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

Benjamin B. Mussey, 1842 - 300 σελίδες

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### Περιεχόμενα

 Literal equations 86 Equations of the first degree with several unknown quanti 96 Numerical substitution of algebraic quantities 105 Negative quantities and the interpretation of negative results 119 Discussion of problems 426 126 Extraction of the second roots of numbers 133 Irrational and imaginary quantities defined 140 SECT PAGE XXXIII Affected equations of the second degree 146 Extraction of the third roots of numbers 155 Third roots of fractions and the extraction of third 163 roots by approximation 164 Questions producing pure equations of the third degree 166 Powers of monomials 168 Powers of polynomials 169 Binomial theorem 172 Roots of numbers to any degree 180
 Inequalities 213 Equidifference 217 Ratio and proportion 219 Progression by difference 229 Examples involving progression by difference 234 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 un known 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 288 Miscellaneous questions 292 Πνευματικά δικαιώματα

### Δημοφιλή αποσπάσματα

Σελίδα 50 - 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.
Σελίδα 46 - ANOTHER. 1. Divide the coefficient of the dividend by the coefficient of the divisor. 2.
Σελίδα 23 - 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.
Σελίδα 226 - 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.
Σελίδα 258 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Σελίδα 260 - 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.
Σελίδα 1 - Algebraic operations are based upon definitions and the following axioms : — 1. If the same quantity, or equal quantities, be added to equal quantities, the sums will be equal. 2. If the same quantity, or equal quantities, be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity, or equal quantities, the products will be equal.
Σελίδα 223 - 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.
Σελίδα 1 - 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.
Σελίδα 137 - 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.