| Similar solid numbers have to one another the ratio which a cubic number has to a cubic number. | |
| Let A and B be similar solid numbers.
I say that A has to B the ratio which cubic number has to cubic number. | |
| Since A and B are similar solid numbers, therefore two mean proportional numbers C and D fall between A and B. | VIII.19 |
| Take E, F, G, and H, the least numbers of those which have the same ratio with A, C, D, and B, and equal with them in multitude. | VII.33 or VIII.2 |
| Therefore the extremes of them, E and H, are cubes. And E is to H as A is to B, therefore A also has to B the ratio which a cubic number has to a cubic number. | VIII.2,Cor. |
| Therefore, similar solid numbers have to one another the ratio which a cubic number has to a cubic number. | |
| Q.E.D. | |
Book VIII Introduction - Proposition VIII.26 - Book IX Introduction.