Tanzeggit

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      <comment>arniɣ ayen ilaqen</comment>
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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).

==Imuren imeqranen n tenzeggit ==

* [[Tanzeggit tuklidit]] 

* [[Tanzeggit artuklidit]] 

* [[Tanzeggit tummit]]

* [[Tanzeggit tigriwt]]

* [[Tanzeggit taljibirt]]

* [[Tanzeggit tanebrurzant]] 

* [[Aljiber imzireg]]

== Amezruy n tenzeggit ==


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  <page>
    <title>Virgil</title>
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      <text bytes="17785" sha1="rr7cpi1pxdv9injbalmwa0dr8dze2yp" xml:space="preserve">{{Infobox biography|item=Q1398|image=[[File:Parco della Grotta di Posillipo5 (crop).jpg|thumb|Virgil]]|date of birth=15 Ktuber 70 send talalit n Ɛisa|nationality=Arumani|date of death=21 Ctember 19 send talalit n Ɛisa}}

'''Virgil''', s yisem-is ummid '''Publius Vergilius Maro''', d amedyaz arumani i ilulen ass n 15 Ktuber 70 send talalit n Ɛisa, i yemmuten ass n 21 Ctember 19 send talalit n Ɛisa. Yettwaḥsab gar yimedyazen imeqqranen n tsekla talaṭinit, ladɣa s udlis-is ''Aeneis'' (Aneid), i d-yettalesen inig n ''Aeneas'' seg Ṭrwa ɣer [[Ṭṭelyan]].

Virgil 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 tezmert, akked tazwara n tmenkda n [[Uɣustus]].

Tasekla-s tettawi ɣef tudert n yimdanen, agama, takerrazt(tafellaḥt), ṭṭrad, tilelli, lḥif, d wassaɣ gar umdan d tmurt-is. Deg yedlisen-is, Virgil yesdukel tamiṭulujit tagrigit d trumanit akked umezruy n Ruma, s uɣanib aseklan i yesɛan tazrirt tameqqrant ɣef tsekla n Turuft.

== 2. Talalit d twacult-is ==

=== 2.1. Tamurt n Mantua ===
Virgil ilul deg temnaḍt n Mantua, deg ugafa n [[ṭṭelyan]], qrib ɣer yidurar n Alpes d urtiyen iɣezzfan n Po.
[[Tugna:Dsc 1150 Mantua.jpg|centré|vignette|450x450px|Tamdint n Mantua n wass-a.]]


Tamnaḍt-a tella tettwassen s tfellaḥt, igran, aman d tmeddurt n yimeksawen. Deg tallit n Virgil, kra n yiɣerfan n ugafa n ṭṭelyan llan mazal ḥerzen kra n yidles-nsen, ɣas akken Ruma tesɛa tazmert tameqqrant fell-asen.

Tawacult n Virgil tettwabder deg kra n yiɣbula iqburen am tin i yesɛan assaɣ d tfellaḥt. Maca isallen ɣef baba-s d yemma-s ur frizen ara meṛṛa, imi kra n wayen i d-yettwabedren deg tudert-is yekka-d seg tmucuha i d-ttawin yimyura n talliyin i d-iḍefren.

Ayen i nezmer ad nini s tidet d akken Virgil yella d amdan n ṭṭelyan talqayt, i yesɛan assaɣ ameqqran d wakal d tfellaḥt, ayen ara d-yettbanen deg yedlisen-is.

=== 2.2. Tamẓi-s ===
Virgil yella d ilemẓi deg tallit anda Tagduda Trumanit tettɛeddi seg kra n tezɣanin tisertanin. Deg useggas 49 send Ɛisa, [[Julius Caesar]] yezger asif Rubicon, d aya i d-yeglan s ṭṭrad n daxel. Virgil yella yesɛa azal n 21 n yiseggasen.

Deg useggas 44 send Ɛisa, mi yettwanɣa Julius Caesar, Virgil yella yesɛa 26 n yiseggasen.

Tallit-a tella d tin n ṭṭrad, tazɣent, d ubeddel n leḥkem. Tidyanin-a ttwabedren s wudem uffir neɣ usrid deg yedlisen-is.

== 3. Aselmed d temẓi n Virgil ==
Virgil yelmed deg kra n temdinin n ṭṭelyan, gar-asent Cremona, Mediolanum (Milan) d Ruma. Yelmed talaṭinit, tasnukyest, asefru, d kra n tɣuriwin tifelsafiyin.

Deg kra n yiɣbula, yettwabder belli yella yesɛa assaɣ d tfelsafit n [[Epikur|Epicurus]], ladɣa deg temdint n Napoli, anda i yella uɣerbaz n ufelsafi Siro.

=== 3.1. Tazrirt n Epicurus ===
[[Epikur|Epicurus]] yella d afelsafi agrigi i yesselmaden belli tudert yelhan ur tebni ara ɣef usɛeddi n yidrimen neɣ tazmert tasertant, maca ɣef talwit n wul, tamusni, d usenqes n tugdi d lḥif.

Virgil ur yelli ara d afelsafi Epicurien s wudem usrid deg yal adlis-is, maca kra n tiktiwin n tfelsafit-a zemrent ad ttwafhament deg yisefra-s, ladɣa deg tmuɣli-s ɣer tudert n tfellaḥt d talwit n ugama.

=== 3.2. Tazrirt n tsekla tagrigit ===
Virgil yella yessen tasekla tagrigit s wudem alqayan.

Gar yimaru i yesɛan tazrirt fell-as:

- [[Humer|Homer,]] amaru n Iliad d Odyssey.

- Hesiod, amaru n ''Works and Days'' d ''Theogony''.

- Theocritus, amesfru n tudert n yimeksawen.

- Apollonius n Rhodes, amaru n ''Argonautica''.

Tasekla tagrigit tefk-as tarrayin n tira, maca Virgil yesseqdec-itent iwakken ad yesnulfu tasekla tarumanit s wudem-is.

=== 4. Tallit n ṭṭrad d tazɣent n Ruma ===
Deg useggasen i d-iḍefren tamettant n [[Julius Caesar]], Ruma tella deg ṭṭrad n daxel. [[Uɣustus|Octavianus]], Mark Untunyus d Lepidus sɛan tazmert tasertant deg tazwara, maca assaɣen-nsen beddlen, d aya i d-yeglan s ṭṭrad gar Octavianus d Mark Untunyus.

Deg useggas 31 send Ɛisa, Octavianus yerbeḥ deg ṭṭrad n Actium.

Deg useggas 27 send Ɛisa, Octavianus yettwafk-as uzwel n Uɣustus, d tazwara n tgelda tarumanit.

Virgil yella d anagi n yibeddilen-a. Tazɣent tasertant d ṭṭrad n daxel sɛan tazrirt ɣef tsekla-s, ladɣa deg ''Aeneis'', anda i yesseqdec timucuha n Ṭrwa d usnulfu n Ruma iwakken ad yessefhem assaɣ gar ṭṭrad, lḥif d usirem n talwit.

== 5. Eclogae — Isefra n yimeksawen ==
[[Tugna:RomanVirgilFolio001rEclogues.jpg|centré|vignette|475x475px|Eclogae n Virgil.]]


