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Definition 1
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A magnitude is a part of a magnitude, the less of the greater, when
it measures the greater.
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Definition 2
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The greater is a multiple of the less when it is measured by the
less.
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Definition 3
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A ratio is a sort of relation
in respect of size between two magnitudes of the same kind.
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Definition 4
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Magnitudes are said to have a
ratio to one another which can, when multiplied, exceed one another.
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Definition 5
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Magnitudes are said to be in
the same ratio, the first to the second and the third to the fourth,
when, if any equimultiples whatever are taken of the first and third, and
any equimultiples whatever of the second and fourth, the former equimultiples
alike exceed, are alike equal to, or alike fall short of, the latter equimultiples
respectively taken in corresponding order.
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Definition 6
Let magnitudes which have the
same ratio be called proportional.