Proof
By V.8 and V.13: if , then . Combined with (the hypothesis), V.13 gives , whence by V.10.
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Depends on (3)
- V.8Proposition V.8Of unequal magnitudes the greater has to the same a greater ratio than the less has, and the same has to the less a…
- V.10Proposition V.10Of magnitudes which have a ratio to the same, that which has a greater ratio is greater; and that to which the same has…
- V.13Proposition V.13If a first magnitude have to a second the same ratio as a third to a fourth, and the third have to the fourth a greater…
Required by (dependents) (3)
- V.20Proposition V.20If there be three magnitudes, and others equal to them in multitude, which taken two and two are in the same ratio, and…
- V.21Proposition V.21If there be three magnitudes, and others equal to them in multitude, which taken two and two together are in the same…
- V.25Proposition V.25If four magnitudes be proportional, the greatest and least are greater than the remaining two.
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