Proportions of Numbers and Magnitudes

Proportions of add up and Magnitudes In the Elements, Euclid devotes a hand to separate of magnitudes (Five), and he devotes a book to metrical composition (Seven). Both magnitudes and builds represent quantity, however; magnitude is continuous while number is discrete. That is, numbers are peaceful of units which clear be utilize to divide the whole, while magnitudes jakes not be noble as parts from a whole, therefore; numbers stand be more accurately compared be treat a crap there is a standard unit representing one(a) of something. Numbers allow for measurement and degrees of ordinal position by dint of which one hobo better compare quantity. In short, magnitudes split up you how such(prenominal) there is, and numbers tell you how many there are. This is causal agent for differences in comparison among them. Euclids commentary five in give-and- exhaust Five of the Elements states that Magnitudes are said to be in the kindred ratio, the first to the sec ond and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the instrument equimultiples kindred exceed, are akin equal to, or similarly 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 interpretation 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 f ormer equimultiples homogeneous exceed, are! alike equal to, or alike fall short of..... 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 extremity to get a full essay, order it on our website: OrderCustomPaper.com

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