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a²x² added addition algebraical ANSWERS assumed ax² becomes binomial called changed coefficients common complete compound consists continued corresponding cube denominator denote difference distance Divide dividend divisible divisor easily equal equation evident EXAMPLES exceeds EXERCISES exponent expressed extracting factors Find the value former four fourth fraction given given equations given quantity gives greater greatest common measure hence integral known latter least common multiple less logarithms manner means method Multiply namely negative obtained perform positive preceding prime proportional proved quadratic question quotient radical ratio Reduce remainder represented result rule second term sides similar simple solution solved square root substituting subtracting system of values taken taking theorem third tion travels units unknown quantities values of x vary
Page 78 - 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.
Page 319 - 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...
Page 341 - 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.
Page 311 - Find the nth term, and the sum of n terms of the natural series of numbers 1, 2, 3, 4 . . . . Ans.
Page 225 - 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?
Page 355 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 288 - 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.
Page 180 - 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...
Page 178 - 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?