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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?
Page 354 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.