Bibliotheca Polyglotta

Euclid: Elementa

Ἐπεὶ οὖν τριγώνου τοῦ ΑΒΓ παρὰ μίαν τῶν πλευρῶν τὴν ΒΓ ἦκται ἡ ΖΔ,

eng

Then, since FD has been drawn parallel to BC, one of the sides of the triangle ABC,

lat Sic

Quoniam ergo trigoni ABG secundum unum laterum BG tracta est DZ,

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san

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lat Clavius

Dico AG, esse partem tertiam imperatam rectae AB. Nam cum in triangulo ABF, lateri FB, parallela sit recta DG;¹ erit ut FD, ad DA, ita BG, ad GA. ² Componendo igitur , ut FA, ad DA, ita BA, erit ad GA: sed FA, ipsius AD, est tripla, ex constructione. Igitur et BA, ipsis AG, erit tripla, ideoque AG, tertia pars erit ipsius AB, quae imperabatur.

1. 2. sexti. 2. 18. quinti.

kin 幾何原本

論曰。甲乙己角形內之丁庚線。旣與乙己邊平行。卽己丁與丁甲之比例。若乙庚與庚甲也。本篇二合之。己甲與甲丁。若乙甲與庚甲也。五卷十八而甲丁旣為己甲三分之一。卽庚甲亦為乙甲三分之一也。

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