## 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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4th power algebra arise arithmetical arithmetical mean arithmetical series binomial coefficients consequently continued fraction cube root cubic equation decimal denoted determined Diophantus divisor equa equal roots expression factors farther find the least find the square find the sum find the value find three numbers find two numbers former formula four roots frac geometrical geometrical series given equation given number Hence infinite series integral kind last term latter least values logarithms method multiplied negative nth root number of terms º º observed proportion proposed equation quadratic equation question quotient rational readily remaining Required the sum required to divide required to find required to reduce resolved result rule scale of relation simple fractions square number square root substituting subtracted surd three roots tion unknown quantity Whence whole numbers

### Popular passages

Page 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.

Page 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.

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 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.

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

Page 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/.

Page 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.

Page 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

Page 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.

Page 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.