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according added addition algebraic quantities amount Answ ANSWER appears application arise arithmetic becomes binomial boards called changed coefficient combinations common denominator compound consequently consisting contained cube root decimal difference digits divided division divisor Edition equal equation evident Exam EXAMPLE expressed Extract factors figure Find the value four fourth fraction given gives greater greatest common measure Hence increase interest inverted known less lesser letters logarithm lowest terms manner means method Multiply negative number of terms observed operation period person population positive proper proportional quadratic equation question quotient raised ratio Reduce relation remainder represent respect resulting Rule shillings side simple solution square root substitute subtracted Suppose Table taken Theor Theorem third units unknown quantities varies whole number
Side 111 - 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.
Side 220 - 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...
Side 46 - 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...
Side 117 - 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.
Side 111 - 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"=^.
Side 78 - The sum of those digits is 5 ; and if 9 be added to the number itself, the digits will be inverted.
Side 153 - Multiply the numerator and denominator of the fraction by such a quantity as will make the denominator a complete power, corresponding to the root...
Side 116 - 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...