## Proposition 4

 If a cubic number multiplied by a cubic number makes some number, then the product is a cube. Let the cubic number A multiplied by the cubic number B make C. I say that C is cubic. Multiply A by itself to make D. Then D is a cube. IX.3 Since A multiplied by itself makes D, and multiplied by B makes C, therefore A is to B as D is to C. And, since A and B are cubic numbers, therefore A and B are similar solid numbers. Therefore two mean proportional numbers fall between A and B, so that two mean proportional numbers fall between D and C also. VII.17 VIII.19 VIII.8 And D is a cube, therefore C is also a cube. VIII.23 Therefore, if a cubic number multiplied by a cubic number makes some number, then the product is cubic. Q.E.D.
Of course, m3n3 = (mn)3.

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