An Introduction to Algebra: With Notes and Observations; Designed for the Use of Schools and Places of Public Education. To which is Added an Appendix, on the Application of Algebra to Geometry
Collins and Hannay, 1834 - 312 σελίδες
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according added Algebra answer appears applied arise arithmetical assumed base become called changed coefficient common compound consequently contains continued cube root decimal denominator denoted determined difference divided division divisor equa equal equation evident EXAMPLES expression extracting factors figure find the sum find the value former formula four fourth fraction geometrical give Given greater greatest Hence integral kind known last term latter least less logarithms manner means method multiplied necessary negative observed obtained operation positive PROBLEM proper proportion proposed quadratic question quotient rational reduced remain Required the sum required to divide required to find resolved respectively result rule side simple solution square number square root substituted subtracted surd taken taking third tion triangle unknown quantity usual value of x Whence whole numbers
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.