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Euclid: Elementa

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Euclid: Elementa
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gre VI,19
Πόρισμα
Ἐκ δὴ τούτου φανερόν, ὅτι, ἐὰν τρεῖς εὐθεῖαι ἀνάλογον ὦσιν, ἔστιν ὡς ἡ πρώτη πρὸς τὴν τρίτην, οὕτως τὸ ἀπὸ τῆς πρώτης εἶδος πρὸς τὸ ἀπὸ τῆς δευτέρας τὸ ὅμοιον καὶ ὁμοίως ἀναγραφόμενον [ἐπείπερ ἐδείχθη, ὡς ἡ ΓΒ πρὸς ΒΗ, οὕτως τὸ ΑΒΓ τρίγωνον πρὸς τὸ ΑΒΗ τρίγωνον, τουτέστι τὸ ΔΕΖ]:
Pic2615
eng
PORISM.
From this it is manifest that, if three straight lines be proportional, then, as the first is to the third, so is the figure described on the first to that which is similar and similarly described on the second.
lat Sic
Quod oportet ostendere.
(Porisma) Ex hoc ergo manifestum quoniam si tres recte proportionales fuerint ut prima ad tertiam ita quod a prima trigonum ad illud quod a secunda simile et similiter descriptum. Quoniam demonstratum est ut recta GB ad BI ita trigonum ABG ad trigonum ABI, hoc est, DEZ.
lat Gerard
No Latin
lat Adelard
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lat Hermann
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ara Uppsala
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ara Tuṣi
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ara Nairizi
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per Shirazi
.
san
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lat Clavius
No Latin
kin 幾何原本
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