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Euclid: Elementa

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Euclid: Elementa
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gre V,0
τεταγμένη ἀναλογία έστίν, ὅταν ᾖ ὡς ἡγούμενον πρὸς ἑπόμενον οὕτως ἡγούμενον πρὸς ἑπόμενον, ᾖ δὲ καὶ ὡς ἑπόμενον πρὸς ἄλλο τι οὕτως ἑπόμενον πρὸς ἄλλο τι.1
1. Heiberg vol. ii, p. 6-7, in note: “Post def 17 seq. ...
eng
An ordered proportion arises when, as antecedent is to consequent, so is consequent to something else.1
1. Interpolation after Theon‘s time, cf. Heath vol. 2, p. 137.
lat Sic
Vel aliter: Sumptio extremorum secundum ablationem mediorum. Ordinata proportionalitas est quando fuerit ut antecedens ad consequens ita antecedens ad consequens, fuerit autem et sicut consequens ad aliud quid ita et consequens ad aliud quid.
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
No Sanskrit
lat Clavius
No Latin
kin 幾何原本
第十八界
有平理之序者。此之前與後。若彼之前與後。而此之後與他率。若彼之後與他率。
甲與乙。若丁與戊。而後乙、與他率丙。若後戊、與他率己。是序也今平推甲與丙。若丁與己也。此與十七界　\\　同‧重宣序義‧以別　\\　後界也(p. 二三○)
證見本卷廿二。
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