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

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Durrie & Peck, 1844 - Algebra - 252 pages

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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 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.
Page 179 - If 36 be added to the number, the digits will be inverted. What is the number] Prob.
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 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 192 - COMPOUND RATIO is the ratio of the PRODUCTS of the corresponding terms of two or more simple ratios. Thus the ratio of 6...

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