## A Treatise on Algebra, in Practice and Theory: With Notes and Illustrations; Containing a Variety of Particulars Relating to the Discoveries and Improvements that Have Been Made in this Branch of Analysis |

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according added algebra answer appears arise arithmetical become binomial called coefficients common compound consequently consisting contained continued fraction denominator denoted determined difference divided division divisor equal equation evident EXAMPLES expression extracting factors farther figures find the value former formula fourth fraction geometrical give Given greater greatest Hence infinite series integral kind known least less letters logarithms manner means mentioned method multiplied nature negative Note observed obtained operation particular performance positive PRACTICE problems progression proportion proposed question quotient rational readily reduced relation remaining render represented Required the sum required to divide required to find resolved respectively result rule side simple solution square number square root substituting subtracted successive supposed surd taken taking third tion unknown quantity usually value of x Whence whole numbers

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Página 39 - 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.

Página 23 - 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.

Página 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...

Página 137 - 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.

Página 3 - Q/~\—C = equal to, the sign of equality; signifying that the quantities between which it is placed are equal to each other. Thus...

Página 119 - A person bought a chaise, horse, and harness for 60?.; the horse came to twice the price of the harness, and the chaise to twice the price of the horse and harness ; what did he give for each ? Ans. 13/.

Página 33 - 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.

Página 360 - N .•. def. (2), x— x1 is the logarithm of that is to say, The logarithm of a fraction, or of the quotient of two numbers, is equal to the logarithm of the numerator minus the logarithm of the denominator. III. Raise both members of equation (1) to the power of n. N" =a

Página 123 - 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 would it take each person to perform the same work alone ? Ans.

Página 49 - ... 2. Subtract the square of the root, thus found from the first term, and bring down the two next terms to the remainder for a dividend.