内容 第10卷 · 284
命题 Propositio X.7
Incommensurable magnitudes have not to one another the ratio which a number has to a number.
不可通约的量之间不具有一个数与另一个数之比。
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分步证明Step-by-step proof
1 / 4Let A, B be incommensurable magnitudes; I say that A has not to B the ratio which a number has to a number.
设A、B为不可通约的量。
For, if A has to B the ratio which a number has to a number, A will be commensurable with B.
假设A与B之比等于一个数与另一个数之比。
[X. 6] But it is not; therefore A has not to B the ratio which a number has to a number.
根据X.6，则A与B可通约。
但A与B不可通约，矛盾，故假设不成立。
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