s wuguren-nniḍen.

=== 3.3. Amgired agejdan ===
Gar Keynes d Friedman, yella umgired ɣef tarrayt ara yessexdem uwanek i wakken ad issezdi tadamsa.

Keynes yefka azal ameqqran i usuter amatu, iseftiyen n uwanek d tsertit n tɣawsiwin tizayezin. Friedman, ma d netta, yesken-d azal n yidrimen d tsertit n '''uqarid''', yernu yessuter ad tili tsertit tamezdit, tettwassnen seg zik, ur tettbeddil ara yal tikkelt s tɣawla.

Ihi, Friedman yesseḥsab belli aselḥu arurad n tdamsa sɣur uwanek yezmer ad yili d aɣbalu n tezɣanin deg kra n tegnatin.

== 4. Tafelsafit-is tagejdant: tilelli n umdan d ulzuz ilelli ==
Yiwen seg yimenziyen igejdanen n Friedman d akken tlelli n umdan deg tdamsa d yiwen seg yizaduren n tlelli tasartant.

=== 4.1. D acu i d ulzuz ilelli? ===
Ulzuz ilelli d anagraw adamsan ideg imdanen d tiṛmisin zemren ad zenzun, ad sɣen, ad fersen, ad sseftin, war ma yella uwanek yettaǧǧa-d i yal yiwen acu ara yexdem.

Amedya: ma yella yiwen yebɣa ad yeldi aɣsur(neɣ luzin) n ufares n yiḍebsiyen, yezmer ad t-yeldi, ad d-isnulfu ifarisen, ad ten-izenz i yimsaɣen.

Ma yella ifarisen-is lhan, wid yettɣen zemren ad ten-fernen. Ma ur lhin ara, zemren ad rnun ɣer yiwen-nniḍen.

Ɣer Friedman, tarrayt-a tesnernay tamsizzelt, tesseḥbibir ɣef tiferni n umsaɣ, yerna tettɛawan ɣef usnerni n ufares.

=== 4.2. Tamsizzelt d wazalen ===
Friedman yesseḥsab belli tamsizzelt gar tiṛmisin tesɛa azal ameqqran.

Ma yella kra n yifarisen ur ttnuzun ara, neɣ ɣlayen aṭas, tiṛmisin-nniḍen zemrent ad d-fkent ifarisen am wigi s wazal yelhan ugar.

Maca aya yella d ayen i yezmer ad yeḍru mi ara tili tamsizzelt s tidet. Ma yella ulzuz deg ufus n yiwet n termist kan, neɣ yella usdukkel gar tiṛmisin i usebɣes n wazalen, tiferni n yimsaɣen tezmer ad tenqes.

Friedman ur yelli ara yesseḥsab belli yal ayen yellan deg ulzuz d ayen yelhan. Yesseḥseb belli tanekra n ulzuz tettili akken ilaq mi ara yilin izerfan n wayla yettwaseḥbibren, ilugan d tamsizzelt war tukerḍa.

=== 4.3. Tlelli tadamsant d tlelli tasartant ===
Deg udlis-is ''Capitalism and Freedom'', Friedman yessefhem-d amek i yezmer unagraw adamsan ilelli ad yesseḥbiber ɣef tlelli tasartant.

Ɣur-s, ma yella akk iferdisen n tdamsa deg ufus n udabu, win yesɛan adabu yezmer ad yessexdem tazmert-nni i useḥbes n yimdanen i as-yemgaraden deg tikti.

Ma yella imdanen zemren ad sseftin, ad snulfun tiṛmisin, ad ttwasekren i wakken ad awḍen ɣer yiswiyen-nsen, ad sɛun aṭas n yiberdan i wakken ad d-qeddcen war ma ḥwajen ad asen-yefk uwanek tasiregt deg yal tikkelt.

Maca tella yiwet n temsalt: tlelli tadamsant iman-is ur tettak ara s wudem awurman tlelli tasartant. Yezmer unagraw n ulzuz ad yili deg tmurt i deg ur ttwaḥerzen ara izerfan n yimdanen. Amezruy n kra n tmura yessekna-d ugur-a.</text>
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