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Euclid: Elementa
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gre V,27
No Greek
eng
Proposition 27. If the ratio between a first and a second [quantity] is greater thatn that between a third and a fourth, then, alternando, the ratio of the first and the third is also greater than that of the second and the fourth. If a:b>c:d then a:c>b:d.1
1. Translation of the Chinese by Engelfriet, p. 257.
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kin 幾何原本 p. 270
第二十七題
第一與二之比例。大於第三與四之比例。更之。則第一與三之比例。亦大於第二與四之比例。
解曰。一甲與二乙之比例。大於三丙與四丁。題言更之。則一甲與三丙之比例。亦大於二乙與四丁。
論曰。試作戊與乙之比例。若丙與丁。卽甲與乙之比例。大於戊與乙。而甲幾何大於戊。本篇　\\　十則甲與丙之比例。大於戊於丙也。本篇　\\　八夫戊與乙之比例。旣若丙與丁。更之。則戊與丙之比例。亦若乙與丁。本篇　\\　十六而甲與丙之比例。大於乙與丁矣。
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