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Euclid: Elementa

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Click to Expand/Collapse OptionTitle
Click to Expand/Collapse OptionPreface
Click to Expand/Collapse OptionBook I
Click to Expand/Collapse OptionBook ΙI
Click to Expand/Collapse OptionBook IΙΙ
Click to Expand/Collapse OptionBook IV
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gre I,7
ἐδείχθη δὲ αὐτῆς καὶ πολλῷ μείζων: ὅπερ ἐστὶν ἀδύνατον.
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Pic635
eng
But it was also proved much greater than it: which is impossible.
lat Sic
Ostensus est autem ipso et multo maior. Quod impossibile.
lat Gerard
Iam vero ostensum fuit quod ipse erat eo maior. Hoc autem est impossibile.
lat Adelard
Angulus itaque DGB angulo ADG maior. Sicque fiet angulus ADG angulo BDG rnaior, minor maiore maior, quod est impossibile.
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lat Hermann
Erit ergo totum parte minus.
ara Uppsala
No Arabic
ara Tuṣi p. 7
هذا خلف
ara Nairizi p. 64
وبينا ان زاوية (ا د ج) اعظم من زاوية (ب ج د) فاذا زاوية (ب د ج) اعظم من زاوية (ب ج د) بكثير وهما متساويان هذا خلف غير ممكن
per Shirazi p. 25,7-8
و این خلف است
san 14,6–8
imau tau (7) samānau koṇau staḥ | kutaḥ | tasmād idam anupapannaṃ (9) yataḥ samānau koṇau viṣamau jātau |
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lat Clavius
Ostensum autem fuit, quod idem angulus C D F, multo sit minor angulo D C E. Idem ergo angulus C D F, & minor est angulo D C E, & eidem æqualis, quod est absurdum. Sit postremo punctum D, extra triangulum A B C. Aut igitur in tali erit loco, vt vna linea super alteram cadat, vt in priori figura, dummodo loco D, intelligas C, & loco C, ipsum D; ex quo rursus colligetur pars æqualis toti, quod est absurdum. Aut in tali erit loco, vt posteriores duæ lineæ ambiant priores duas, ceu in posteriori figura, si modo loco D, iterum intelligas C, & D, loco C. Quo posito, inidem absurdum incidemus, nempe angulum D C F, & minorem esse angulo C D E, & eidem æqualem, vt perspicuum est. Aut denique punctum D, ita erit extra triangulum A B C, vt altera linearum posteriorum, nempe A D, secet alteram priorum, vt ipsam B C. Ducta igitur recta C D, cum in triangulo A C D, latera A C, A D, ponantur æqualia, erunt anguli A C D, A D C, supra basim C D, æquales: Ac proinde cum angulus A D C, minor sit angulo B D C, pars toto, erit & angulus A C D, minor eodem angulo B D C. Quare multo minor erit angulus B C D, pars anguli A C D, angulo eodem B D C. Rursus, cum in triangulo B D C, latera B C, B D, ponantur æqualia, erunt anguli B C D, B D C, super basim C D, æquales: Est aut etiam ostensum, angulum B C D, multo esse minorem angulo B D C. Idem igitur angulus B C D, & minor est angulo B C D, & eidem æqualis, quod est absurdum. Non ergo æquales sunt inter se A C, A D, & inter se quoque B C, B D.
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