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Proportions Of Numbers And Magnitudes
Beginning of essay
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 essay
....ken of c and d, then a and b are in same ratio with c
and d, that is, a : b :: c : d, only if:
(m)a > (n)b and (m)c > (n)d, or
(m)a = (n)b and (m)c = (n)d, or
(m)a < (n)b and (m)c < (n)d.
Though, because magnitudes are continuous quantities, and an exact measurement
of magnitudes is impossible, it is not possible to say by how much one exceeds
the other, nor is it possible to determine if a > b by the same amount that c >
d.
Now, it is important to realize that taking equimultip.... |
| Number of words: 809 |
Approximate pages: 3 |
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