← euclid / The Thirteen Books of Euclid’s Elements Volume II / Book VII / Propositions / VII.38 ← Prev Proposition · Commentary Next → [Folio 0348 | p. 342] PROPOSITION 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. A B C D 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. [Folio 0349 | p. 343] Therefore, alternately, the unit D measures the number B the same number of times that C measures A. [VII. 15] Therefore C measures A. Q. E. D. 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