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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Common terms and phrases
a+b+c added algebraic algebraic quantities antecedent apples arithmetical progression bx-ab change the signs Clear the equation cleared of fractions coefficient common denominator Consequently cube root decimal denote digits Divide the number divisor equal equation of fractions EXAMPLES exponent Extracting the square favorable find the values find x formula four quantities geometrical gives Hence inequality letters metical mixed quantity monomial NEGATIVE PRODUCTS negative quantities nth root number of combinations number of permutations number of terms number sought numerator and denominator obtain OPERATION placed polynomial POSITIVE PRODUCTS pressions proportion quadratic equation question quotient rate per cent reciprocal Reduce remainder repetend Rule under Art second power second term simple chance simple equations simplest form solved square root subscript numbers substituted subtract symbol things taken third tions tity Transposing and uniting twice uniting terms unknown quantity values of x VULGAR FRACTIONS
Popular passages
Page 38 - ... 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 75 - 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 106 - 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.
Page 81 - 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 185 - One hundred stones being placed on the ground, in a straight line, at the distance of a yard from each other, how far will a person travel who shall bring them one by one to a basket, which is placed one yard from the first Stone ? Ans.
Page 44 - To reduce a mixed quantity to the form of a fraction. RULE. Multiply the entire part by the denominator of the fraction...
Page 54 - Subtract the numerator of the subtrahend from the numerator of the minuend, and place the difference over the common denominator.
Page 122 - Since the square of a binomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second...
Page 10 - It denotes that the quantities between which it is placed, are to be multiplied together.
Page 169 - A calculates that he can reach the place D in 4 days, and that B can arrive at the place C in 9 days. What is the distance between C and DI Ans.