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a² b² algebraic arithmetical arithmetical means Binomial Theorem cent Clearing of fractions coefficient Completing the square cube root degree divided dividend EXAMPLES exponent expression Extract the square 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 loga logarithm mantissa method miles monomial multiplying each term negative quantity Number corresponding number of terms obtain order of differences polynomial positive problem proportion quadratic equation quotient radical sign ratio remainder result second term simple equation simplest form Solve the equation Solve the following square root Substituting these values Subtracting tion Transposing unknown quantity Whence
Popular passages
Page 32 - 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 58 - The LEAST COMMON MULTIPLE of two or more quantities is the least quantity that can be divided by each of them without a remainder.
Page 160 - ... 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 50 - The GREATEST COMMON DIVISOR of two or more quantities is the greatest quantity that will divide each of them without a remainder.
Page 149 - RULE. Raise the numerical coefficient to the required power, and multiply the exponent of each letter by the exponent of the required power.
Page 263 - 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 133 - A banker has two kinds of money. It takes a pieces of the first kind to make a dollar, and b pieces of the second kind. If he is offered a dollar for с pieces, how many of each kind must he give ? 81.
Page 83 - 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 145 - 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 269 - 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.