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

A.S. Barnes & Burr, 1860 - Algebra - 320 pages
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### Contents

 INTRODUCTION 9 CHAPTER II 18 Multiplication 26 Useful Formulas 39 CHAPTER III 46 Least Common Multiple 53 Transformations 60 Addition of Fractions 68
 Roots of Polynomials 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 CHAPTER X 227

 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 Higher Roots of Numbers 149
 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 of Binomial Theorem 314

### 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. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 39 - 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 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.
Page 257 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Page 81 - 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 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 91 - 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 72 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.