Lecture on the History of Mathematics

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"Gazette Office," A. Waddill, printer, 1841 - Mathematics - 35 pages
 

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Page 15 - Beautiful and dear Lilavati, whose eyes, are like a fawn's ! tell me what is the number resulting from one hundred and thirty-five taken into twelve? if thou be skilled in multiplication by whole or by parts, whether by sub-division of form or separation of digits. Tell me auspicious woman, what is the quotient of the product divided by the same multiplier.
Page 17 - Theorem — The square described on the hypotenuse of a right angled triangle is equivalent to the sum of the squares described on the two legs.
Page 22 - Indivisibles, which was published in 1635, he considered a line as composed of an infinite number of points, a surface of an infinite number of lines, and a solid of an infinite number of surfaces ; and he...
Page 22 - The rule for summing an infinite series of terms in arithmetical progression had been long known, and the application of it to find the area of a triangle, according to the method of indivisibles, was a matter of no difficulty. The next step was, supposing a series of lines in arithmetical progression, and squares to be described on each of them, to find what ratio the sum of all these squares bears to the greatest square, taken as...
Page 22 - To find the approximate value of the ratio of the circumference to the diameter of a circle.
Page 30 - It was thus prepared for the step which was about to be taken by Descartes, and which forms one of the most important epochas in the history of the mathematical sciences. This was the application of the algebraic analysis, to define the nature, and investigate the properties, of curve lines, and, consequently, to represent the notion of variable quantity. It...
Page 23 - II est impropre si 1'on veut square multiplied by the number of terms. Hence the cone is one third of a cylinder of the same base and altitude, and similar proof may be given as to the ratios of other solids. 14. This bolder geometry was now very generally applied in difficult investigations. A proof was Pr0b!emof given in the celebrated problems relative to the thc c>Tlold...
Page 34 - ... &c., of curves thus formed, vary according to a regular law depending on the equation of the curve, he deduces from this equation the velocities with which these quantities are generated ; and by the rules of infinite series he obtains the ultimate value of the quantity required.
Page 26 - Leonardo has been represented as flourishing in the end of the fourteenth century, instead of the very beginning of the thirteenth. It appears by an extract from his manuscript, published by the above author, that his knowledge of Algebra extended as far as quadratic equations. The language was very imperfect, corresponding to the infancy of the science ; the quantities and the operations being expressed in words, with the help only of a few abbreviations. The rule for resolving quadratics by completing...
Page 26 - ... minus gives minus, but minus into minus gives plus. Thus the first appearance of Algebra is merely that of a system of short-hand writing, or an abbreviation of common language, applied to the solution of arithmetical problems. It was a contrivance merely to save trouble ; and yet to this contrivance we are indebted for the most philosophical and refined art which men have yet employed for the expression of their thoughts. This scientific language, therefore, like those in common use, has grown...

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