University Algebra: Designed for the Use of Schools and Colleges
R. S. Davis, 1880 - Algebra - 475 pages
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added applying approximate arithmetical assume becomes binomial called cent changed coefficient complete containing corresponding cube root decimal denominator derived determine difference distance divided division equal EXAMPLES Expand exponent expression Extract the square factors figures Find Find the value four fourth fraction give given equation greater greatest Hence increased indicates integral interest last term less letter limit logarithm means method miles multiplied negative Note observe obtain polynomial positive preceding problem progression proportion quadratic quotient ratio Reduce remainder result RULE second term solution Solve the equation square root Substituting Subtracting taken term Theorem third tion Transform Transposing twice unknown quantity variations Whence write zero
Page 36 - 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 87 - A Complex Fraction is one having a fraction in its numerator or denominator, or both. It may be regarded as a case in division ; its numerator answering to the dividend, and its denominator to the divisor. EXAMPLES. 1. Reduce — — to it
Page 164 - Find the greatest square in the left period, and place its root on the right, after the manner of a quotient in division. Subtract the square of the root from the left period, and to the remainder bring down the next period for a dividend.
Page 54 - The GREATEST COMMON DIVISOR of two or more quantities is the greatest quantity that will divide each of them without a remainder.
Page 172 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Page 267 - Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d...
Page 137 - ... of the second to make the same sum. Some one offers him a crown for c pieces. How many of each kind must the banker give him ? Ans.
Page 149 - If the signs of all the terms of an inequality be changed, the sign of inequality must be reversed. For, to change all the signs is equivalent to...
Page 273 - If the illumination from a source of light varies inversely as the square of the distance, how much farther from a candle must a book, which is now 15 inches off, be removed, so as to receive just one-third as much light ? 20.
Page 112 - A vessel can be emptied by three taps; by the first alone it could be emptied in 80 minutes, by the second in 200 minutes, and by the third in 5 hours. In what time will it be emptied if all the taps are opened?