An Elementary Treatise on Algebra: Theoretical and PracticalCollins and Hannay, 1824 - 516 |
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according added algebraic quantities arithmetical becomes binomial changing the signs coefficient common denominator completing the square compound quantity consequently cube root DEMONSTRATION difference digits divi divided dividend division equa equal exponent expressed extracting the root factors find the values formula fourth given equation greater greatest common divisor Hence integral least common multiple less letter logarithm lowest terms lues magnitudes manner method miles multiplied negative number of terms observed positive Prob problem proportionals proposed equation quadratic equations quadratic surds quan quotient radical quantities radical sign ratio Reduce remainder Required the cube Required the square required to find result RULE second equation shillings side simple equations square root substituting subtracted surd third tion tity transposition unity unknown quantity values of x whence whole number
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Strona 489 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Strona 239 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Strona 318 - 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.
Strona 323 - ... and the quotient will be the next term Of the root. Involve the whole of the root, thus found, to its proper power...
Strona 498 - 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.
Strona 452 - 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?
Strona 493 - 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...
Strona 501 - 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...
Strona 285 - 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...
Strona 490 - 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...