### тИ КщМЕ ОИ ВЯчСТЕР -сЩМТАНГ ЙЯИТИЙчР

дЕМ ЕМТОПъСАЛЕ ЙЯИТИЙщР СТИР СУМчХЕИР ТОПОХЕСъЕР.

### пЕЯИЕВЭЛЕМА

 DEFINITIONS AND NOTATION 7 Interpretation 16 Theorems 53 Greatest Common Divisor 64 Least Common Multiple 71 Addition 87 Division 97 SIMPLE EQUATIONS 103
 Reduction of Radicals 187 Subtraction of Radicals 194 Radical Equations 208 Simultaneous Equations 216 Problems 253 RATIO AND PROPORTION 259 Theorems relating to Proportion 262 Problems in Proportion 267 Problems 276

### дГЛОЖИКч АПОСПэСЛАТА

сЕКъДА 95 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
сЕКъДА 54 - 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 279 - Multiply the last term by the ratio, from the product subtract the first term, and divide the remainder by the ratio, less 1; the quotient will be the sum of the series required.
сЕКъДА 265 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
сЕКъДА 257 - ... if the circumference of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel, in the same distance ; required the circumference of each wheel. SOLUTION. Let x = circumference of hind wheel in yards. and y = circumference of fore wheel in yards. 120 Then — = number of revolutions of hind wheel.
сЕКъДА 104 - An equation of the second degree is one in which the highest power of the unknown quantity is the second power, or square ; as, 3 x2 — 2 x = 65.
сЕКъДА 90 - SUBTRACTION OF FRACTIONS is the process of finding the difference between two fractions.
сЕКъДА 257 - 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.
сЕКъДА 133 - 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.
сЕКъДА 175 - ... 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.