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affected algebraic quantities approximating fractions arithmetical arranged binomial binomial formula co-efficient common factor consequently contain continued fraction contrary sign cube root deduce denominator denote different powers divide dividend division entire number enunciation equa equal equation becomes example exponent extract the square figure Find the greatest formula fourth given number gives greater greatest common divisor Hence last term least common multiple less logarithm manner method monomial multiplied necessary negative nth power nth root number of terms obtain operation perfect square positive numbers positive roots preceding principal letter principle problem proposed equation proposed polynomials quotient rational reduced remainder resolve result rule second degree second member second term square root subtract suppose suppressed take the equation tion transformed equation transposing unity unknown quantity whence whole number
Page 185 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 148 - B, departed from different places at the same time, and travelled towards each other. On meeting, it appeared that A had travelled 18 miles more than B ; and that A could have gone B's journey in 15| days, but B would have been 28 days in performing A's journey. How far did each travel ? Ans.
Page 183 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus, A : B : : C : D.
Page 127 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 112 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 190 - That is, the last term of a geometrical progression is equal to the first term multiplied by the ratio raised to a power whose exponent is one less than the number of terms.
Page 92 - If A and B together can perform a piece of work in 8 days, A and c together in 9 days, and B and c in 10 days, how many days will it take each person to perform the same work alone.
Page 115 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 124 - These expressions may sometimes be simplified, upon the principle that, the square root of the product of two or more factors is equal to the product of the square roots of these factors ; or, in algebraic language, Vabcd . . . = Va.
Page 91 - A person bought a chaise, horse, and harness, for £60 ; the horse came to twice the price of the harness, and the chaise to twice the price of the horse and harness. What did he give for each ? ^ £13 6s.