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affected algebraic quantities arithmetical arithmetical means arrangements binomial cents co-efficient common difference common factor consequently contain contrary signs cube root decimal deduce denominator denote divide dividend division double product entire number enunciation equa equal equation becomes equation involving example exponent expression extract the square figure find the square find the values formula fourth fraction given number gives greater greatest common divisor greyhound Hence inequality irreducible fraction last term least common multiple less letters taken logarithm manner monomial multiplied negative nth root number of terms obtain operations perfect square permutations positive preceding problem progression proportion proposed equation proposed number quotient reduced remainder required root result satisfy second degree second member second term square root substituting subtract suppose take the equation tens third tion transformation transposing units unity unknown quantity verified whence whole number
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 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 174 - It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference.
Page 28 - Multiply each term of the multiplicand by each term of the multiplier, and add the partial products.
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 ; and read, A is to B as C to D.
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 228 - Divide the first term of the remainder by three times the square of the root already found, and write the quotient for the next term of the root.
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 116 - ... brought down, there is no remainder, the proposed number is a perfect square. But if there is a remainder, you have only found the root of the greatest perfect square contained in the given number, or the entire part of the root sought. For example, if it were required to extract the square root of...