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, 1846 - 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 T T 33 Multiplication illustrated c 39 Page 44 General Rule of Division 51
 Reduction of Radical Quantities 124 Subtraction of Radical Quantities 133 Involution of Radical Quantities e 140 Reduction of Equations by Evolution 146 First method of completing the Square 153 Other methods of completing the Square pointed out 159 Two Unknown Quantities 173 To Exterminate c by Substitution 175

 Addition of Fractions 63 Simple Equations illustrated c 71 Clearing of Fractions c 77 SECTION VIII 91 To involve a binomial or residual quantity 97 Subtraction of Powers 106 Greatest Common Measure 112 Powers of Roots 118
 SECTION XII 188 Proportion its different kinds c 196 Various rules or formulas in Arithmetical Progression 204 Case 1Changes in the order of the Terms 210 Involution and Evolution of the Terms 217 Various rules or formulas in Geometrical Progression 224 Extraction of the Square Root of Compound Quantities 230 Miscellaneous Problems 246

Popular passages

Page 234 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 220 - What two numbers are as 2 to 3 ; to each of which, if 4 be added, the sums will be as 5 to 7 ? ., / } Prob.
Page 212 - It may undergo any change which will not affect the equality of the ratios ; or which will leave the product of the means equal to the product of the extremes.
Page 53 - 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 62 - 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 200 - 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., are all equal ; the quantities are said to be in continued proportion.
Page 194 - COMPOUND RATIO is THE RATIO OF THE PRODUCTS, OF THE CORRESPONDING TERMS OF TWO OR MORE SIMPLE RATIOS.* Thus the ratio of 6...
Page 47 - 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.
Page 226 - In geometrical progression, the last term is equal to the product of the first, into that power of the ratio whose index is one less than the number of terms. When the least term and the ratio are the same, the equation becomes z=rr"~ l =r".