# An Elementary Treatise on Algebra: For the Use of Students in High Schools and Colleges

Sanborn, Carter, Bazin, 1841 - Algebra - 300 pages

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### Contents

 SECT PAGE 49 Ill Least common multiple 74 Literal equations 86 Equations of the first degree with several unknown quan 96 Negative quantities and the interpretation of negative 119 Discussion of problems 126 Extraction of the second roots of numbers 133 SECT PAGE XXXV Third roots of fractions and the extraction of third roots by approximation 140
 Operations on irrational quantities with fractional ex ponents 194 Operations on irrational quantities with radical signs 201 Negative exponents 209 Inequalities 213 Equidifference 217 Ratio and proportion 219 Progression by difference 229 Examples involving progression by difference 234

 roots by approximation 141 Extraction of the third roots of numbers 155 Questions producing pure equations of the third degree 100 166 Powers of monomials 168 Binomial theorem e 172 Roots of numbers to any degree 180 Roots of monomials 183 Origin and signification of fractional exponents 185 Separation of a quantity into any number of factors 186 XLI1 Roots of polynomials 188 Simplification of irrational or radical quantities 191
 Progression by quotient 236 Examples in progression by quotient 242 Exercises in equations of the second degree 244 Exercises in equations of the second degree with two unknown quantities 250 Logarithms 258 Use of the tables in finding the logarithms of given num bers and the reverse 265 Application of logarithms to arithmetical operations 272 Compound interest 282 Annuities e e e e e e e e 288 Miscellaneous questions 292

### Popular passages

Page 48 - ANOTHER. 1. Divide the coefficient of the dividend by the coefficient of the divisor. 2.
Page 52 - 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 139 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 25 - A shepherd in time of war was plundered by a party of soldiers, who took \ of his flock and \ of a sheep ; another party took from him \ of what he had left and \ of a sheep ; then a third party took \ of what now remained and J of a sheep.
Page 228 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 124 - What fraction is that, to the numerator of which if 1 be added, the value will be •£ ; but if 1 be adde.d to the denominator, its value will be | ? Let — denote the fraction.
Page 78 - Multiply all the numerators together for a new numerator, and all the denominators together for a new denominator.
Page 262 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Page 225 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Page 3 - If equal quantities be divided by the same or 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.