University Algebra: Designed for the Use of Schools and CollegesR. S. Davis, 1880 - 475 σελίδες |
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a² b² added algebraic arithmetical arithmetical means Binomial Theorem cent Clearing of fractions coefficient Completing the square cube root degree denominator divided dividend division EXAMPLES exponent expression Extract the square factors figures Find the sum Find the value find two numbers following equations following RULE given equation greatest common divisor Hence indicates integral last term least common multiple less loga logarithm mantissa method miles monomial multiplying each term negative quantity Number corresponding number of terms obtain order of differences polynomial problem quadratic equation quotient radical sign ratio remainder result second term simplest form Solve the equation Solve the following square root Sturm's Theorem Substituting these values Subtracting third tion Transposing unknown quantity Whence
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Σελίδα 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.
Σελίδα 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
Σελίδα 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.
Σελίδα 54 - The GREATEST COMMON DIVISOR of two or more quantities is the greatest quantity that will divide each of them without a remainder.
Σελίδα 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...
Σελίδα 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...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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?