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a-Ha Algebra answer arise arithmetical mean arithmetical series binomial coefficient consequently cube root cubic equation decimal denominator denoted determined division divisor equa equal EXAMPLES FOR PRACTICE expression factors find the root find the square find the sum find the value find two numbers former formula four roots fraction geometrical give given equation given number greater greatest common measure Hence improper fraction infinite series integral last term latter logarithms method multiplied negative nth root number of terms observed perpendicular plane triangle PROBLEM proportion quadratic equation quadratic surd question quotient ratic rational remain Required the product Required the sum required to divide required to find required to reduce resolved result rule second term side simple form square number square root substituted subtracted taken third tion transposition unknown quantity Whence whole numbers
Page 45 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Page 48 - ... be the power required. Or, multiply the quantity into itself as many times, less one, as is denoted by the index of the power, and the last product will be tJie answer.
Page 124 - 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 123 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Page 95 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 55 - ... and the quotient will be the next term Of the root. Involve the whole of the root, thus found, to its proper power, which subtract from the given quantity, and divide the first term of the remainder by the same divisor as before; and proceed in this manner till the whole is finished.* EXAMPLES.
Page 139 - It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference. Ans. 10 and 14.
Page 95 - When three magnitudes, a, b, c, have the relation of a: c : : a — b : b — c ; that is, the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.