# New Higher Algebra: An Analytical Course Designed for High Schools, Academies, and Colleges

R.S. Davis, 1873

### Contents

 Addition 75 Transformation of Equations 85 Problems One Unknown Quantity 93 Equations containing Two Unknown Quantities 102 Equations containing Three or more Unknown Quantities 109 General Solution of Problems 119 Interpretation of Negative Results 126 Inequalities 135 67 141 EVOLUTION 148 Cube Root of Numbers 155 Cube Root of Polynomials 163 Reduction 169 Addition 175 75 176 Powers 181 Imaginary Quantities 188 Radical Equations 196
 Problems in Proportion 257 Geometrical Progression 266 Problems 273 Binomial Theorem Positive Integral Exponent 280 Undetermined Coefficients 289 Binomial Theorem 296 Summation of Infinite Series 303 LOGARITHMS 313 79 324 GENERAL THEORY OF EQUATIONS 334 Composition of Coefficients 340 Transformation of Equations 347 Derived Polynomials 358 SOLUTION OF HIGHER NUMERICAL EQUATIONS 372 APPENDIX 381 Cardans Rule for Cubics 388 Newtons Method of Approximation 394

### 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.