Proof
If and , then for any equimultiples the same
inequality test holds for as for , and that same test
holds for as for ; hence by transitivity of the
inequality test, the test holds for versus .
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Required by (dependents) (6)
- 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…
- V.16Proposition V.16If four magnitudes be proportional, they will also be proportional alternately.
- VI.2Proposition VI.2If a straight line be drawn parallel to one of the sides of a triangle, it will cut the sides of the triangle…
- VI.8Proposition VI.8If in a right-angled triangle a perpendicular be drawn from the right angle to the base, the triangles adjoining the…
- VI.14Proposition VI.14In equal and equiangular parallelograms the sides about the equal angles are reciprocally proportional; and equiangular…
- VI.21Proposition VI.21Figures which are similar to the same rectilineal figure are also similar to one another.
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