# 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 - 252 sider

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### Innhold

 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 50 Addition of Fractions 63 Simple Equations illustrated c 81
 SECTION X 144 Quadratic Equations Pure and Affected 150 150 Second method of completing the Square 156 General Rule for reducing Quadratic Equations 163 Two Unknown Quantities 173 To Exterminate c by Substitution 175 Four or more Unknown Quantities 183 Different kinds of Ratio 189

 SECTION VIII 91 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
 Proportion its different kinds c 196 Various rules or formulas in Arithmetical Progression 204 Changes in the order of the Terms 210 Involution and Evolution of the Terms 217 Various rules or formulas in Geometrical Progression 224 SECTION XVI 232 Miscellaneous Problems 246

### Populćre avsnitt

Side 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.
Side 197 - The first and last terms are called the extremes, and the other two the means. Homologous terms are either the two antecedents or the two consequents. Analogous terms are the antecedent and consequent of the same couplet.
Side 179 - If 36 be added to the number, the digits will be inverted. What is the number] Prob.
Side 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.
Side 210 - 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.
Side 121 - Required the second root of x". 14. Required the fifth root of d3. 15. Required the 8th root of a3. 210. a. The rule in the preceding article may be applied to every case in evolution. But when the quantity whose root is to be found, is composed of several factors, there will frequently be an advantage in taking the root of each of the factors separately. This is done upon the principle that the root of the product of several factors, is equal to the product of their roots. Thus ^/a6=^/ax Vb.
Side 209 - Art. 374, that in a proportion, either extreme is equal to the product of the means, divided by the other extreme; and either of the means is equal to the product of the extremes, divided by the other mean. 1. If a : b :: c : d, then ad=bc 2.
Side 91 - The distance from A to D is 34 miles. The distance from A to B is to the distance .from C to D as 2 to 3. And ± of the distance from A to B, added to half the distance from C to D, is three times the distance from B to C. What are the respective distances ? Ans. From A to 5=12 ; from B to C=4 ; from C to JD=18. Prob. 48. Divide the number 36 into 3 such parts, that \ of the first, i of the second, and i of the third, shall be equal to each other.
Side 252 - It is required to find three numbers in geometrical progression, such that their sum shall be 14, and the sum of their squares 84.
Side 192 - COMPOUND RATIO is the ratio of the PRODUCTS of the corresponding terms of two or more simple ratios. Thus the ratio of 6...