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

A.S. Barnes & Burr, 1863 - Algebra - 311 pages

### Contents

 INTRODUCTION 9 Definitions and Explanation of Terms 11 CHAPTER II 18 Subtraction 22 Division 31 Useful Formulas 39 CHAPTER III 46 Least Common Multiple 53
 Higher Roots of Numbers 149 Roots of Polynemials 155 Addition of Radicals 170 Division of Radicals 176 Radical Equations 185 Trinomial Equations 199 General Properties of Equations of Second Degree 207 Problem of the Lights 213

 Transformations 60 Addition of Fractions 68 Division of Fractions 75 CHAPTER V 81 Problems 89 Equations of the First Degree containing Two Unknown Quantities 97 Problems 107 Discussion of Problems 113 CHAPTER VI 119 Powers of Polynomials 132 Square Root of Fractions 140
 CHAPTER X 227 Series 234 Indeterminate Coefficients 246 I 255 General Properties 263 Properties and Transformations 267 Derived Polynomials 289 Solution of Higher Equations 295 Sturms Theorem 302 APPENDIX 308 General Demonstration cf Binomial Theorem 314

### Popular passages

Page 248 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 226 - 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 220 - In any proportion, the product of the means is equal to the product of the extremes.
Page 26 - 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 29 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, plus the square of the second.
Page 245 - 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.
Page 71 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.
Page 226 - That is, any term is equal to the first term, plus the product of the common difference by the number of preceding terms.
Page 81 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare ? Let x be the number of leaps taken by the hound.
Page 232 - To find the ratio, when the extremes and the number of terms are given. Divide the last term by the first, and extract that root of the quotient whose index is one less than the number of terms. To find the number of terms, when the ratio and the extremes are given.