'''Eclogae''', i yettwasemman daɣen '''Bucolica''', d ammud n 10 n yisefra i yura Virgil azal n yiseggasen 42–39 send Ɛisa. Deg yisefra-a, yettmeslay ɣef tudert n yimeksawen, izugar, tayri, agama d talwit n tmurt. Maca deg deffir n tugniwin-a, yella umezruy n Ruma d ṭṭrad n daxel.

=== 5.1. Asefru amezwaru ===
Deg usefru amezwaru, Virgil yessefk-d sin n yimeksawen: ''Tityrus'' d ''Meliboeus''.

Tityrus yezmer ad yeqqim deg wakal-is, maca Meliboeus ilaq ad yeǧǧ tamurt-is.

Asefru-a yettwafham s waṭas n tikkal d amedya n yibeddilen n wayla n wakal deg Italya mi ttwabḍan yigran i yiserdasen i d-yuɣalen seg ṭṭrad. Deg tallit-nni, aṭas n yifellaḥen ttwakksen seg wakal-nsen. Virgil yesseqdec timucuha n yimeksawen iwakken ad yessefhem lḥif n yimdanen i yettwakkesen seg tmurt-nsen.

=== 5.2. Asefru wis kuẓ ===
Asefru wis kuẓ d yiwen seg yisefra yettwassnen n Virgil.

Deg-s, yessefk-d tikti n tlalit n uqcic i d-yeglan s tallit tamaynut n talwit d usirem.

Deg tallit talemmast, kra n yimsiḥiyen fkan-as anamek asɣanan, ḥesben belli d asefru i d-yettmeslayen ɣef talalit n Ɛisa.

Maca aya d tarrayt n usefhem i d-yellan deffir, mačči d tidet tamezruyant ɣef wayen i yebɣa Virgil ad yini. Virgil yura asefru-a uqbel talalit n Ɛisa.

=== 5.3. Azal n Eclogae ===
Eclogae yesɛa azal ameqqran deg tsekla, imi yesseqdec tudert n ugama iwakken ad yessefhem isental imeqqranen n tmetti.

Deg-s, agama ur yelli ara kan d amkan n thuski. Yella d amkan n talwit, n tayri, d lḥif mi yettwakkes umdan seg tmurt-is.

== 6. Georgica — Tafellaḥt d ugama ==
[[Tugna:Meister des Vergilius Romanus 001.jpg|centré|vignette|450x450px|Georgica n Virgil.]]


Georgica d adlis n Virgil i d-yettawin ɣef tfellaḥt, akal, isekla, iɣersiwen d tmeddurt n yimdanen deg ugama.

Yettwasuffeɣ azal n useggas 29 send Ɛisa, yebḍa ɣef kuẓ n yiḥricen.

Adlis-a yella d amaynut deg tsekla tarumanit imi Virgil yesseqdec aselmed n tfellaḥt am asentel n usefru ameqqran.

=== 6.1. Aḥric amezwaru: akal d yigran ===
Deg uḥric amezwaru, Virgil yessefhem amek i yettwaxdem wakal, amek i ttwasenqaden yigran, d wamek i yesseqdec ufellaḥ akud d tɣawsiwin n ugama.

Yettmeslay ɣef yiṭij, igenni, aman, agris d wayen i d-yettawin lɣella.

Maca ur yelli ara d adlis ussnan n tfellaḥt. D asefru i d-yettawin ɣef umennuɣ n umdan akked ugama.

=== 6.2. Aḥric wis sin: isekla d tẓurin ===
Deg uḥric wis sin, Virgil yessawel ɣef isekla, tiẓurin d uzemmur.

Yessefhem amek i ttwasnernayen, amek i ttwaseḥrazen d wamek i ttwaseknen yigran.

Deg-s, yella usefru i d-yettmeslayen ɣef thuski n ṭṭelyan, d wayen i t-yeǧǧan d tamurt iḥemmel.

=== 6.3. Aḥric wis kraḍ: iɣersiwen ===
Deg uḥric wis kraḍ, Virgil yessefhem tudert n yiɣersiwen n tfellaḥt, ladɣa izgaren, iɛudiwen d wulli.

Yettmeslay ɣef tazmert n yiɣersiwen, lehlak d tmettant.

Deg taggara n uḥric-a, yessefk-d tugna n lehlak ameqqran i d-yettawin tamettant i waṭas n yiɣersiwen.

Ayen-a yeskan-d belli agama yezmer ad yili d aɣbalu n tudert, maca daɣen d aɣbalu n lḥif.

=== 6.4. Aḥric wis kuẓ: tizizwit ===
Deg uḥric wis kuẓ, Virgil yessawel ɣef tizizwit, tudert-is deg tgemma, d wamek i tetteddu tmetti-s.

Yesseqdec tizizwit am amedya n tuddsa, leqdic d usdukel n tmetti.

Deg taggara n uḥric-a, yessefk-d tamacahut n Aristaeus d Orpheus, i d-yettawin ɣef tayri, tamettant d tuɣalin ɣer tudert.

== 6.5. Tikti tagejdant n Georgica ==
Georgica ur yelli ara kan d adlis ɣef tfellaḥt. D adlis i d-yettmeslayen ɣef wassaɣ gar umdan d ugama.

Virgil yessefk-d belli tudert ur tettnerni ara war leqdic. Akal yezmer ad yefk lɣella, maca ilaq ad yettwaxdem.

Deg waya, tafellaḥt tettwaḥsab d amedya n umennuɣ n umdan akked ugama, d usirem n talwit deg tmetti.

== 7. Aeneis — Aneid ==
[[Tugna:Vergils Aeneis 1910 06.jpg|centré|vignette|550x550px|Aeneis n Virgil.]]


Aeneis d adlis ameqqran n Virgil, d win i t-yesseǧǧan gar yimedyazen imeqqranen n umaḍal. Yebḍa ɣef 12 n yiḥricen, yesɛa azal n 9 900 n yifyar.

Virgil yebda tira-s azal n useggas 29 send Ɛisa, yekkemmel armi d tamettant-is deg useggas 19 send Ɛisa.

Adlis-a d asefru aɣezzfan i d-yettalesen inig n Aeneas, yiwen seg yimeqqranen n Ṭrwa, seg tmettant n temdint-is armi d tuɣalin ɣer ṭṭelyan, anda ara yebnu aẓar n Ruma n deffir.

=== 7.1. Aeneas d Ṭrwa ===
Aeneas d yiwen seg yimeqqranen n Ṭrwa, mmi-s n Anchises d Venus.

Mi teɣli Ṭrwa deg ṭṭrad i d-yettwabedren deg Iliad n [[Humer|Homer]], Aeneas yezmer ad irewel seg temdint i yettwaserɣen.

Yettawi baba-s Anchises ɣef tuyat-is, mmi-s Ascanius, d kra n yimdanen i d-yeslek seg Ṭrwa.

Tugna-a d yiwet seg tugniwin yettwassnen n tmiṭulujit tarumanit: Aeneas yettawi baba-s ɣef tuyat-is, d amedya n wassaɣ gar yizri, tmetti d yimal.

