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added addition algebraical ANSWERS assumed becomes binomial called changed coefficients compound consists constant continued corresponding cube denominator denote difference digits Divide dividend divisible divisor easily equal equation equations containing evident EXAMPLES exceeds EXERCISES exponent expressed extracting factors Find the value former four fourth fraction function given given equations given quantity gives greater greatest common measure hence integral known latter least common multiple less logarithms manner means method miles Multiply namely negative perform positive preceding prime proportional proved quadratic question quotient radical ratio Reduce remainder represented respectively result rule second term sides similar similarly simple solution solved square root substituting subtract taken taking theorem third tion travels units unknown quantities values of x vary
Página 74 - Multiply each numerator by all the denominators except its own, for the new numerators ; and all the denominators together for A COMMON denominator. NOTE 1.
Página 315 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Página 337 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.
Página 307 - Find the nth term, and the sum of n terms of the natural series of numbers 1, 2, 3, 4 . . . . Ans.
Página 221 - If A and В together can perform a piece of work in 8 days, A and С together in 9 days, and В and С in 10 days; how many days would it take each person to perform the same work alone?
Página 349 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 284 - If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Página 176 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive $ '75, and, for every day he was idle, he should forfeit $ '25 ; at the expiration of the time, he received $ 27'50 ; how many days did he work...
Página 174 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?