Practical Elementary Algebra

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American Book Company, 1908 - Algebra - 420 pages


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Page 296 - ... the square of the second. _ Again, (a — by = (a — 5) (a — 5) = a2 — 2a6 + 52. (2) That is, 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 269 - Multiply the index of the quantity by the index of the power to which it is to be raised, and the result will be -the power required.
Page 273 - and — are equivalent expressions, also of and — — , we conclude that any factor may be transferred from the numerator to the denominator, or from the denominator to the numerator, by changing the sign of its exponent.
Page 260 - The area of a rectangle is equal to the product of its base and altitude ; that is, A = ab. 443. Corollary 1. The area of a square is equal to the square of its side. 444. Corollary 2. Tiro rectangles are to each other as the products of their bases and altitudes.
Page 110 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.
Page 380 - My lord, I have undertaken this long journey purposely to see your person, and to know by what engine of wit or ingenuity you came first to think of this most excellent help into astronomy, viz. the logarithms ; but, my lord, being by you found out, I wonder nobody else found it out before, when now known it is so easy.
Page 215 - The same quantity may be added to, or subtracted from, both sides of an equation. To...
Page 347 - The first term of a ratio is called the antecedent, and the second term the consequent. Thus, in the ratio a : b, a is the antecedent, and b is the consequent. The first and fourth terms of a proportion are called the extremes, and the second and third terms the means.
Page 168 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes ; but the denominator being doubled, and the numerator increased by 2, the value becomes f 1 Ans.
Page 10 - ... girls. Altogether there are the sum of 22 and 66, or 88 pupils, which is the number the problem says there are. Hence, the answer is right. 2. There are 7 sheep for every lamb in a pasture, and 96 sheep and lambs altogether. How many lambs are there ? Work by both arithmetic and algebra, following the models on p. 9, and prove answer. 3. There are three packages, the second of which weighs twice as much as the first, and the third three times as much as the first. When put together on the scales...

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