=== 7.2. Inig ɣer ṭṭelyan ===
Aeneas d yimdanen-is ttɛeddin seg yilel ɣer yilel, ttwalin temnaḍin yemgaraden n umaḍal agrakal.

Juno, tarebbit i ur nḥemmel ara Aeneas, tettɛaraḍ ad tesseḥbes inig-is. Venus, yemma-s, tettɛawan-it.

Deg tmucuha-a, irebbiten sɛan tazmert ɣef tudert n yimdanen, maca imdanen ilaq ad fernent daɣen iberdan-nsen.

== 8. Aeneas d Dido, tagellidt n Qerṭaj ==
[[Tugna:Jacopo Amigoni (c.1682-1752) - Aeneas and Achates Wafted in a Cloud before Dido, Queen of Carthage, with Cupid at Her Feet - 772276 - National Trust.jpg|centré|vignette|450x450px|Tmlilitt n Aenead d Dido.]]


Yiwet seg tmucuha yettwassnen n Aeneis d tin n Dido, tagellidt n Qerṭaj, akked Aeneas.

=== 8.1. Aeneas deg Qerṭaj ===
Mi yewweḍ Aeneas ɣer [[Qerṭaj]], Dido teqbel-it, tefk-as aɣbalu d uḥraz. Dido tella d tagellidt i d-yessnulfan Qerṭaj deg timiṭulujit.

Aeneas yessawel-as ɣef Ṭrwa, ɣef ṭṭrad d wayen i yeḍran i yimdanen-is. Deg tallit-a, Dido tebda tettḥemmil Aeneas.

=== 8.2. Tayri d tɣawsa n umezruy ===
Dido tebɣa ad yeqqim Aeneas deg Qerṭaj, maca netta yesɛa tuɣdaḍt-nniḍen: ad yewweḍ ɣer ṭṭelyan, iwakken ad d-yales lebni n yiẓuran n Ruma.

''Mercure(Mirkur)'', amezni n yirebbiten, yessefhem-as belli ilaq ad ikemmel inig-is.

Aeneas yeǧǧa Qerṭaj, d aya i d-yeglan s lḥif ameqqran i Dido. Deg taggara, Dido tenɣa iman-is.

=== 8.3. Anamek n tmucuha ===
Tamacahut n Dido d Aeneas tettawi ɣef assaɣ gar tayri d tuɣdaḍt.

Aeneas yezmer ad yefren tayri, maca yefren abrid i as-yettwafken s yirebbiten.

Dido, deg tmuɣli n Virgil, d tameṭṭut i yesɛan tazmert d leḥkem, maca tettwaḥbes s lḥif n tayri.

Tamacahut-a tesɛa diɣen anamek asertan: Ruma d Qerṭaj llan d sin n yiɣerfan i yellan deg ṭṭrad ameqqran deg umezruy.

Maca ilaq ad nefrez gar tmiṭulujit d umezruy. Dido d Aeneas n Aeneis d imdanen n tmucuha, mačči d anagi amezruyan n ṭṭrad n Ruma d Qerṭaj.

== 9. Aeneas deg umaḍal n yimettanen ==
Deg uḥric wis sḍis n Aeneis, Aeneas yekcem ɣer umaḍal n yimettanen. Yettɛawan-it Sibyl, tameṭṭut i yesɛan tamusni n yirebbiten. Deg umaḍal-a, Aeneas yettwali kra n yimdanen i yemmuten, gar-asen baba-s Anchises. Anchises yessefhem-as ayen ara yeḍrun deg yimal, ladɣa ɣef Ruma d yigelliden-is. Deg waya, Virgil yesseqdec timiṭulujit iwakken ad yessefhem uamezruy n Ruma.

Yessefk-d tugniwin n yimdanen i ara d-yilin deg yimal, armi d tallit n [[Uɣustus]]. D yiwen seg yiḥricen i yesɛan azal ameqqran deg udlis, imi yessefk-d assaɣ gar yizri, tura d yimal.

== 10. Ṭṭrad deg Italya ==
Mi yewweḍ Aeneas ɣer ṭṭelyan, ur yufi ara talwit. Yella ṭṭrad gar yimdanen-is d kra n yiɣerfan i zedɣen dinna. Turnus, aqeṛṛu n Rutuli, yella d axṣim-is agejdan n Aeneas. Aeneas yebɣa ad yesseǧhed assaɣ d Latinus, agellid n Latium, akked yelli-s Lavinia. Maca Turnus yebɣa ad yezweǧ Lavinia, d aya i d-yeglan s ṭṭrad.

=== 10.1. Aeneas d Turnus ===
Deg taggara Aeneas d Turnus kecmen deg uymennuɣ. Mi yerbeḥ Aeneas Turnus deg umennuɣ, yella yezmer ad as-yeǧǧ tudert. Maca mi iwala taḥzamt n Plallante i yelsa Turnus, yemmekta-d amek i yenɣa Turnus Pallante. Deg wakud-nni, Aeneas yerfa, yenɣa Turnus. Adlis yekfa deg tmettant-a, war ma yessefhem Virgil amek i d-teḍra talwit deffir ṭṭrad. Taggara-a tesɛa azal ameqqran, imi tettawi ɣef tuccḍa, lḥif d wayen i d-yettawi ṭṭrad deg tudert n yimdanen.

== 11. Aeneis d tasertit n Uɣustus ==
[[Tugna:Publius Vergilius Maro, Opera omnia, comm. Servius.jpg|centré|vignette|YIwen seg dilisen n Virgil ɣef Aeneis.]]


Aeneis yella d adlis i d-yettawin ɣef aẓar n Ruma, d waya i t-yeǧǧan ad yesɛu assaɣ d tsertit n [[Uɣustus]]. Deg tallit n Virgil, Uɣustus yebɣa ad yesseǧhed talwit deffir ṭṭrad n daxel, d usdukel n Ruma deg yiwen n leḥkem.

Aeneis yeskan-d belli Ruma tesɛa aẓar ameqqran deg tmiṭulujit, d akken asnerni-is yella d aḥric n wakud aɣezzfan. Maca ur ilaq ara ad neḥseb adlis-a d asefru n usenmer i August kan.

Deg-s, Virgil yessefk-d aṭas n tugniwin n lḥif, tmettant d wayen i d-yettawi ṭṭrad.

Kra n yimnadiyen ḥesben belli Aeneis d adlis i yesseǧhaden tazmert n Uɣustus, ma d wiyaḍ ḥesben belli yesɛa daɣen azɣan uffir i ṭṭrad d tazmert tasertant.

Tarrayt tis kraḍ tettwali belli sin n yisental-a zemren ad ilin deg yiwen n udlis.

== 12. Aɣanib aseklan n Virgil ==
Virgil yella d amedyaz i yessnernan aɣanib n usefru alaṭini.

=== 12.1. Tazmert n tefyirt ===
Virgil yesseqdec tafyirt s wudem yettqenɛen, s yisental n thuski, lḥif d tazmert.

