# A Treatise on the Elements of Algebra

R. Watts: and sold by T. Cadell, Strand, London; Deightons, Nicholsons, and Barrett, Cambridge; and Parker, Oxford., 1821 - Algebra - 227 pages
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### Contents

 CHAP I 5 V 12 VII 19 CHAP II 27 XI 38 On the Involution and Evolution of Numbers 44 XV 56 CHAP IV 64
 103 132 CHAP VII 142 On geometrical progression 149 On the summation of an infinite series of fractions 157 On the reduction of surds 162 CHAP IX 177 On the method of finding the approximate ratio 190 On the comparison and reversion of series 197

### Popular passages

Page 107 - Of the four terms of which every proportion consists, the first and last terms are called the extremes, and the second and third the means, of that proportion.
Page 118 - It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference. Ans. 10 and 14.
Page 216 - Elements of General History, Ancient and Modern. To which are added, a Comparative View of Ancient and Modern Geography, and a Table of Chronology. By ALEXANDER FRASER TYTLER, Lord Woodhouselee, formerly Professor of History in the University of Edinburgh. New Edition, with the History continued. With two large Maps, etc. 3s. 6d. Watts...
Page 42 - Thus, in the case of 53361 (whose square root is a number consisting of three figures) ; since the square of the figure standing in the hundred's place cannot be found either in the last period...
Page 113 - Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 107 - If four quantities are proportional, the quotient of the first divided by the second, is equal to the quotient of the third divided by the fourth. (Alg. 364.) Thus, if a : b : : c : d, then |=|, and"=^.
Page 74 - The sum of those digits is 5 ; and if 9 be added to the number itself, the digits will be inverted.
Page 149 - Multiply the numerator and denominator of the fraction by such a quantity as will make the denominator a complete power, corresponding to the root...
Page 112 - IF magnitudes, taken separately, be proportionals, they shall also be proportionals when taken jointly, that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together to the fourth...
Page 88 - A merchant bought cloth for which he paid £33 15s., which he sold again at £2 8s. per piece, and gained by the bargain as much as one piece cost him : how many pieces did he buy ? Ans.