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according added addition appears arise arithmetical becomes called coefficient common denominator common measure completing compound consequently consisting contains continued cube root demonstrated denominator determined difference divi Divide dividend division equal equation evident example exponent expressed extracting factors figure find the values formula four fourth fraction Given gives greater greatest common divisor Hence indicated integral involving known least common multiple less letter logarithm magnitudes manner means method miles mixed multiplied necessary negative observed obtained operation performed positive preceding Prob problem proper proportionals proposed quadratic quan quotient radical ratio Reduce remainder represent respect result RULE shillings side simple solution square root substituting subtracted suppose surd taken third tion tity transposition travelled units unity unknown quantity values of x whence
Page 487 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Page 316 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 321 - ... and the quotient will be the next term Of the root. Involve the whole of the root, thus found, to its proper power...
Page 496 - IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents.
Page 450 - There are four numbers in arithmetical progression : the sum of the squares of the two first is 34 ; and the sum of the squares of the two last is 130. What are the numbers?
Page 491 - Likewise, if the first has the same ratio to the second, which the third has to the fourth, then also any equimultiples whatever of the first and third shall have the same ratio to the second and fourth...
Page 499 - IF magnitudes, taken separately, be proportionals, they shall also be proportionals when taken jointly, that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together to the fourth...
Page 283 - A cask, which held 146 gallons, was filled with a mixture of brandy, wine, and water. In it there were 15 gallons of wine more than there were of brandy, and as much water as both wine and brandy. What quantity was there of each...
Page 488 - When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth; then the first is said to have to the second a greater ratio than the third...