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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 .... Middle of Paper .... 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 exceed, are alike equal to, or alike fall short of….". .... 809 words | 3 pages Subscription Length Price Join 30 days membership (recurring) $19.95 90 days membership (recurring) $39.95 180 days membership (non-recurring) $69.95