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PROPOSITION 7.

If there be as many numbers as we please in continued proportion, and the first measure the last, it will measure the second also.

Let there be as many numbers as we please, A, B, C, D, in continued proportion; and let A measure D; I say that A also measures B.

For, if A does not measure B, neither will any other of the numbers measure any other. [VIII. 6]

But A measures D.

Therefore A also measures B. Q. E. D.

Euclid. Euclid's Elements. Sir Thomas Little Heath. New York. Dover. 1956.

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