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Euclid: Elementa
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gre V,29
No Greek
eng
Proposition 29. If the ratiio of a first and second [quantity] together to the second is greater than that of a third and a fouth, then the ratio of the first and the second is also greater than that of the third and the fourth. If (a+b):b>(c+d):d then a:b>c:d.1
1. Translation of the Chinese by Engelfriet, p. 258.
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kin 幾何原本 p. 271
第二十九題
第一合第二、與二之比例。大於第三合第四、與四之比例。分之。則第一與二之比例。亦大於第三與四之比例。
解曰。甲丙與乙丙之比例。大於丁己與戊己。題言分之。則甲乙與乙丙之比例。亦大於丁戊與戊己。
論曰。試作庚丙與乙丙之比例。若丁己與戊己。卽甲丙與乙丙之比例。亦大於庚丙與乙丙。而甲丙幾何大於庚丙矣。本篇　\\　十此二率者。每減一同用之乙丙。卽甲乙亦大與庚乙。而甲乙與乙丙之比例。大於庚乙與乙丙也。本篇　\\　八夫庚丙與乙丙之比例。旣若丁己與戊己。分之。則庚乙與乙丙之比例。亦若丁戊與戊己也。本篇　\\　十七而甲乙與乙丙之比例。大於丁戊與戊己矣。
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