The Elements of Algebra: Designed for the Use of Common Schools: Also Serving as an Introduction to the "Treatise on Algebra"D. Appleton and Company, 1850 - 251 σελίδες |
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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 digits Divide the number divisor equal EXAMPLES exponent Extracting the square favorable fifth root find the values find x formula four quantities geometrical geometrical progression gives Hence inequality letters metical mixed quantity monomial multiply 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 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 Y₁
Δημοφιλή αποσπάσματα
Σελίδα 44 - Subtract the numerator of the subtrahend from the numerator of the minuend, and place the difference over the common denominator.
Σελίδα 28 - ... 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.
Σελίδα 96 - 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.
Σελίδα 71 - 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.
Σελίδα 173 - 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.
Σελίδα 66 - ... of two persons are in the ratio of 3 to 4, but 5 years ago the ratio of their ages was that of 2 to 3 ; what are their ages ? Ans. 15 and 20. 50. Two pieces of cloth were purchased at the same price per yard, but as they were of different lengths, the one cost $ 5, and the other $ 6.50. If each had been 10 yards longer, their lengths would have been as 5 to 6. Required the length of each piece.
Σελίδα 56 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Σελίδα 112 - 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...
Σελίδα 186 - Proportion is when, of three numbers, the first has the same proportion to the third, as the difference between the first and second, has to the difference between the second and third. As in these three, 6, 8, 12 ; where 6 : 12 : : 8 — 6 : 12 — 8, that is 6 : 12 : : 2 : 4. When four numbers are in musical proportion ; then...
Σελίδα 160 - A's money was 3 months in trade, and his gain was $60 less than his -took : B's money was $50 more than A's» and was in trade 5 months: what was A's stock 1 Ans.