Bibliotheca Polyglotta

Euclid: Elementa

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eng

Proposition 30. If the ratio of a first and a second [quantity] together to the second is greater than that of a third and a fourth together to the fourth, then, invertendo, the ratio of the first and the second together to the first is lesser than that of the third and the fourth together to the third. If (a+b):b>(c+d):d then (a+b):a<(c+d):c.¹

1. Translation of the Chinese by Engelfriet, p. 258.

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lat Clavius

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kin 幾何原本 p. 271-272

第三十題
(p. 二七二)第一合第二、與二之比例。大於第三合第四、與四之比例。轉之。則第一合第二、與一之比例。小於第三合第四、與三之比例。
解曰。甲丙與乙丙之比例。大於丁己與戊己。題言轉之。則甲丙與甲乙之比例。小於丁己與丁戊。
論曰。甲丙與乙丙之比例。旣大於丁己與戊己。分之。卽甲乙與乙丙之比例。亦大於丁戊與戊己也。本篇　\\　廿九又反之。乙丙與甲乙之比例。小於戊己與丁戊矣。本　\\　篇廿　\\　六又合之。甲丙與甲乙之比例。亦小於丁己與丁戊也。本篇　\\　廿八

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