Yella yessen amek ara yessekcem anamek aɣezzfan deg yiwen n tefyirt.

Deg Aeneis, yesseqdec asefru n ''hexameter'', talɣa n tefyar i yellan tettwaseqdec deg yisefra imeqqranen n Homer.

=== 12.2. Timucuha d yimdanen ===
Virgil yesseqdec timucuha n yirebbiten d yimdanen, maca yessefk-asen iḥulfan n tidet.

Aeneas yezmer ad yili d amdan i yesɛan tuɣdaḍt, maca yettḥulfu s lḥif d tugdi.

Dido d tagellidt i yesɛan tazmert, maca tettḥulfu s tayri d tissas.

Turnus d axṣim n Aeneas, maca ur yettwabdar ara kan d amdan n diri. Yesɛa daɣen tuɣdaḍt d wazalen-is.

=== 12.3. Assaɣ gar umdan d tmetti ===
Deg yedlisen-is, Virgil yesseqdec amdan am uḥric n tmetti. Ayen i yexdem yiwen yezmer ad yesɛu tazrirt ɣef waṭas n yimdanen.

Deg Aeneis, Aeneas ur yettidir ara kan i yiman-is. Yettawi assaɣ d twacult-is, imdukal-is, d yimal n Ruma.

== 13. Virgil d tfelsafit ==
Virgil ur yelli ara d afelsafi s unamek n [[Flaṭun|Plato]] neɣ [[Aristot|Aristote]], maca yesseqdec isental ifelsafiyen deg yisefra-s.

=== 13.1. Agama d umdan ===
Deg Georgica, Virgil yessefhem belli agama d aɣbalu n tudert, maca ur yelli ara d amkan n talwit i lebda.

Amdan ilaq ad yexdem akal, ad yesseḥrez iɣersiwen, ad yessen akud n tẓuri. D tarrayt i d-yettawi ɣef leqdic, tazmert d tḥerci n umdan.

=== 13.2. Tuɣdaḍt d tilelli ===
Deg Aeneis, Aeneas yella yettɛeddi gar sin n yiberdan: ayen i yebɣa d wayen i ilaq ad yeg.

Tamacahut-a tettawi ɣef ussaɣ gar tlelli n umdan d tuɣdaḍt-is ɣer tmetti.

Virgil ur d-yefki ara tiririt taḥerfit i usentel-a, maca yesseqdec timucuha iwakken ad yessefhem lḥif i d-yettawi.

=== 13.3. Ṭṭrad d talwit ===
Virgil yedder deg tallit n ṭṭrad n daxel, d aya i t-yeǧǧan ad yesseqdec ṭṭrad am usentel ameqqran.

Deg Aeneis, ṭṭrad yezmer ad yili d abrid ɣer talwit, maca yettawi daɣen lḥif d tmettant.

Tamuɣli-a ur tella ara d tin i yessawalen ɣer ṭṭrad s wudem aḥerfi, maca d tin i d-yesskanen azal n lḥif i d-yettawi.

== 14. Virgil d Ovid ==
Virgil d [[Ovid]] llan d sin n yimedyazen imeqqranen n tallit taɣustit, maca isental-nsen yemgaraden.
{| class=&quot;wikitable&quot;
|+
!Taɣawsa
!Virgil
!Ovid
|-
|Tallit
|70-19 SN.Ɛ
|43 SN.Ɛ - 17/18 SLD.Ɛ
|-
|Adlis ameqqran
|Aeneis
|Metamorphoses(Tuttyiwin)
|-
|Asentel agejdan
|Ruma, tuɣdaḍt, ṭṭrad, imal
|Tayri, abeddel, Timiṭulujit
|-
|Aɣanib
|Ameqqran, iḥulfan, amezruyan
|Aḥric, asugnan, yettbeddilen
|-
|Assaɣ d Uɣustus
|Tallit n usnerni n tezmert-is
|Yettwanjli seg Ruma s lamer-is
|-
|Tazrirt
|Asefru ameqqran arumani
|Timucuha n ubeddel d tayri
|}
Ovid yella yesɛa tazrirt seg Virgil, maca yesseqdec timiṭulujit s wudem yemgaraden.

Virgil yesseqdec timucuha iwakken ad yessefhem aẓar n Ruma d yimal-is.

Ovid yesseqdec timucuha iwakken ad yessefhem abeddel n yimdanen d umaḍal.

== 15. Tamettant n Virgil ==
Deg useggas 19 send Ɛisa, Virgil iruḥ ɣer Yunan, anda i yebɣa ad yesseǧhed tira n Aeneis.

Deg ubrid n tuɣalin, yella yewweḍ ɣer Megara, anda i d-yettwabder belli yehlak.

Mi d-yuɣal ɣer ṭṭelyan, yemmut di Brundisium, ass n 21 Ctember 19 send Ɛisa, deg 50 n yiseggasen-is.

Kra n yiɣbula iqburen qqaren belli Virgil yebɣa ad yesserɣ Aeneis imi ur t-yekmil ara s wudem i yebɣa.

Maca Uɣustus yefka lamer ad yettwaḥrez udlis, d adlis i d-yettwasuffeɣ deffir tmettant n Virgil.

Isallen-a kkan-d seg yimyura n talliyin i d-iḍefren, ur nezmir ara ad neḥseb yal aḥric deg-sen d tidet yettwasnen s wudem ummid.

Virgil yettwanḍel qrib ɣer Napoli, deg temnaḍt n Posillipo, maca amḍiq n uẓekka-s ur yettwassen ara s tidet s yisallen n unadi amezruyan.</text>
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  </page>
  <page>
    <title>Nvidia</title>
    <ns>0</ns>
    <id>25632</id>
    <revision>
      <id>117828</id>
      <parentid>117818</parentid>
      <timestamp>2026-10-31T14:27:17Z</timestamp>
      <contributor>
        <username>Gurzil90x</username>
        <id>14292</id>
      </contributor>
      <comment>arniɣ ayen ilaqen</comment>
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      <text bytes="11307" sha1="ckkfelqxze9t6ddkklqk4kvksbp9wb8" xml:space="preserve">{{Infobox company
| name = Nvidia
| official_name = Nvidia Corp.
| image = [[File:NVIDIA Headquarters.jpg|thumb|Tasɣimt n NVIDIA]]
| type = Titiknulujit
| founded = 5 yebrir, 1993
| founder = Jensen Huang
Chris Malachowsky
Curtis Priem
| headquarters = Santa Klara, Kalifurnya, Marikan
| country = Iwunak Yedduklen n Marikan
| industry = GPU
| products = Tikarḍiwin n GPU(GeForce  • RTX / Quadro)
CUDA
CPUs (Grace)
DPUs (BlueField)
SoCs (Tegra  • Drive)
DGX
| website = https://www.nvidia.com/
| wikidata_revenue = yes
| wikidata_operating_income = yes
| wikidata_net_income = yes
| logo = [[File:NVIDIA logo.svg|thumb|Alugu n NVIDIA]]
}}

'''Nvidia''' d tarmiṣt tamirikanit n titiknulujit, tettnadi, tessalay yerna tessuffuɣ-d tiɣeṛɣaṛ n yisekkaren udlifen (GPU), inagrawen n usiḍen arurad, iseɣẓanen d wallalen n tigzi taragmawant.

