# Elements of Algebra: Embracing ... the Theory and Application of Logarithms ... with an Appendix Containing Infinite Series ...

Harper & Bros., 1844 - 346 σεκΏδερ

### ‘ι κίμε οι ςώόστερ -”ΐμτανγ ξώιτιξόρ

Ρεμ εμτοπΏσαλε ξώιτιξίρ στιρ σθμόηειρ τοποηεσΏερ.

### –εώιεςϋλεμα

 Equations involving three or more Unknown Quantities 182185 102 SECTION V 110 Algebraic Demonstration of certain Properties of Numbers 207213 119 Discussion of Equations of the First Degree 226231 129 Inequations 245250 136 Binomial Theorem 259272 147 Roots of Numbers 273288 e 155 Evolution of Algebraic Quantities 289295 176
 SECTION IX 257 Computation of Logarithmic Tables 401402 264 Multiplication and Division by Logarithms 404 267 Compound Interest 410 273 General Demonstration of the Binomial Theorem 419431 282 Continued Fractions 432 288 Infinite Series 433 294 Summation of Infinite Series 438 300

 Calculus of Radicals 296314 184 SECTION VII 199 Problems producing Pure Equations 321 208 Particular Cases of Affected Quadratic Equations 331337 214 Problems producing Affected Quadratic Equations 221 SECTION VIII 234 Arithmetical Progression 373379 246
 Method of Differences 445450 306 Reversion of Series 451 312 Composition of Equations 454456 318 SECTION XII 332 Des Cartes 44 Equations of the Fourth Degree 473476 343 Youngs Method of Resolving Higher Equations 484 351

### Ργλοωικό αποσπήσλατα

”εκΏδα 163 - Bring down the first figure of the next period to the remainder for a new dividend, to which find a new divisor as before, and in like manner proceed till the whole be finished.
”εκΏδα 164 - Subtract this square number from the first period, and to the remainder bring down the next period for a dividend.
”εκΏδα 38 - 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.
”εκΏδα 64 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
”εκΏδα 57 - To reduce fractions of different denominators to equivalent fractions, having a common denominator. RULE. — Multiply each numerator into all the denominators except its own for the new numerators ; and multiply all the denominators together for a common denominator.
”εκΏδα 151 - 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. V. Double the whole root already found, for a new divisor, and continue the operation as before, until all the periods are brought down.
”εκΏδα 227 - If the numerator and denominator of each fraction is multiplied (or divided) by the same number, the value of the fraction will not change.
”εκΏδα 226 - BY RATIO is meant the relation which one quantity bears to another, with respect to magnitude. It is evident that this relation can exist only between quantities of a similar kind ; thus, a number must be compared with a number; a line with a line; &c. &c. ; and it would be absurd to compare a certain number of feet with a certain number of pomds; &c.
”εκΏδα 68 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.
”εκΏδα 16 - To raise a whole number or a decimal to any power, use it as a factor as many times as there are units in the exponent.