Bibliotheca Polyglotta

Euclid: Elementa

eng

18. A perturbed proportion arises when, there being three magnitudes and another set equal to them in multitude, as antecedent is to consequent among the first magnitudes, so is antecedent to consequent among the second magnitudes, while, as the consequent is to a third among the first magnitudes, so is a third to the antecedent among the second magnitudes.

lat Clavius

No Latin

kin 幾何原本 p. 230-231

第十九界
有平理之錯者。此數幾何。彼數幾何。此之前與後。若彼之前與後。而此之後與他率。若彼之他率與其前。
甲、乙、丙、數幾何。丁、戊、己、數幾何。其甲與乙。若戊與己。又此之後乙、與他率丙。若彼之他率丁、與前戊。是錯也。今平推甲與丙、若丁與己也。十八、十九、界推法。於十七界　\\　中通論之。故兩題中不再著也。(p. 二三一)
證見本卷廿三。
增。一幾何。有一幾何、相與為比例。卽此幾何。必有彼幾何、相與為比例。而兩比例等。一幾何。有一幾何、相與為比例。卽必有彼幾何、與此幾何為比例。而兩比例等。此例同理。省　\\　曰比例等。
甲幾何。與乙幾何、為比例。卽此幾何丙。亦必有彼幾何、如丁。相與為比例。若甲與乙也。丙幾何。與丁幾何、為比例。卽必有彼幾何、如戊。與此幾何丙、為比例。若丙與丁也。此理推廣無礙。於理有之。不必舉其率也。舉率之理。備見後卷。

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