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added Addition amount annex arithmetical arranged Assume balls becomes binomial called changed CHAPTER coefficient common compound consists cube denominator denote the number descending difference Divide dividend Division divisor double eliminated equal equation EXERCISES expressed Extract factor Find a number Find the number Find the sum following quantities formula four fourth fraction geometric greater half Hence hour increased indices infinite known less letters manner means method miles multiplied negative number of combinations number of permutations number of terms numerator and denominator obtained persons placed positive pounds prefixed proceed Prove putting quadratic quotient ratio Reduce remainder respectively result rule sheep shillings sides simple square root standing substitution subtracting Suppose surd things taken third travelled true twice unknown quantity whole write
Seite 65 - To divide a given straight line into two parts, so that the rectangle contained by the -whole, and one of the parts, may be equal to the square of the other part.
Seite 84 - The fore-wheel of a carriage makes six revolutions more than the hind-wheel in going 120 yards ; but if the circumference of each wheel be increased one yard, it will make only four revolutions more than the hind-wheel in going the same distance.
Seite 64 - Divide the number 24 into two such parts, that their product shall be to the sum of their squares, as 3 to 10.
Seite 16 - If the numerator and denominator of a fraction be both multiplied or both divided by the same number, the value of the fraction is not altered.
Seite 48 - Divide the first term of the remainder by three times the square of the first term of the root, and write the result as the next term of the root.
Seite 9 - A power of a quantity is divided by any other power of the same quantity by subtracting the index of the divisor from that of the dividend, the quotient being that power of the quantity whose index is the remainder so obtained.
Seite 70 - From the preceding, it appears, that the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.
Seite 45 - ... be divided by the number of terms to that place, it will give the coefficient of the term next following.
Seite 48 - Take the root of the first term, for the first term of the required root...