# University Algebra: Embracing a Logical Development of the Science, with Numerous Graded Examples

A.S. Barnes and Company, 1870
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### Contents

 Addition 12 Useful Formulas 39 CHAPTER I 46 CHAPTER IV 58 FractionsDefinitions 68 Division of Fractions 75 Explanation of 0 81 Problems 89
 135 178 Radical Equations 185 140 189 Trinomial Equations 199 General Properties of Equations of Second Degree 207 147 211 Problem of the Lights 213 149 218

 Equations of the First Degree containing Two Unknown Quantities 98 46 106 Problems 107 Discussion of Problems 113 CHAPTER VI 119 Powers of BinomialsBinomial Formula 132 Square Root of Fractions 140 68 146 Higher Roots of Numbers 149 123 161 Addition of Radicals 170 132 172 Division of Radicals 176
 CHAPTER X 227 152 228 Series 234 Indeterminate Coefficients 246 CHAPTER XI 255 General Properties 263 Properties and Transformations 267 Derived Polynomials 289 Solution of Higher Equations 295 APPENDIX 308 General Demonstration cf Binomial Theorem 314 70

### Popular passages

Page 36 - Divide the first term of the remainder by the first term of the divisor, for the second term of the quotient. Multiply the divisor by this term, and subtract the product from the first remainder, and so on : IV.
Page 136 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 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.
Page 236 - In arithmetical progression there are five parts to be considered, viz : the first term, the last term, the number of terms, the common difference, and the sum of all the terms.
Page 258 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 230 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
Page 230 - In any proportion, the product of the means is equal to the product of the extremes.
Page 255 - THE LOGARITHM: of a number is the exponent of the power to which it is necessary to raise a fixed number, to produce the given number. The fixed number is called the base of the system.