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Proportions Of Numbers And Magnitudes
Start 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 o .... Middle of Term Paper
... 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 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 former equimultiples alike ex ... |
| Number of Words: 809 |
Approximate Pages: 3 |
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