Tettwasbedd deg 5 yebrir 1993 deg [[Kalifurnya]], deg [[Iwunak Yeddukklen n Temrikt|Marikan]]. Deg tazwara, iswi-is yella deg usnerni n wudlifen s kraḍ n tsekkiwin (3D), ladɣa i wuraren n yiselkimen. Maca, seg useggas n 2006, tebda tarmiṣt ad tesnerni tiknulujit i yessawaḍen GPU ad yexdem asiḍen ur cudden ara kan ɣer tugniwin.

Ass-a, NVIDIA ur teqqim ara d tarmiṣt n tikarḍiwin tudlifin kan. Tuɣal d yiwet seg tiṛmisin tigejdanin deg usali n inagrawen n [[Tigzi Taragmawant|tigzi taragmawant]], aselmed n tmudmiwin n tutlayt, tusna, arrubutik, timacinin tifulmanin d yisekkaren imeqqranen.

Deg 2026, afaris-is ur yettwasres ara kan deg yiselkimen n yimdanen, maca daɣen deg yimmasen n yisefka, i deg xeddmen yiwalen n GPU s umata akken ad siḍnen isefka iṭṭuqqten s zreb.

== 3. Amezruy n NVIDIA ==

=== 3.1. Tallit n tlalit: 1993–1997 ===
Deg yebrir 1993, kraḍ n yijenyuṛen, Jensen Huang, Chris Malachowsky d Curtis Priem, sbeddan NVIDIA. Ɣur-sen, tikti tagejdant tella d asnerni n tiknulujit n tugniwin i yiselkimen.

Deg tallit-nni, uranen n yiselkimen bdant ad sɛun azal ameqran. Maca isekkaren n wakud-nni ur zmiren ara ad siḍnen s lemɣawla akk isefka ilaqen i usken n wudlifen 3D.

Deg 1995, NVIDIA tessufeɣ-d NV1, yiwen seg yifarisen-is imezwura. Ur yewwi ara lebɣi n tnezzut acku tasegda-s temgarad ɣef kra n yilugan i yettwasqedcen deg tallit-nni.

Deg 1997, tarmiṣt tessufeɣ-d RIVA 128, asekkar udlif i yesɛan amhaz meqqren deg usefrak n tugniwin 3D. Afaris-a yefka-as i NVIDIA tagnit ad tebnu azadur n tnezzut-is.

=== 3.2. GeForce d tlalit n GPU: 1999 ===
Deg 1999, NVIDIA tessufeɣ-d GeForce 256, i tessekna am uGPU amezwaru.

GPU d agzul n Graphics Processing Unit, d asekkar yettwaselɣen i usiḍen n tugniwin d wudlifen. GeForce 256 yesdukkel deg yiwen n uceṛṛun kra n yimahilen udlifen i yellan uqbel xeddmen-ten yiferdisen yemgaraden.

Ilaq ad nefhem dakken NVIDIA d nettat i d-yessumren GPU s wudem-a n tnezzut deg 1999, maca isekkaren n tugniwin llan yakan uqbel-as.

S GeForce 256, NVIDIA tebda ad tettwasnen ugar deg tnezzut n uraren d yiselkimen n yimeẓla.

=== 3.3. Tallit n CUDA: 2006 ===
Deg 2006, NVIDIA tessufeɣ-d CUDA (Compute Unified Device Architecture).

D yiwet seg tneqqiḍin tigejdanin deg umezruy-is.

Uqbel CUDA, GPU yettwasqedc s waṭas i tugniwin. S CUDA, imsihelen zemren ad arun ahilen i yessawaḍen GPU ad yexdem isḍanen n tusna, tusnakt, tusnengama d tasleṭ n yisefka.

S waya, GPU yuɣal d allal n usiḍen arurad, ur yeqqim ara kan d allal n uraren.

=== 3.4. NVIDIA d tigzi taragmawant: 2012 ===
Deg 2012, tamudemt AlexNet, i d-yessuffɣen Alex Krizhevsky, Ilya Sutskever d Geoffrey Hinton, tewwi-d agmuḍ yelhan deg timsizzelt ImageNet.

Imnadiyen-a sqedcen GPU n NVIDIA i uselmed n uzeṭṭa n yiṛununen.

Agmuḍ-a yessekna dakken almad alqay (deep learning) yezmer ad yili d tarrayt tafessast ugar deg waṭas n tɣawsiwin n ussugen d tasleṭ n tugniwin.

Seg tallit-a, aseqdec n GPU deg tigzi taragmawant ibeddel amek xeddmen imnadiyen d yimsihelen.

=== 3.5. Tallit n RTX: 2018 ===
Deg 2018, NVIDIA tessufeɣ-d tasegda RTX, i yessawaḍen ad yettwaxdem uskan n yizirigen n tafat (ray tracing) deg wakud ilaw.

Tatiknulujit-a tezmer ad tesɛeddi aselɣu n tafat, tilisa n tili d yimeclalen n tugniwin akken ad d-banent s wudem iqerrben ugar ɣer tilawt.

RTX tessnerna daɣen aseqdec n tigzi taragmawant i usnerni n tbadut d tɣara n tugniwin.

=== 3.6. Seg 2022 ar 2026: tallit n inagrawen imeqqranen n AI ===
Deg yiseggasen-a, NVIDIA teffeɣ seg wudem n tarmiṣt i yeznuzun GPU ɣer tarmiṣt i yessalayn anagraw ummid: isekkaren, takatut, azeṭṭa, iseɣẓanen, allalen n usihel d yimmasen n yisefka.

Tiɣeṛɣaṛ Hopper, Blackwell d Rubin ttwasnernant iwakken ad siḍnent timudmiwin timeqqranin n tigzi taragmawant.

Deg 2026, NVIDIA tebda asnerni n tɣessa Vera Rubin, i yesdukklen GPU Rubin, CPU Vera d yiferdisen n uzeṭṭa, akken ad yili usiḍen s waṭas n yisekkaren i d-yettmeslayen gar-asen.

Amezruy-a yeskan-d abeddel agejdan: seg usken n tugniwin 3D, ɣer tɣessa n tigzi taragmawant n umaḍal.

== 4. D acu i d GPU? Amek i iteddu? ==
GPU (Graphics Processing Unit) d asekkar udlif, yettwaselɣen iwakken ad yexdem aṭas n usiḍen s yiwet n tikelt, s tarrayt n umahil amsadaɣ (parallel processing).

Tifrat-a temgarad ɣef CPU (Central Processing Unit), i yellan d asekkar agejdan n uselkim.

=== 4.1. Amgired gar CPU d GPU ===
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-29 14-53-10.png|centré|575x575px]]                                                      


&lt;small&gt;'''Unuɣ n usegzi, ur d-yettmeslay ara ɣef umḍan n yiferdisen n CPU neɣ GPU n tidet.'''&lt;/small&gt;

CPU yelha i yimahilen yemgaraden, i usendeh n unagraw, i usefrek n yisefka d tigawin i yesran ad myezwarent.

