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2d Rem 3d root 4th power 4th root approximate values arithmetical mean arithmetical progression Binomial Theorem coefficient commensurable roots contains the highest continued fraction continued product Corollary deficient terms denote Divide dividend Elimination equal roots factor Find the 3d Find the 4th Find the continued Find the greatest Find the square Find the sum Free the equation Geometrical Progression given equation given number gives greatest common divisor Hence highest power integer last term least common multiple logarithm monomials number of terms obtained places of decimals Polynomial Theorem positive roots preceding article Problem quantities in example Questions into Equations quotient radical quantities radical signs ratio real root reduced remainder required equation required root Scholium second term Solution Solve the equation square root substitution subtracted tained term multiplied tity unity unknown quantity whence
Page 47 - 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 149 - 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 197 - Problem. To find the last term of an arithmetical progression when its first term, common difference, and number of terms are known. Solution. In this case a, r, and n are supposed to be known, and I is to be found.
Page 262 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 62 - A term may be transposed from one member of an equation to the other by changing its sign.
Page 44 - Arrange the terms in the statement so that the causes shall compose one couplet, and the effects the other, putting ( ) in the place of the required term. II. If the required term be an extreme, divide the product of the means by the given extreme ; if the required farm be a mean, divide the product of the extremes by the given mean.
Page 46 - Likewise, the sum of the antecedents is to their difference, as the sum of the consequents is to their difference.
Page 99 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes §; but the denominator being doubled, and the numerator increased by 2, the value becomes f?