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according added addition Algebra angle answer applied approximate arise arithmetical base changed coefficient common compound consequently constant contains continued cube root decimal denoted determine difference divided division divisor Edition equal equation evident EXAMPLES expression extracting factors figure find the sum find the value former four fourth fraction geometrical give given greater greatest Hence integral kind known latter least less logarithms manner means method multiplied nature negative observed obtained operation performed perpendicular person positive PRACTICE PROBLEM proper proportion quadratic question quotient rational reduced remaining Required the sum required to divide required to find resolved result rule second term side simple solution sought square number square root substituted subtract surd taken taking third tion triangle unknown quantity usual value of x vary Whence whole numbers
Page 36 - 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 40 - ... 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 117 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the less, is equal to 12 ? Ans.
Page 26 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Page 48 - ... 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 116 - Divide the number 24 into two such parts, that their product shall be to the sum of their squares, as 3 to 10.
Page 76 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.
Page 82 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.