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Proportions Of Numbers And Magnitudes
Part one of term paper
In the Elements, Euclid devotes a book to magnitudes (Five), and he devotes a
book to numbers (Seven). Both magnitudes and numbers represent quantity,
however; magnitude is continuous while number is discrete. That is, numbers are
composed of units which can be used to divide the whole, while magnitudes can
not be distinguished as parts fr ...
Part two of term paper ... 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." From ...
Word count: 809 | Approximate pages: 3
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