An elementary treatise on algebra, theoretical and practical
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added addition admit algebraic already amount annuity appears application arithmetical assumed becomes binomial called changed coefficients combinations common completing compound consequently consist containing continually cube cx² denominator determined difference Divide division divisor equal equation evidently EXAMPLES exponent expression factors find the values former four fourth fraction Given gives happen hence increased infinite integral interest known leading least less letters logarithms manner means measure method multiplied negative obtained operation positive possible preceding present value probability PROBLEM progression proportion proposed quadratic QUESTION quotient rational Reduce remainder represent Required the sum respectively result root rule side simple solutions square square root substituting subtracting successively Suppose taken theorem third trial unknown quantity values of x whence
Page 90 - Ratio is the relation which one quantity bears to another of the same kind, the comparison being made by considering what multiple, part, or parts, one quantity is of the other.
Page 149 - Til., and found that if he had bought 6 more for the same money, he would have paid 1 /. less for each. How many did he buy, and what was the price of each ? Ans.
Page 48 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend. 5. Double the whole root already found for a new divisor, and continue the operation as before, until all the periods are brought down. NOTE.
Page 77 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes §; but the denominator being doubled, and the numerator increased by 2, the value becomes f?
Page 174 - It is required to find three numbers in geometrical progression, such that their sum shall be 14, and the sum of their squares 84. Ans. 2, 4, and 8. 8. There are four numbers in geometrical progression...
Page 150 - The plate of a looking-glass is 18 inches by 12, and it is to be surrounded by a plain frame of uniform width/ having a surface equal to that of the glass.
Page 66 - What part of the distance will each have travelled when they meet ? Ans. One 45 miles, and the other 105. 12. Divide the number 60 into two such parts, that their product may be equal to three times the square of the less ? Ans. The parts are 15 and 45. 13. Divide the number 45 into two parts, such that their product may be equal to the greater minus the square of the less. Ans. The parts are ff and 2f|514.
Page 106 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?
Page 39 - Multiply the logarithm of the number given, by the index of the power to which the quantity is to be raised ; the product will be the logarithm of the power sought But in raising the powers of any decimal fraction, it must...
Page 92 - If four quantities be in arithmetical proportion, the sum of the extremes is equal to the sum of the means.