An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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126 become zero 3d root arithmetical progression Binomial Theorem coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equation x² 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 proportion 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 tity unity unknown quantity whence
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Page 119 - 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 40 - 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 260 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 47 - 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 184 - 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 55 - A term may be transposed from one member of an equation to the other by changing its sign.
Page 37 - Thus, in the, proportion a : b = b : c, b is a mean proportional between a and c, and ca third proportional to a and b.
Page 91 - What fraction is that, whose numerator being doubled, and the denominator increased by 7, the value becomes f ; but the denominator being doubled, and the numerator increased by 2, the value becomes f 1 Ans.
Page 188 - Hence, to find the sum, multiply the first term by the difference between unity and that power of the ratio whose exponent is equal to the number of terms, and divide the product by the difference between unity and the ratio. Examples in Geometrical Progression. 260. Corollary. The two equations...
Page 24 - I is the 5th line, multiplied by 7 in order to render its first term divisible by the first term of the divisor...