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Đây là cuốn sách tiếng anh trong bộ sưu tập "Mathematics Olympiads and Problem Solving Ebooks Collection",là loại sách giải các bài toán đố,các dạng toán học, logic,tư duy toán học.Rất thích hợp cho những người đam mê toán học và suy luận logic.
[...]... solid as the root, the lower-order terms arethe cube the sixth power the ninth power or the solid the square of the solid the cube of the solid 15 The square, the fourth power, the eighth power and others that are produced in like manner by squaring a power are powers of the simple mean The others are powers of a multiple mean 59 16 The fixed magnitude with which the other terms are compared is the homogeneous... is the root that is being sought, the last is that which is one step below the power on the scale and is customarily called the epanaphora II Any term lower than the power is the complement58 of [another] lower term if the product of the two is [of the same rank as] the power Thus a coefficient is the complement of the term that it supports 12 Beginning with a length as the root, the steps below the. .. attentive to these [rules} 2 Magnitudes that ascend or descend proportionally in keeping with their nature from one kind to another are called scalar terms 3 The first of the scalar magnitudes is the side or root 16 [Then follow:} 2 3 4 5 6 7 8 9 The square The cube The square-square The square-cube The cubo-cube The square-square-cube The square-cubo-cube The cu bo-cu bo-cu be and so on, naming the others... INTRODUCTION 15 15 If there are three or four terms such that the product of the extremes is equal to the square of the mean or the product of the means, they are proportionals Conversely, 16 If there are three or four terms and the first is to the second as the second or third is to the last, the product of the extremes will be equal to the product of the means Thus a proportion may be said to be that from... of the use Viete makes of it On Adrastos himself-he lived in Aphrodias in the first half of the second century-see George Sarton, Introduction to the History of Science (Baltimore, 1927), vol I, p 271 16 THE ANALYTIC ART If one magnitude is divided 15 by another, [the quotient] is heterogeneous to the former [i.e., to the dividend] Much of the fogginess and obscurity of the old analysts is due to their... 28 THE ANALYTIC ART form prescribed by the art comformably to the laws 47 Kina 7T'lX/lTOS, mO aVTa, KaOi)>-.ov 7T'pWTO/l 48 Such [theorems], although they are demonstrated by and grounded in zetetics, are still subject to the rules of synthesis, which is rated the most rational method of demonstration 49 If necessary, they are confirmed by it, this being a great miracle of the inventive art So the. .. by the former or, otherwise, that the result is A by B [The magnitudes are stated] simply if A and B are simple lengths or breadths, but if they are higher up on the scale or if, by their nature, they correspond to higher terms, it is well to give them the proper designations of the scalar terms or of those of corresponding nature, as, say, A2 times B or A2 times BP or 8', and so on for the others The. .. I 'art sont soumis aux lois " And Smith reads it this way: "When the zetesis has been completed, the analyst turns from hypothesis to thesis and presents theorems of his own finding, theorems that obey the regulations of the art and are subject to the laws " 4I1 AO)'lKWTfCP1/ 50 1591,1624, and 1631 have eaque; 1635 and 1646 have atque INTRODUCTION 29 most especially to the general ordering of the art. .. the others The operation is no different if the magnitudes to be multiplied or either of them consist of two or more terms, since the whole is equal to [the sum of] its parts and, therefore, the [sum of the] products of the parts of any magnitude is equal to the product of the whole If a positive term of one quantity is multiplied by a positive term of 27These two Greek terms have been variously translated... below the power are those given in the scale 13 Beginning with a plane as the root, the lower-order terms arethe square the fourth power the sixth power or the plane the square of the plane the cube of the plane and so on in regular order S4 radix vel potestas Viete uses the word radix in two senses: In some places he uses it as a synonym for latus the first power; in others (for examples, see paragraphs . the formulae n(n - l)(n - 2)(n - 3) n-4 • 4a + cos a Sm - 1·2·3·4 • n I' n(n - l)(n - 2) n 3 • 3 Sm nO' = n cos - a sma -. - a sma - cos - a Sm a 1 . 2 . 3 n(n - l)(n - 2)(n - 3)(n - 4) n-5 . 5 + - COS a Sm 0&apos ;- 1·2·3·4·5 Beyond these rather general contributions