# Elements of Algebra: An Abridgment of Day's Algebra

Durrie & Peck., 1848 - Algebra

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### Contents

 Introduction 13 Addition of Powers 105 20 Operations stated in common language translated into algebraic 21 Adding quantities which are alike and have like signs 27 Proof 33 Multiplication illustrated c 39 Division illustrated c 44 47 Algebraic Fractions explained c 53 54
 To involve a binomial or residual quantity 97 Subtraction of Powers 106 Greatest Common Measure 112 Powers of Roots 118 Reduction of Radical Quantities 124 Subtraction of Radical Quantities 131 Division of Radical Quantities 137 SECTION X 144

 Addition of Fractions 61 Division of Fractions 68 Reduction of Equations by Multiplication 76 General Rule for solving Simple Equations 83 SECTION VIII 91
 Quadratic Equations Pure and Affected 151 Demonstration of the second method c 157 General Rule for reducing Quadratic Equations 163 Two Unknown Quantities 173

### Popular passages

Page 51 - 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 210 - It is evident that the terms of a proportion may undergo any change which will not destroy the equality of the ratios ; or which will leave the product of the means equal to the product of the extremes.
Page 232 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 198 - When there is a series of quantities, such that the ratios of the first to the second, of the second to the third, of the third to the fourth, &c.
Page 94 - Hence any odd power has the same sign as its root. But an even power is positive, whether its root is positive or negative.
Page 65 - To multiply a fraction by a fraction. Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 58 - To reduce fractions of different denominators to a common denominator. Multiply each numerator into all the denominators except its own for a new numerator ; and all the, denominators together^ for a common denominator. 8. Reduce -r, and -,, and — to a common denominator. 6
Page 21 - One quantity is said to be a measure of another, when the former is contained in the latter any number of times, without a remainder.
Page 228 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.
Page 183 - The same method which is employed for the reduction of three equations, may be extended to 4, 5, or any number of equations, containing as many unknown quantities. The unknown quantities may be exterminated, one after another, and the number of equations may be reduced by successive steps from five to four, from four to three, from three to two, &c. !' I"*! *t y t