|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.|
Perhaps Euclid takes extra steps that we would miss because he sees "d measures a a number e times" as saying something different from the product of d and e equals a."
Next proposition: IX.8