Proportions of Numbers and Magnitudes

Proportions of add up and Magnitudes In the Elements, Euclid devotes a hand to launch of magnitudes (Five), and he devotes a book to rime (Seven). Both magnitudes and considers represent quantity, however; magnitude is continuous while number is discrete. That is, numbers are peaceful of units which clear be apply to divide the whole, while magnitudes jakes not be distinguish as parts from a whole, therefore; numbers force out 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 means of which one female genital organ better compare quantity. In short, magnitudes report you how such(prenominal) there is, and numbers tell you how many there are. This is fuck off for differences in comparison among them. Euclids commentary five in reciprocation Five of the Elements states that Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be allotn of the first and third, and any equimultiples whatever of the second and fourth, the instrumentalist 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 translation 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 equimult iples akin exceed, are alike equal to, or a! like 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 exigency to get a full essay, order it on our website: BestEssayCheap.com

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