GPU, s tama-nniḍen, yelha ladɣa i yimahilen i nezmer ad nebḍu ɣef waṭas n yiferdisen ad ten-nsiḍen s wudem amsadaɣ.

Amedya: ad neḥseb timernit n sin yisurta, yal yiwen deg-sen yesɛa 1 000 000 n yimḍanen.

&lt;math&gt;
C_i = A_i + B_i, \qquad 0 \leq i &lt; 1\,000\,000
&lt;/math&gt;

Imi yal timernit ur teḥwaǧ ara agmuḍ n tin nniḍen, GPU yezmer ad yebḍu amahil-a ɣef waṭas n yiḥricen. D tamiḍrant-a i d azadur n usiḍen amsadaɣ.

=== 4.2. Iferdisen igejdanen n GPU ===
GPU amiran yesɛa aṭas n yiferdisen, gar-asen:

- '''CUDA Cores''': iferdisen n usiḍen i yimahilen n tusnakt d usiḍen amatu.

- '''Tensor Cores''': iferdisen yettwaselɣen i yimahilen n yisiraw (matrices), i yesɛan azal meqqren deg almad alqay.

- '''RT Cores''': iferdisen n uskan n yizirigen n tafat deg tugniwin 3D.

- '''VRAM''': takatut n GPU, i deg ttwaḥrazen yisefka i yettwasiḍnen.

- '''Takatut L2''': takatut taruradt i yellan qrib ɣer yigrawen n usiḍen.

- '''NVLink''': tarrayt n tuqqna taruradt gar GPU d GPU, neɣ gar yiferdisen n unagraw, ilmend n tasegda.

Amedya, RTX 5090 yesɛa 32 GB n tkatut GDDR7, ma d isekkaren n yimmasen n yisefka zemren ad sɛun takatut HBM s wazal d tɣara yemgaraden.

== 5. CUDA: azadur n tzemmert n NVIDIA ==
CUDA d yiwen n unagraw n usihel d tɣessa n usiḍen amsadaɣ i d-tesnulfa NVIDIA. Tessawaḍ i umsihel ad yesseqdec GPU i yimahilen ur nelli ara d tugniwin kan. Deg CUDA, imahilen ttwasuddsen s wudem-a:
[[Tugna:Tuṭṭfa n ugdil seg 2026-10-30 13-33-01.png|centré|670x670px]]


&lt;small&gt;Yal akala afessas(thread) yezmer ad yesɛu amḍiq-is, ad iɣer isefka, ad yexdem asiḍen, syin ad yerr agmuḍ.&lt;/small&gt;

D acu kan, ur ilaq ara ad neḥseb dakken GPU dima yif CPU deg yal amahil. Ma yella amahil yesɛa aṭas n tigawin i yemyuqqnen, neɣ yesra abrid amezwaru uqbel win wis sin, CPU yezmer ad yili yif-it.

=== 5.1. Aseqdec n CUDA deg usihel ===
CUDA yettwasqedc deg waṭas n tutlayin d yisnasen. Gar-asen C++, Python, PyTorch d TensorFlow.

Amedya amezwaru d agzul n wamek i yezmer umsihel ad yesseqdec GPU i tmernit n yisurta:&lt;syntaxhighlight lang=&quot;c++&quot;&gt;
__global__ void add(const float *a,
                    const float *b,
                    float *c, int n) {
    int i = blockIdx.x * blockDim.x + threadIdx.x;
    if (i &lt; n) {
        c[i] = a[i] + b[i];
    }
}
&lt;/syntaxhighlight&gt;Deg uhil-a, yal akala afessas(thread) yettawi yiwen n umḍiq '''i''', syin yesiḍin '''a[i] + b[i]'''. S waya, aṭas n yiḥricen zemren ad xedmen deg wakud-nni kan. Amedya-a yeskan kan iɣes(''kernel)''; akken ad yeddu, yesra asenker-is d usefrek n tkatut.

=== 5.2. Ayɣer CUDA yesɛa azal meqqren? ===
Azal n CUDA ur yelli ara kan deg tzemmert n GPU.

NVIDIA tebna-d fell-as aṭas n temkarḍiwin n usihel (software libraries), gar-asent cuDNN, cuBLAS, NCCL d TensorRT.

Asihel n waṭas n yisnasen n tigzi taragmawant teqqen ɣer tɣessa-a. Aya yessawaḍ-d i NVIDIA azal nniḍen deg tnezzut, acku amsihel ur yessutur ara GPU kan: yesra daɣen iseɣẓanen, allalen n usenqed d temkarḍiwin i yettwasenqden.

== 6. Tiɣeṛɣaṛ n NVIDIA: seg Tesla ɣer Vera Rubin ==
NVIDIA tessnerna aṭas n tisegda n GPU deg umezruy-is.
{| class=&quot;wikitable&quot;
|+
!Tallit
!Tasegda
!Azal-is agejdan
|-
|2006
|Tesla
|Asnerni n usiḍen amsadaɣ
|-
|2010
|Fermi
|Asnerni n usiḍen ussnan
|-
|2012
|Kepler
|Tazmert akked tɣellist n useqdec asrurad
|-
|2014
|Maxwell
|Aseqdec yelhan n usrurad
|-
|2016
|Pascal
|Asnerni n tigzi taragmawant d GPU
|-
|2017
|Volta
|Asekcem n Tensor Cores
|-
|2018
|Turing
|RTX d ray tracing
|-
|2020
|Ampere
|A100 d RTX 30
|-
|2022
|Hopper
|H100 d usiḍen n tmudmiwin timeqqranin
|-
|2024
|Blackwell
|B200, GB200 d RTX 50
|-
|2026
|Rubin / Vera Rubin
|Inagrawen imeqqranen n AI
|}

=== 6.1. Hopper d H100 ===
H100 d asekkar i d-tessufeɣ NVIDIA iwakken ad yexdem almad alqayan d usiḍen n tmudmiwin timeqqranin.

Yesɛa Tensor Cores n tziri tis kuẓ, takatut HBM d tigawin n usiḍen i yettwaselɣen i tigzi taragmawant.

H100 yesɛa azal deg umezruy n tmudmiwin n tutlayt timeqqranin (LLM), acku aṭas n yimmasen n yisefka sqedcen-t deg yiseggasen imezwura n tnerni n tigzi taragmawant turriwt.

=== 6.2. Blackwell ===
[[Tugna:Jensen Huang - RTX Blackwell - Nvidia Keynote - CES 2025 Las Vegas (2).jpg|gauche|vignette|Jensen Huang - RTX Blackwell - Nvidia Keynote - CES 2025 Las Vegas]]


Blackwell d tasegda i d-tessufeɣ NVIDIA deg 2024, i d-tefka azadur i yisekkaren B200, GB200 d yifarisen nniḍen.

Yiwen seg usnifel-is agejdan d asdukkel n sin yiḥricen n GPU deg yiwen n uceṛṛun ameqran, s tuqqna taruradt gar-asen.

