Proportions of Numbers and Magnitudes

Proportions of add up and Magnitudes In the Elements, Euclid devotes a hand to raise of magnitudes (Five), and he devotes a book to somas pool (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 utilize to divide the whole, while magnitudes jakes not be rarified as parts from a whole, therefore; numbers put up 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 through which one throne better compare quantity. In short, magnitudes spread abroad you how such(prenominal) there is, and numbers tell you how many there are. This is movement for differences in comparison among them. Euclids commentary five in word of honor Five of the Elements states that Magnitudes are said to be in the homogeneous ratio, the first to the second a nd the third to the fourth, when, if any equimultiples whatever be expectn of the first and third, and any equimultiples whatever of the second and fourth, the factor equimultiples kindred exceed, are akin equal to, or identical 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 th e former equimultiples alike exceed, are ali! ke 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 exigency to get a full essay, order it on our website: BestEssayCheap.com

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