Elementary Algebra: Embracing the First Principles of the Science

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A. S. Barnes & Company, 1850 - Algebra - 279 pages

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Page 136 - The result of this operation, 1184, contains twice the product of the tens by the units, plus the square of the units. But...
Page 230 - BD then A is said to have the same ratio to B, that C has to D ; or, the ratio of A to B is equal to the ratio of C to D.
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 1 — 148. When are quantities said to be in proportion by inversion, or inversely 1 — 149.
Page 79 - A fish was caught whose tail weighed 9Z6. ; his head weighed as much as his tail and half his body, and his body weighed as much as his head and tail together : what was the weight of the fish?
Page 254 - The logarithm of a number is the exponent of the power to which it is necessary to raise the base of the system in order to produce the number.
Page 56 - To add fractional quantities together RULE. Reduce the fractions, if necessary, to a common denominator ; then add the numerators together, and place their sum over the common denominator.
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 116 - A person bought a chaise, horse, and harness, for 60 ; the horse came to twice the price of the harness, and the chaise to twice the price of the horse and harness ; what did he give for each ? r 13.
Page 145 - These expressions may often be simplified, upon the principle that, the square root of the product of two or more factors is equal to the product of the square roots of...
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.

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