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algebraic quantities Answ Answer arithmetic means arithmetic series binomial quadratic surd Binomial Theorem CHAP coefficient common denominator common difference compound interest consequently cube root decimal digits divide the number dividend divisor equal Exam Example expressed Extract the square Find the sum Find the value four quantities fraction required geometric progression geometric series given number greatest common measure improper fraction infinitum inversely irrational irreducible surd last term least common multiple lesser number lowest terms means method of finding Multiply nth root number of permutations number of terms numerator and denominator odd number proper fraction quadratic equation quan question quotient radical sign rational quantity Reduce remainder REVERSION OF SERIES Rule shewn side solution square root substitute subtracted Theor things taken three and three three numbers transposition unknown quantities whole number x=the
Page 123 - 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 232 - 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 58 - 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 129 - 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 123 - 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 90 - The sum of those digits is 5 ; and if 9 be added to the number itself, the digits will be inverted.
Page 165 - 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 128 - 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...