# The Elements of Algebra

Harper & Bros., 1856 - Algebra - 268 pages
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### Popular passages

Page 75 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Page 96 - To reduce fractions to a common denominator. RULE. Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Page 73 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
Page 94 - To reduce a mixed number to an improper fraction, — RULE : Multiply the whole number by the denominator of the fraction, to the product add the numerator, and write the result over the denominator.
Page 85 - ... 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...
Page 134 - 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 76 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 225 - Three quantities are in proportion when the first has the same ratio to the second, that the second has to the third ; and then the middle term is said to be a mean proportional between the other two.
Page 192 - Multiply the divisor thus increased by the last term of the root, and subtract the product from the last remainder.
Page 174 - RULE. 1. Separate the given number into periods of two figures, each, beginning at the units place.