An Introduction to Algebra: Being the First Part of a Course of Mathematics Adapted to the Method of Instruction in the American Colleges

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Durrie & Peck, 1841 - Algebra - 332 pages

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Page 57 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 152 - The equality of the two sides is not affected by this alteration, because we only change one quantity x for another •which is equal to it. By this means we obtain an equation which contains only one unknown quantity.
Page 213 - Here we discover the important property, that, in an arithmetical progression, the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.
Page 229 - 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.
Page 31 - We have seen that multiplying by a whole number, is taking the multiplicand as many times as there are units in the multiplier.
Page 161 - 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 47 - The value of a fraction, is the quotient of the numerator divided by the denominator.
Page 18 - ... 6. If a quantity be both multiplied and divided by another, the value of the former will not be altered.
Page 120 - ... 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 107 - Whenever, therefore, we meet with a quantity of this description, we may know that its square root is a binomial ; and this may be found, by taking- the root of the two terms which are complete powers, and connecting them by the sign -|-. The other term disappears in the root.

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