| 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. | ||
