Elementary Treatise on Algebra |
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126 become zero 3d root arithmetical progression Binomial coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equal to zero factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Free the equation Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots last term least common multiple letter logarithm monomials multiplied number of real number of terms polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem subtracted Theorem unity unknown quantity variable whence
Popular passages
Page 48 - In any proportion the terms are in proportion by Composition and Division ; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Page 266 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 55 - There is a number consisting of two digits, the second of which is greater than the first, and if the number be divided by the sum of its digits, the quotient is 4...
Page 192 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.
Page 130 - The rule of art. 28, applied to this case, in which the factors are all equal, gives for the coefficient of the required power the same power of the given coefficient, and for the exponent of each letter the given exponent added to itself as many times as there are units in the exponent of the required power. Hence...
Page 47 - Whence it follows that the sum of the antecedents is to their difference as the sum of the consequents is to their difference...
Page 266 - The logarithm of the quotient is equal to the logarithm of the dividend, diminished by the logarithm of the divisor.
Page 127 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 230 - A complete equation cannot have a greater number of positive roots than there are variations in the...
Page 69 - Ans. — ; — . m-\-n 13. Divide the number 46 into two parts, so that when the one is divided by 7, and the other by 3, the sum of the quotients = 10. Ans. 28 and 18. 14. All my journeyings taken together, says a...