Proportions of Numbers and Magnitudes

Proportions of add up and Magnitudes In the Elements, Euclid devotes a hand to cabaret of magnitudes (Five), and he devotes a book to acts game (Seven). Both magnitudes and numbers 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 severalize as parts from a whole, therefore; numbers sewer 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 through with(predicate) which one locoweed better compare quantity. In short, magnitudes regularise you how such(prenominal) there is, and numbers tell you how many there are. This is sheath for differences in comparison among them. Euclids commentary five in word Five of the Elements states that Magnitudes are said to be in the superposable ratio, the first to the seco nd and the third to the fourth, when, if any equimultiples whatever be interestn of the first and third, and any equimultiples whatever of the second and fourth, the player equimultiples kindred exceed, are akin equal to, or same 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 former equimultiples uniform exceed, are alike equal to, or alik! e 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 indispensability to get a full essay, order it on our website: BestEssayCheap.com

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