Reseña del editor
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1807 edition. Excerpt: ...is applied immediatel!/ to solving equations of the second degree, and therefore deserves great attention. The general rule, just given, can be followed, when an exact root is required; but when the quantity is such, that an exact root cannot be obtained, but only something near it, we must have recourse to the binomial rule of Newton, whose method for raising a quantity to an integral exponent, may be ap plied in the same way to fractionary exponents, so 5--m a. TT--1: r that ( + a)--x-axu H. a x n n 2 m 2_i a_2 -3-f..--.. a3 x + &C. n 2 3 Let m zz 1, and n = 2; upon performing the ope i a a ration, we shall have (+ai=T+ 1 1 2 xT 8 T a3 5a J-&c. 16 123 This series would extend ad infinitum. In order to obtain a proximate root of x + a, we should simply take the first terms of the series, with this caution, that this means is never to be used, but when the terms of the series diminish continually; and it is evident, that the proximate value will be so much the more exact as the series decreases more rapidly, since then the terms that will be thrown away, will be trifling, and may be considered as nothing. It is-very perceptible, that, if the terms of a series increased continually, it would not be possible to gain any thing near the value of that series. Those series which continually decrease, are called tonverging ones; and those that continually increase, are called diverging ones. The Binomial Rule can be readily applied to numbers, to extract any of their roots; in order to do it, the number should be divided into two parts, the first of which should be always greater than the second, and an exact power of the required root; which can always be done by making the second part positive or negative; then...
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