## New Higher Algebra: An Analytical Course Designed for High Schools, Academies, and CollegesR.S. Davis, 1873 |

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### Common terms and phrases

algebraic arithmetical progression binomial factors bushels cent Clearing of fractions coefficient common difference common logarithm Completing the square cube root decimal degree denominator denote Divide dividend equal equation Art EXAMPLES exponent expression Extracting the square Find the cube Find the square Find the sum find the values formula given equation Given x² greatest common divisor GREENLEAF'S imaginary inequality infinite series last term least common multiple logarithm miles Multiply negative nth root number of terms obtain OPERATION permutations polynomial positive problem proportion quadratic equation quan quotient radical sign ratio real roots Reduce remainder required root Required the number required to find result rods second term simplest form solution square root Substituting the value Subtracting tity Transposing and uniting unknown quantity Whence

### Popular passages

Page 41 - 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.

Page 61 - 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 79 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.

Page 141 - Hence, for raising a monomial to any power, we have the following RULE. Raise the numerical coefficient to the required power, and multiply the exponent of each letter by the exponent of the required power.

Page 157 - Find the greatest square in the first- period on the left, and place its root on the right after the manner of a quotient in division. Subtract the square of the root from the first period, and to the remainder bring down the second period for a dividend.

Page 82 - A Complex Fraction is one having a fraction in its numerator, or denominator, or both. It may be regarded as a case in division, since its numerator answers to the dividend, and its denominator to the divisor.

Page 273 - ... travel over, who gathers them up singly, returning with them one by one to the basket ? Ans.

Page 253 - 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 314 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 180 - I. Divide the coefficient of the dividend by the coefficient of the divisor.