# New Elementary Algebra: in which the First Principles of Analysis are Progressively Developed and Simplified for Common Schools and Academies ...

Robert S. Davis & Company, 1863 - 324 pages
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### Contents

 Algebraic Notation 10 Addition 23 Subtraction 30 Multiplication 36 Division 45 Definitions 77 FRACTIONS 87 Algebraic Processes 107
 Simple Equations containing three 153 Interpretation of Negative Results 161 Zero and Infinity 161 Powers of Monomials 168 Definitions 181 Reduction of Radicals 201 Subtraction of Radicals 208 Pure Quadratic Equations 227 Problems leading to Pure Equa 234

### Popular passages

Page 56 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Page 55 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 305 - ... that is, Any term of a geometric series is equal to the product of the first term, by the ratio raised to a power, whose exponent is one less than the number of terms. EXAMPLES. 1.
Page 294 - ... two triangles are to each other as the products of their bases by their altitudes.
Page 73 - The LEAST COMMON MULTIPLE of two or more quantities is the least quantity that can be divided by each of them without a remainder.
Page 46 - The exponent of a letter in the quotient is equal to its exponent in the dividend, minus its exponent in the divisor. 439. Let it be required to divide a* by a1.
Page 176 - ... found by multiplying the coefficient of the preceding term by the exponent of the leading letter of the same term, and dividing the product by the number which marks its place.
Page 281 - Divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5. Ans. 20 and 40.
Page 139 - The method thus exemplified is expressed in the following RULE. . Find an expression for the value of the same unknown quantity in each of the equations, and form a new equation by placing these values equal to each other.
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.