An Elementary Treatise on Algebra: To which are Added Exponential Equations and LogarithmsJames Munroe and Company, 1860 - 284 σελίδες |
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126 become zero 3d root approximate values coefficient commensurable roots contain continued fraction continued product Corollary courier decimals deficient terms denote derivative dividend equal roots equal to zero Find the 3d Find the continued Find the greatest Find the square Find the sum Free the equation gallons given equation gives greatest common divisor Hence last term least common multiple letter logarithm monomials Multiply negative exponents nth root number of real number of terms Obtain one equation positive roots preceding article Problem proportion quantities in example Questions into Equations quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Solution Solve the equation square root Sturm's Theorem substitution subtracted suppressed Theorem three equations unity unknown quan unknown quantity whence wine
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 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.
Σελίδα 159 - A certain capital is let at 4 per cent. ; if we multiply the number of dollars in the capital, by the number of dollars in the interest for 5 months, we obtain 11?041§.
Σελίδα 172 - Ans. 15 and 26. 31. What two numbers are they, whose sum is a, and the sum of whose squares is b 1 Ans.
Σελίδα 232 - An equation of any degree whatever cannot have a greater number of positive roots than there are variations in the signs of Us terms, nor a greater number of negative roots than there are permanences of these signs.
Σελίδα 63 - A term may be transposed from one member of an equation to the other by changing its sign.
Σελίδα 45 - Given three terms of a proportion, to find the fourth. Solution. The following solution is immediately obtained from the test. When the required term is an extreme, divide the product of the means by the given extreme, and the quotient is the required extreme. When the required term is a mean, divide the product of the extremes by the given mean, and the quotient is the required mean.
Σελίδα 196 - 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.