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Proportions Of Numbers And Magnitudes
Beginning of 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 par .... Middle of paper
.... magnitudes in the same ratio are proportional. Thus, we can use the
following algebraic proportion to represent definition 5.5:
(m)a : (n)b :: (m)c : (n)d.
However, it is necessary to be more specific because of the way in which the
definition was worded with the phrase "the former equimultiples alike exceed,
are alike equal to, or alike fall short of….". Thus, if we take any four
magnitudes a, b, c, d, it is defined that if equimultip ....
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Number of words: 809
Number of pages: 3 (approx. 250 words per double-spaced page)
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