Blackwell tesnerna daɣen aseqdec n yimḍanen s tiseddi taẓẓayant (low precision), iwakken ad yettwasiḍen ulmad n tmudmiwin d useqdec-nsent s tazzla d taɛkwamt n tazzla tameẓẓyant ugar.

Deg 2025 d 2026, NVIDIA tessnerna talɣa Blackwell Ultra, i yettwaselɣen ladɣa i usnerni n tzemmert n usiḍen n tigzi taragmawant.

=== 6.3. Vera Rubin ===
Vera Rubin d tasegda i d-yernan ɣef Blackwell. Ur d yiwen n GPU kan, maca d anagraw yesdukklen aṭas n yiferdisen:

- GPU Rubin: i usiḍen n tigzi taragmawant.

- CPU Vera: i usendeh d usefrek n yisefka.

- NVLink: i tuqqna taruradt gar GPU.

- ConnectX d BlueField: i usefrek n uzeṭṭa d yisefka.

- InfiniBand d Ethernet: i tuqqna gar yimmasen n yisekkaren d yimmasen n yisefka.

Anagraw Vera Rubin NVL72 yesdukkel 72 n GPU Rubin d 36 n CPU Vera deg yiwen n unagraw n yiṛak imeqqranen (rack-scale system).

Deg 2026, NVIDIA teqqar-d dakken tasegda-a tettwasnerna ladɣa i tmudmiwin n tigzi taragmawant i yesseqdecen aseɣẓen d yimeggan ifulmanen.</text>
      <sha1>ckkfelqxze9t6ddkklqk4kvksbp9wb8</sha1>
    </revision>
  </page>
  <page>
    <title>Tiberyus</title>
    <ns>0</ns>
    <id>25634</id>
    <revision>
      <id>117831</id>
      <parentid>117820</parentid>
      <timestamp>2026-10-31T18:01:19Z</timestamp>
      <contributor>
        <username>Gurzil90x</username>
        <id>14292</id>
      </contributor>
      <comment>seɣtiɣ kra n tucdiwin, syin arniɣ aḍris amaynut</comment>
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      <text bytes="6336" sha1="9tqdk2jtrmj8s919djixw6efeu2w1z3" 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.

== 5. 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.

=== 5.1. 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.

=== 5.2. 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.

=== 5.3. 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.

=== 5.4. 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]].

=== 5.5.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.

=== 5.6. 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.</text>
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  </page>
  <page>
    <title>Stuxnet</title>
    <ns>0</ns>
    <id>25635</id>
    <revision>
      <id>117829</id>
      <parentid>117824</parentid>
      <timestamp>2026-10-31T16:18:59Z</timestamp>
      <contributor>
        <username>Gurzil90x</username>
        <id>14292</id>
      </contributor>
      <comment>arniɣ ayen ilaqen</comment>
      <origin>117829</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3787" sha1="kmo5otkyh4qaf5n0106kshyyg55uepc" xml:space="preserve">[[Tugna:Cyber Serpent Infiltrates the Control Plant.png|droite|448x448px]]
'''Stuxnet''' d avirus aselkiman n wanaw n ijirmeḍ aselkiman(neɣ aḥermeččal aselkiman), i yettwafkan i yiman-is ad yernu ad yeẓẓu iman-is deg yiselkimen nniḍen. Maca, Stuxnet ur yettwabna ara kan iwakken ad yessexser ifuyla, ad yekker isefka neɣ ad yaɣ isallen. Yettwasnulfa iwakken ad ibeddel tikli n yiseɣẓanen i iseddun timacinin n usnerni n uṛanyum, alamma yessawaḍ ad d-yeglu s uxessar deg wallalen n tilawt.

Yettwaf deg 2010, maca anadi ussnan yesken-d belli kra n yileqman-is llan seg yiseggasen i d-yezwaren. Iswi-ines agejdan, akken i d-skanen yinadiyen, d asḍaɛef n usefrek n uranyum deg yigrawen yisgammasen i yettwasqedcen i usnerni n uṛanyum n Natanz, deg Iran.

Stuxnet d yiwen gar yimedyaten imezwura i yettwassnen n unṭag aselkiman i d-yettawin axessar afizikan. Aya yessebgan-d belli anṭag s yiseɣẓanen yezmer ad yuɣal seg umaḍal umḍin ɣer umaḍal n tmaccinin timguranin.

== 2. Ayɣer Stuxnet d amaynut deg umezruy n tesenselkimt? ==
Deg waṭas n yinṭagen iselkimanen, iswi d tukerḍa n isefka, tukksa n yisefka, tukerḍa n tneflit neɣ asḥebbes n yisnasen. Ma d Stuxnet, yettwabna i kra nniḍen.

Yessexdem iselkimen am wakken d abrid ara t-yawin ɣer yisefraken n tmaccinin. Mi ara yaweḍ ɣer unagraw i yebɣa, ad ibeddel kra n tinaḍin n useddu, ad yessexdem isallen nniḍen iwakken imahalen ur ttafaren ara ayen yeḍerrun s tidet.

Ihi, ur yettnadi ara kan ad yessexser aselkim, maca ad yessexdem aselkim iwakken ad yessexser tamacint.

D aya i yeǧǧan Stuxnet ad yili d amedya agejdan deg umezruy n tɣellist n yinagrawen n usbuɣer n yuṛanyum akked ṭṭrad umḍin. 

== 3. Amezruy n Stuxnet d tegnit tasertant deg Iran ==

=== 3.1. Iswi agejdan: Natanz ===
[[Tugna:NASA FIRMS 2025-06-19 Natanz (close-up).png|centré|vignette|Adeg n ulemmas aɣisan i Natanz.]]


Timacinin n usnerni n uranyum deg ulemmas aɣisan n Natanz. D anaw-a n tmaccinin iɣef yella ussumer n unṭag n Stuxnet.Deg yiseggasen n 2000, Iran yebna akked usegmi n yiɣawasen-is i usnerni n uranyum. Uranyum yettusexdam deg ufares n tẓwert taɣisant, maca yezmer daɣen ad yettusemres deg ufares n yimrigen iɣisanen ma yewweḍ ɣer usnerni afellay ilaqen.

Tignit-a teǧǧa ad ilin ccwal d umgired asertan gar Iran, Marikan, Israyil akked kra n tmura n Urupa.

Ma d Iran, yeqqar-d belli iswi n uɣawas-is d asnas n tẓwert taɣisant. Maca Marikan d Israyil ttwalin deg-s amihi iɣef ilaq ad ttwaseqdacen wallalen n usenqes n tnezmart n Iran.

Deg tegnit-a i d-yebda usenfar uffir i d-yettwasnen deffir s yisem Olympic Games. Imagraden n 2012 i d-yeffɣen deg yiɣmisen n Marikan, s usekcem n yisallen sɣur yimḍebren iqburen d wid yellan deg udabu, qqaren-d belli asenfar-a yebda deg tallit n George W. Bush, yerna ikemmel deg tallit n Barack Obama. 

