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Essay text:
Numbers allow for measurement and degrees of ordinal position
through which one can better compare quantity. In short, magnitudes tell you
how much there is, and numbers tell you how many there are. This is cause for
differences in comparison among them.
Euclid's definition five in Book Five of the Elements states that " 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 be 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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