G.336 composite number multiplying — Heath

IX.7

If a composite number by multiplying any number make some number, the product will be solid.

For let the composite number A by multiplying any number B make C;

I say that C is solid.

For, since A is composite,

it will be measured by some number. [G.286]

Let it be measured by D; and, as many times as D measures A, so many units let there be in E.

Since then D measures A according to the units in E,

[G.269]therefore E by multiplying D has made A.

And, since A by multiplying B has made C, and A is the product of D, E,

therefore the product of D, E by multiplying B has made C.

Therefore C is solid, and D, E, B are its sides.

Q. E. D.

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