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, 1842 - Algebra - 332 pages
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Page 59 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 300 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 217 - 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 72 - If four magnitudes are in proportion, the product of the two extremes is equal to the product of the two means.
Page 298 - The area of a triangle is equal to half the product of the base and height.
Page 233 - 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. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 124 - ... 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 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 81 - It is required to divide the number 99 into five such parts, that the first may exceed the second by 3, be less than the third by 10, greater than the fourth by 9, and less than the fifth by 16.
Page 306 - There are two rectangular vats, the greater of which contains 20 cubic feet more than the other. Their capacities are in the ratio of 4 to 5 ; and their bases are squares, a side of each of which is equal to the depth of the other vat. Required the depth of each 1 Prob.

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