## An introduction to algebra. To which is added an appendix containing a synopsis on variable quantities by S. Maynard |

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Algebra answer arithmetical mean arithmetical series base binomial coefficient common denominator compound quantity consequently constant quantity cube root cubic equation decimal denoted determine diff dividend division divisor equal EXAMPLES FOR PRACTICE expression figure find the difference find the square find the sum find the value find three find two numbers geometrical mean geometrical progression geometrical series give given number greatest common measure Hence improper fraction infinite series last term latter less logarithms method multiplied natural numbers negative nth root number of terms number required orders of differences perpendicular plane triangle PROBLEM quadratic equation question quotient rational remaining Required the sum required to convert required to divide required to find required to reduce result right-angled rule second term simple form square number square root substituted subtracted surd third tion unknown quantity varies directly Whence whole numbers

### Popular passages

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 18 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.

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.

Page 2 - It denotes that the quantities between which it is placed are equal to each other. Thus, o=3, denotes that the quantity represented by a is equal to 3.