|If two numbers measure any number, then the least number measured by them also measures the same.|
|Let the two numbers A and B measure any number CD, and let E be the least that they measure.
I say that E also measures CD.
|If E does not measure CD, let E, measuring DF, leave CF less than itself.
Now, since A and B measure E, and E measures DF, therefore A and B also measure DF. But they also measure the whole CD, therefore they measure the remainder CF which is less than E, which is impossible.
|Therefore E cannot fail to measure CD. Therefore it measures it.|
|Therefore, if two numbers measure any number, then the least number measured by them also measures the same.|
Next proposition: VII.36
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