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. In short, magnitudes tell you how much there is, and numbers tell you how many there are. This is cause for differences in comparison among them. Euclid's definition five in Book Five of the Elements states that " Magnitudes are said to be in the same ratio, th....

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