|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.|
Next book: Book IX
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