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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
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gre ΙΙI,14
Τῶν γὰρ αὐτῶν κατασκευασθέντων ὁμοίως δείξομεν, ὅτι διπλῆ ἐστιν ἡ μὲν ΑΒ τῆς ΑΖ, ἡ δὲ ΓΔ τῆς ΓΗ:
Pic2526
eng
For, with the same construction, we can prove, similarly, that AB is double of AF, and CD of CG.
lat Sic
Eisdem enim dispositis similiter ostendemus quoniam dupla est recta quidem AB recte AZ, recta vero GD recte GI.
lat Gerard
Probatio huius: Quoniam iam protracta est a centro circuli ab linea HT ad lineam GD que non transit per centrum et secat eam super rectos angulos. Ergo secat eam in duo media, linea ergo GT linee TD est equalis, linea itaque DG linee GT dupla existit. Et ita erit linea ZE dupla linee EK,
lat Adelard 49v
Rationis causa: si enim a centro circuli AB linea HT extrahatur usque ad lineam GD que supra centrum non transit, erit eius divisio in duo media supra angulum rectum et GT sicut TD. Quare GD sicut GT bis. Atque eodem modo ZH dupla HK.
lat Hermann
No Latin
ara Uppsala
No Arabic
ara Tuṣi
No Arabic
ara Nairizi
No Arabic
san
No Sanskrit
lat Clavius
No Latin
kin 幾何原本
No Chinese
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