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

R.S. Davis & Company, 1864 - Algebra - 394 pages
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### Contents

 24 92 Problems One Unknown Quantity 93 Equations containing Two Unknown Quantities 102 Equations containing Three or more Unknown Quantities 109 34 118 General Solution of Problems 119 Interpretation of Negative Results 126 36 134 Inequalities 135 Powers of Monomials 141 EVOLUTION 148 Cube Root of Numbers 155 Cube Root of Polynomials 163 Reduction 169 Addition 175 43 181 Imaginary Quantities 188 Radical Equations 196 Pure Quadratics 200 45 204 Methods of Completing the Square 206 Problems leading to Affected Quadratic Equations 217
 Geometrical Progression 266 Problems 273 Binomial Theorem Positive Integral Exponent 280 Undetermined Coefficients 289 Binomial Theorem Any Exponent 296 Summation of Infinite Series 303 Interpolation 311 67 312 The Common System 314 Common Logarithms 321 75 324 Exponential Equations 327 GENERAL THEORY OF EQUATIONS 334 Composition of Coefficients 340 Transformation of Equations 347 Derived Polynomials 358 Sturms Theorem 364 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 157 - Subtract the square of the root from the left period, and to the remainder bring down the next period for a dividend. 3d. Double the root already found, and place it on the left for a divisor. Find how many times the divisor is contained...
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 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 275 - ... travel over, who gathers them up singly, returning with them one by one to the basket ? Ans.
Page 165 - Find the cube root of the first term, write it as the first term of the root, and subtract its cube from the given polynomial.
Page 255 - 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 316 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.