Elementary Algebra: Embracing the First Principles of the Science

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A. S. Barnes & Company, 1848 - Algebra - 279 pages
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Page 230 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Page 136 - The result of this operation, 1184, contains twice the product of the tens by the units, plus the square of the units.
Page 231 - Quantities are said to be in proportion by alternation, or alternately, when antecedent is compared- with antecedent and consequent with consequent. Thus, if we have the proportion 3 : 6 : : 8 : 16, the alternate proportion would be 3 : 8 : : 6 : 16. QUEST. — 147. When are three quantities proportional ? What is the middle one called ? — 148. When are quantities said to be in proportion by inversion, or inversely?
Page 155 - Divide the coefficient of the dividend by the coefficient of the divisor.
Page 233 - AC and by clearing the equation of fractions we have BO=AD; that is, Of four proportional quantities, the product of the two extremes is equal to the product of the two means.
Page 234 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 138 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 273 - A person has four casks, the second of which being filled from the first, leaves the first four-sevenths full. The third being filled from the second, leaves it one-fourth full, and when the third is emptied into the fourth, it is found to fill only nine-sixteenths of it. But the first will fill the third and' fourth, and leave 15 quarts remaining.
Page 79 - Ibs., his head weighed as much as his tail and half his body, and his body weighed as much as his head and t.ail together : what was the weight of the fish ? Let 2x = the weight of the body, in pounds.
Page 116 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans. A 14JA days, B 17fa, and C 23JT.

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