G.294 number part whatever — Heath

VII.38

If a number have any part whatever, it will be measured by a number called by the same name as the part.

For let the number A have any part whatever, B, and let C be a number called by the same name as the part B;

I say that C measures A.

For, since B is a part of A called by the same name as C, and the unit D is also a part of C called by the same name as it,

therefore, whatever part the unit D is of the number C, the same part is B of A also;

therefore the unit D measures the number C the same number of times that B measures A.

Therefore, alternately, the unit D measures the number B the same number of times that C measures A. [G.268]

Therefore C measures A.

Q. E. D.

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G.295