### тИ КщМЕ ОИ ВЯчСТЕР -сЩМТАНГ ЙЯИТИЙчР

дЕМ ЕМТОПъСАЛЕ ЙЯИТИЙщР СТИР СУМчХЕИР ТОПОХЕСъЕР.

### пЕЯИЕВЭЛЕМА

 Reduction 66 Addition 74 Reduction of Complex Forms 81 Transformation of Equations 85 Problems 94 Two Unknown Quantities 103 Three or more Unknown Quantities 112 Problems 118 General Solution of Problems 124 Discussion of Problems 131 Problem of the Couriers 138 Inequalities 145 SECTION III 151 Powers of Polynomials 157 Boots of Monomials 163 Square Root of Numbers 171 SECTION IV 182 Multiplication of Radicals 190 General Theory of Exponents 197
 SECTION VI 265 Permutations and Combinations 278 SECTION VII 285 Problems 291 Problems 298 Decomposition of Rational Fractions 306 Application of the Binomial Formula 313 Development of Surd Roots into Series 820 320 Reversion of Series 823 328 Differential Method 336 Logarithms 343 Use of Tables 353 SECTION VIII 359 Commensurable Roots 371 Transformations 380 Detached Coefficients 388 Surd and Imaginary Roots 398 SECTION IX 405 Horners Method of Approximation 416

### дГЛОЖИКч АПОСПэСЛАТА

сЕКъДА 167 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
сЕКъДА 66 - To reduce a fraction to its lowest terms. A Fraction is in its lowest terms when the numerator and denominator are prime to each other. 1. Reduce - to its lowest terms.
сЕКъДА 176 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
сЕКъДА 167 - Subtract the square number from the left hand period, and to the remainder bring down the next period for a dividend. III. Double the root already found for a divisor ; seek how many times the divisor is contained...
сЕКъДА 141 - But the relations of these quantities will not be changed, if we suppose the path of motion to be a curve, instead of a straight line. The above formula will therefore apply to the hands of a clock moving around the dial-plate, or to the planets moving in the circle of the heavens. It will thus afford a direct solution to the following problems : 1. The hour and minute hands of a clock are together at 12 o'clock ; when are they next together ? The circumference of the dial-plate is divided into 12...
сЕКъДА 36 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first multiplied by the second, plus the square of the second.
сЕКъДА 31 - That the exponent of any letter in the product is equal to the sum of its exponents in the two factors.
сЕКъДА 36 - 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.
сЕКъДА 264 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
сЕКъДА 266 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.