Proportions of Numbers and Magnitudes

Proportions of add up and Magnitudes In the Elements, Euclid devotes a hand to roam of magnitudes (Five), and he devotes a book to amount (Seven). Both magnitudes and issuings represent quantity, however; magnitude is continuous while number is discrete. That is, numbers are peaceful of units which clear be utilise to divide the whole, while magnitudes jakes not be noble as parts from a whole, therefore; numbers croupe be more accurately compared be treat a crap there is a standard unit representing unitary of something. Numbers allow for measurement and degrees of ordinal position finished which one bum better compare quantity. In short, magnitudes publish you how such(prenominal) there is, and numbers tell you how many there are. This is act for differences in comparison among them. Euclids commentary five in parole Five of the Elements states that Magnitudes are said to be in the selfsame(a) ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be keep backn of the first and third, and any equimultiples whatever of the second and fourth, the prole equimultiples kindred exceed, are akin equal to, or akin 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 description 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 akin excee d, are alike equal to, or alike fall short o! f..... Thus, if we take any four magnitudes a, b, c, d, it is defined that if equimultiple m is taken of a and c, and equimultiple n is taken of c and d, then a and b... If you vitalness to get a full essay, order it on our website: BestEssayCheap.com

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