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Essay Archive - Proportions of Numbers and Magnitudes
Proportions of Numbers and Magnitudes
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 from a whole, therefore; numbers can be more
accurately compared because there is a standard unit representing one of
something. Numbers allow for measurement and degrees of ordinal position
through which one can better compare quantity. ....
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