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Proposition 7

If a composite number multiplied by any number makes some number, then the product is solid.
Let the composite number A multiplied by any number B make C. I say that C is solid.
| Since A is composite, it is measured by some number D. Let there be as many units in E as times that D measures A | VII.Def.13
Since D measures A according to the units in E, therefore E multiplied by D makes A. And, since A multiplied by B makes C, and A is the product of D and E, therefore the product of D and E multiplied by B makes C. | VII.Def.15
Therefore C is solid, and D, E, and B are its sides.
Therefore, if a composite number multiplied by any number makes some number, then the product is solid.
Q.E.D.

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(Forthcoming)

Book IX Introduction - Proposition IX.6 - Proposition IX.8.

© 1996
D.E.Joyce
Clark University