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 ma ....
Middle of paper
.... 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 this it follows
that 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 ....
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Word count: 809
Page count: 3 (approximately 250 words per page)
