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Euclid: Elementa

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gre I,27
τριγώνου δὴ τοῦ ΗΕΖ ἡ ἐκτὸς γωνία ἡ ὑπὸ ΑΕΖ ἴση ἐστὶ τῇ ἐντὸς καὶ ἀπεναντίον τῇ ὑπὸ ΕΖΗ: ὅπερ ἐστὶν ἀδύνατον:
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Pic645
eng
Then, in the triangle GEF, the exterior angle AEF is equal to the interior and opposite angle EFG: which is impossible. [I. 16]
lat Sic
Trigoni ergo IEZ exterior angulus AEZ equalis est interiori et opposito EZI. Quod est impossibile.
lat Gerard
Et quia angulus AEZ extrinsecus est trianguli HEZ, angulo DZE intrinseco qui ei opponitur maior existit. Sed ipse ei fuit equalis. Hoc autem contrarium est et impossibile.
lat Adelard
Erit itaque angulus AHT trianguli extra positus angulo intrinseco HTK equalis, quod est impossibile.
lat Hermann
erit igitur intrinsecus angulus extrinseco equalis.
ara Uppsala
No Arabic
ara Tuṣi p. 16
زاوية (ا ه ز) الخارجة من مثلث (ه زح) مساوية لداخلة (ه زد) هذا خلف [يو]
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ara Nairizi p. 114-116
فتصير ١١٦ زاوية (ا ح ط) الخارجة من مثلث (ح ط ك) اعظم من زاوية (ح ط ك) الداخلة كما بين ببرهان (يو) من (ا) وهذا خلف لان زاوية (ا ح ط) فرضت مساوية لزاوية (ح ط د)
san 36,7-9
tatra vahajhatribhujaṃ bhaviṣyati | evaṃ tribhujād bahisthaḥ ahajhakoṇas tribhujāntargataḥ hajhavakoṇaś caitau tulyau syātām | idam anupapannam |
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lat Clavius
Quoniam igitur triangulum est G I H, (cum A B, recta continuata sit, item recta C D, usque ad punctum I,) & angulus A G H, positus est æqualis angulo D H G; erit externus angulus A G H, æqualis interno, & opposito D H G, quod est absurdum; quoniam externus interno maior est.
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