## The Elements of Algebra: Designed for the Use of Common Schools: Also, Serving as an Introduction to the "Treatise on Algebra" |

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2abc added algebraic algebraic quantities antecedent arithmetical progression becomes change the signs cleared of fractions coefficient common denominator consequently cube root denote difference digits Divide the number dividend divisor English English language equal EXAMPLES exponent expression Extracting the square fifth root Find a number find the values Find two numbers find x formula fourth geometrical progression Given gives Hence imaginary inequality letters lowest terms mixed quantity monomial multiply NEGATIVE PRODUCTS nth root number of dollars number of permutations number of terms number sought numbers whose sum numerator and denominator obtain placed polynomial POSITIVE PRODUCTS Price $1 quadratic equation quotient rate per cent reciprocal remainder Rule under Art Schools SECOND OPERATION second term simplest form square root subscript numbers substituted subtract surd tion Transposing and uniting twice uniting terms unknown quantity values of x vulgar fractions

### Popular passages

Page 39 - ... the first term of the quotient ; multiply the• divisor by this term, and subtract the product from the dividend. II. Then divide the first term of the remainder by the first term of the divisor, which gives the second term of the quotient ; multiply the divisor by this second term, and subtract the product from the result of the first operation. Continue the same process, and if you obtain 0 for a remainder, the division is said to be exact.

Page 69 - Prob. 34-. A farmer had two flocks of sheep, each containing the same number. Having sold from one of these 39, and from the other 93, he finds twice as many remaining in the one as in the other. How many did each flock originally contain 1 Prob.

Page 74 - Two persons, A and B, lay out equal sums of money in trade ; A gains $126, and B loses $87, and A's money is now double of B's : what did each lay out ? Ans. $300.

Page 102 - A cistern containing 210 buckets, may be filled by 2 pipes. By an experiment, in which the first was open 4, and the second 5 hours, 90 buckets of water were obtained. By another experiment, when the first was open 7, and the other 3£ hours, 126 buckets were obtained. How many buckets does each pipe discharge in an hour ? Ans. The first pipe discharges 15, and the second pipe discharges 6 buckets.