=== 3.2. Amseḍfer n tedyanin tigejdanin ===
'''2007'''

Ileqman imezwura

Yella yiwen n uleqqem aqbur n Stuxnet i yettwaf deffir deg tesleḍt n yifuyla n yiseggasen-nni. Anadi yesken-d amek i yettwasɣiwes unṭag ɣef yinagrawen n Natanz

'''2009'''

Asnerni n unṭag

Tban-d snat n tarrayin n uxessar: yiwet teqqen ɣer ṣṣda n tmacinin, tayeḍ ɣer urured n tuzzya-nsent

'''2010'''

Tifin n Stuxnet

Deg 17 Yunyu, VirusBlokAda, tarmiṣt n tɣellist taselkimant deg Belarus, tesken-d yiwen n useɣẓan araɣelsan ur yettwassnen ara. Syin akin, imazzagen zerwen Stuxnet s telqey

'''2012'''

Asufeɣ n yisallen isertanen

Imagraden n yiseɣmisen n Marikan qqaren-d belli Stuxnet d afares n temlilit tuffirt gar Marikan d Israyil

'''2013'''

Tasleḍt tussnant lqayen

Ralph Langner yessufeɣ-d tazrawt ''To Kill a Centrifuge'', anda i d-yessufeɣ aglam ussnan n snat n tarrayin n uxessar</text>
      <sha1>kmo5otkyh4qaf5n0106kshyyg55uepc</sha1>
    </revision>
    <revision>
      <id>117830</id>
      <parentid>117829</parentid>
      <timestamp>2026-10-31T16:19:27Z</timestamp>
      <contributor>
        <username>Gurzil90x</username>
        <id>14292</id>
      </contributor>
      <comment>seɣtiɣ kra n tuccḍiwin</comment>
      <origin>117830</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3796" sha1="oo3vd4md5fv7wploxlxpd7idfg7w0xr" xml:space="preserve">[[Tugna:Cyber Serpent Infiltrates the Control Plant.png|droite|448x448px]]
'''Stuxnet''' d avirus aselkiman n wanaw n ijirmeḍ aselkiman(neɣ aḥermeččal aselkiman), i yettwafkan i yiman-is ad yernu ad yeẓẓu iman-is deg yiselkimen nniḍen. Maca, Stuxnet ur yettwabna ara kan iwakken ad yessexser ifuyla, ad yekker isefka neɣ ad yaɣ isallen. Yettwasnulfa iwakken ad ibeddel tikli n yiseɣẓanen i iseddun timacinin n usnerni n uṛanyum, alamma yessawaḍ ad d-yeglu s uxessar deg wallalen n tilawt.

Yettwaf deg 2010, maca anadi ussnan yesken-d belli kra n yileqman-is llan seg yiseggasen i d-yezwaren. Iswi-ines agejdan, akken i d-skanen yinadiyen, d asḍaɛef n usefrek n uranyum deg yigrawen yisgammasen i yettwasqedcen i usnerni n uṛanyum n Natanz, deg Iran.

Stuxnet d yiwen gar yimedyaten imezwura i yettwassnen n unṭag aselkiman i d-yettawin axessar afizikan. Aya yessebgan-d belli anṭag s yiseɣẓanen yezmer ad yuɣal seg umaḍal umḍin ɣer umaḍal n tmaccinin timguranin.

== 2. Ayɣer Stuxnet d amaynut deg umezruy n tesenselkimt? ==
Deg waṭas n yinṭagen iselkimanen, iswi d tukerḍa n isefka, tukksa n yisefka, tukerḍa n tneflit neɣ asḥebbes n yisnasen. Ma d Stuxnet, yettwabna i kra nniḍen.

Yessexdem iselkimen am wakken d abrid ara t-yawin ɣer yisefraken n tmaccinin. Mi ara yaweḍ ɣer unagraw i yebɣa, ad ibeddel kra n tinaḍin n useddu, ad yessexdem isallen nniḍen iwakken imahalen ur ttafaren ara ayen yeḍerrun s tidet.

Ihi, ur yettnadi ara kan ad yessexser aselkim, maca ad yessexdem aselkim iwakken ad yessexser tamacint.

D aya i yeǧǧan Stuxnet ad yili d amedya agejdan deg umezruy n tɣellist n yinagrawen n usbuɣer n yuṛanyum akked ṭṭrad umḍin. 

== 3. Amezruy n Stuxnet d tegnit tasertant deg Iran ==

=== 3.1. Iswi agejdan: Natanz ===
[[Tugna:NASA FIRMS 2025-06-19 Natanz (close-up).png|centré|vignette|Adeg n ulemmas aɣisan n Natanz deg Iran.]]


Timacinin n usnerni n uranyum deg ulemmas aɣisan n Natanz. D anaw-a n tmaccinin iɣef yella ussumer n unṭag n Stuxnet.Deg yiseggasen n 2000, Iran yebna akked usegmi n yiɣawasen-is i usnerni n uranyum. Uranyum yettusexdam deg ufares n tẓwert taɣisant, maca yezmer daɣen ad yettusemres deg ufares n yimrigen iɣisanen ma yewweḍ ɣer usnerni afellay ilaqen.

Tignit-a teǧǧa ad ilin ccwal d umgired asertan gar Iran, Marikan, Israyil akked kra n tmura n Urupa.

Ma d Iran, yeqqar-d belli iswi n uɣawas-is d asnas n tẓwert taɣisant. Maca Marikan d Israyil ttwalin deg-s amihi iɣef ilaq ad ttwaseqdacen wallalen n usenqes n tnezmart n Iran.

Deg tegnit-a i d-yebda usenfar uffir i d-yettwasnen deffir s yisem Olympic Games. Imagraden n 2012 i d-yeffɣen deg yiɣmisen n Marikan, s usekcem n yisallen sɣur yimḍebren iqburen d wid yellan deg udabu, qqaren-d belli asenfar-a yebda deg tallit n George W. Bush, yerna ikemmel deg tallit n Barack Obama. 

=== 3.2. Amseḍfer n tedyanin tigejdanin ===
'''2007'''

Ileqman imezwura

Yella yiwen n uleqqem aqbur n Stuxnet i yettwaf deffir deg tesleḍt n yifuyla n yiseggasen-nni. Anadi yesken-d amek i yettwasɣiwes unṭag ɣef yinagrawen n Natanz

'''2009'''

Asnerni n unṭag

Tban-d snat n tarrayin n uxessar: yiwet teqqen ɣer ṣṣda n tmacinin, tayeḍ ɣer urured n tuzzya-nsent

'''2010'''

Tifin n Stuxnet

Deg 17 Yunyu, VirusBlokAda, tarmiṣt n tɣellist taselkimant deg Belarus, tesken-d yiwen n useɣẓan araɣelsan ur yettwassnen ara. Syin akin, imazzagen zerwen Stuxnet s telqey

'''2012'''

Asufeɣ n yisallen isertanen

Imagraden n yiseɣmisen n Marikan qqaren-d belli Stuxnet d afares n temlilit tuffirt gar Marikan d Israyil

'''2013'''

Tasleḍt tussnant lqayen

Ralph Langner yessufeɣ-d tazrawt ''To Kill a Centrifuge'', anda i d-yessufeɣ aglam ussnan n snat n tarrayin n uxessar</text>
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