Elements of Algebra |
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affected algebraic quantities arithmetical arrangements binomial co-efficient common factor consequently contain continued fraction 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 logarithm manner method monomial multiplied negative nth root number of terms obtain operations perfect square positive roots preceding problem proposed equation quotient reduced remainder required root result second degree second member second term square root substituted subtract suppose take the equation tens third tion transformation twice the product units unity unknown quantity verified vulgar fraction whence whole number
Popular passages
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 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 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 218 - Take three times the square of the root just found for a trial divisor, and see how often it is contained in the dividend, and place the quotient for a second figure of the root. Then cube the figures of the root thus found, and if their cube...
Page 214 - ... plus three times the product of the square of the tens by the units, plus three times the tens by the square of the units, plus the cube of the units.
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 1 5| 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 ; and read, A is to B as C to D.
Page 269 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
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.