Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the Capacities of the Young, and the Method of Instruction, in Schools and Academies

Durrie & Peck, 1844 - Algebra - 252 pages

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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
 Subtraction of Powers 106 188 107 Greatest Common Measure 112 199 115 Powers of Roots 118 211 122 224 128 Reduction of Radical Quantities 129

 Addition of Fractions 63 SECTION VII 71 Clearing of Fractions c 77 General Rule for solving Simple Equations 83 SECTION VIII 91 To involve a binomial or residual quantity 97
 Division of Radical Quantities 137 SECTION X 144 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 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 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 21 - One quantity is said to be a multiple of another, when the former contains the latter a certain 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 60 - RULE. Multiply all the numerators together for a new numerator, and all the denominators for a new denominator: then reduce the new fraction to its lowest terms.
Page 35 - MULTIPLYING BY A WHOLE NUMBER is TAKING THE MULTIPLICAND AS MANY TIMES, AS THERE ARE UNITS IN THE MULTIPLIER.
Page 112 - II. Divide the greater number by the less and the preceding divisor by the last remainder till nothing remains. The last divisor is the...
Page 45 - As the product of the divisor and quotient is equal to the dividend, the quotient may be found, by resolving the dividend into two such factors, that one of them shall be the divisor. The other will, of course, be the quotient. Suppose abd is to be divided by a. The factor a and bd will produce the dividend. The first of these, being a divisor, may be set aside.