New University Algebra: A Theoretical and Practical Treatise, Containing Many New and Original Methods and Applications for Colleges and High Schools

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Ivison, Blakeman, Taylor & Company, 1872 - Algebra - 420 pages
 

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Page 209 - ... 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 66 - To reduce a fraction to its lowest terms. A Fraction is in its lowest terms when the numerator and denominator are prime to each other. 1. Reduce - to its lowest terms.
Page 169 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 286 - In arithmetical progression there are five parts to be considered, viz : the first term, the last term, the number of terms, the common difference, and the sum of all the terms.
Page 294 - In any proportion, the product of the means is equal to the product of the extremes.
Page 169 - Subtract the square number from the left hand period, and to the remainder bring down the next period for a dividend. III. Double the root already found for a divisor ; seek how many times the divisor is contained...
Page 42 - 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 52 - Measure, of two or more quantities, is the greatest quantity that will exactly divide each of them.
Page 300 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.
Page 286 - ... than the last. After the same method of reasoning, we infer that the sum of any two terms equidistant from the extremes, is equal to the sum of the extremes. Hence, it follows that the terms will average just half the sum of the extremes.

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