Arxmides

Arxmides yezdeɣ tuget n tudert-is deg Syrakusa (d tamdint tagrikit meqqren akk deg Sičilya), anda yella d imqerreb n ugellid-is Hieron II. Yella icɣel-d d inadiyen ussnan deg waṭas n taɣulin em tanzeggit, tasengama ed tmikanikt. Yella yetturar tamlilt d taxatart deg aḥuddu n Syrakusa mgal yirumyen deg 213 Üqbel Ɛisa (yebna tinaεurin n ṭṭrad), deffir irumyen kecmen ɣar Syrakusa deg 212 neɣ 211 Uqbel Ɛisa, irumyen i t-yenɣan Arxmides deg tamdint-is.

Arxmides yufa-d wassaɣ ger tajumma ed ubleɣ n takurt ed awlellu-is, yufa-d daɣen umenzay n Arxmides ed tafetlit n Arxmides.

Ɣef takurt ed awlellu

 

Deg sin n yidlisen Arxmides yessken : Tajumma n ayen tellan takurt (aqqaṛ-is ${\displaystyle r}$ ) teɛdil uqus (rebɛa) tikkelt n tajumma n tawinest-is tameqqerant : (${\displaystyle 4\pi r^{2}\,}$ ). Ableɣ n takurt yeɛdil sin n ttlut (${\displaystyle {\frac {2}{3}}}$ ) n ubleɣ n awlellu-is : ${\displaystyle {\frac {4}{3}}\pi r^{3}}$ .

Ableɣ n awlellu (i yesɛan llsas-is yeɛdil tawinest tameqqerant n takurt, ed asawen-is yeɛdel ukdu n takurt-nni) d yeɛdel kraḍ tikkelt azgen (${\displaystyle {\frac {3}{2}}}$ ) n ubleɣ n takurt-nni, ed tajumma n awlellu-nni teɛdel daɣen kraḍ tikkelt azgen (${\displaystyle {\frac {3}{2}}}$ ) n tajumma n takurt-nni.

Umenzay n Arxmides

 

Asaḍuf n tasengama ad d-teskan : anda tella tafekka yebbeẓ (uzgen neɣ merra) deg amazzal neɣ lgaz, ittemlili-d tadusi s ukessar ɣer usawen, teɛdel azuk n umazzal neɣ lgaz wi yettwakkes s tafekka-nni, ed ableɣ n amazzal neɣ lgaz wi yettwakkes yeɛdel ubleɣ n tafekka-nni^,.

$${\displaystyle F_{a}=\rho gV}$$

 

${\displaystyle F_{a}}$  : tadusi n itekk-d nnig amazzal.

${\displaystyle \rho }$  : tneẓẓi.

${\displaystyle g}$  : ameɣlal n tajebda.

${\displaystyle V}$  : ableɣ n amazzal neɣ lgaz wi yettwakkes.

${\displaystyle \rho =m/V}$  ⇒ ${\displaystyle m=\rho V}$  ⇒ ${\displaystyle F_{a}=m_{a}g}$  ; akked ${\displaystyle m_{a}}$  : tneẓẓi n amazzal neɣ lgaz wi yettwakkes.

⇒ ${\displaystyle m_{a}g=W}$  ; akked ${\displaystyle W}$  : azuk n amazzal neɣ lgaz wi yettwakkes.

$${\displaystyle F_{a}=W}$$

 

Tafetlit n Arxmides

 

Arxmides i d-yesnulfan tafetlit-is (tafetlit n Arxmides); d tnaεurt tella i wakken ad tessnekreḍ aman, d yiwent seg talɣiwin n ujeɛbub deg-s talɣa n tafetlit yekna akked tiɣmeṛt n ahat 45 n tfesniwin (45°) yebbeɣ deg waman ɣer yixef-is amedda. Amussu n tnaεurt-nni yessuli aman deg ujeɛbub.