# An Elementary Treatise on Algebra: Theoretical and Practical

J. Ernst, 1846 - Algebra - 262 pages

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### Contents

 Definitions and Axioms page 9 Subtraction 15 Division 25 Algebraic Fractions 33 Addition of Fractions e 6 44 Simple Equations chapter 1 49 67 Simple Equations chapter 3 80 Interpretation of Minus Signs 91
 Peculiar Modes of Completing a Square Art 79 157 Quadratics containing more than one Unknown Quantity 171 Questions Producing Quadratic Equations 178 SECTION V 184 Harmonical Proportion 193 SECTION VI 204 Infinite Series 212 Recurring Series 218

 Its Application 99 Evolution chapter 2 110 Abbreviations in Cube Root Art 78 132 Problems Producing Pure Equations 143
 Compound Interest 327 227 General Theory of Equations 241 Equal Roots 247 Examples in Quadratics 258

### Popular passages

Page 11 - If equal quantities be divided by the same, or by equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be altered.
Page 33 - To reduce a mixed quantity to an improper fraction, multiply the integer by the denominator of...
Page 195 - 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?
Page 184 - If the sum of an arithmetical series is 567, the first term 7, and the common difference 2; what is the number of terms?
Page 202 - There are two numbers, which are to each other, as 16' to 9, and 24 is a mean proportional between them. What are the numbers ? Ans. 32 and 18. 13. The sum of two numbers is to their difference as 4 to 1, and the sum of their squares is to the greater as 102 to 5. What are the numbers 1 Ans.
Page 145 - Prob. 9. It is required to divide the number 18 into two such parts, that the squares of those parts may be to each other as 25 to 16.
Page 42 - Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Page 155 - Any trinomial can be separated into two binomial factors, when the extremes are squares and positive, and the middle term is twice the product of the square roots of the extremes.
Page 191 - When three magnitudes, a, b, c, have the relation of a: c: : a—b : b—c ; that is, the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.
Page 143 - A and B, set out to meet each other; A leaving the town C at the same time that B left D. They travelled the direct road...