A Treatise on AlgebraHarper & Brothers, 1886 - 384 páginas |
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Términos y frases comunes
algebraic arithmetical progression binomial binomial theorem cent Clearing of fractions coefficient common denominator common difference continued fraction cube root decimal denote Divide the number dividend divisible dollars equa equal equation whose roots equations containing EXAMPLES exponent expression factors figure Find the cube Find the fourth Find the number Find the square Find the sum find the values following RULE four fourth power geometrical progression Given greatest common divisor Hence indicates infinite series last term least common multiple less logarithm method monomial Multiply negative nth root number of terms obtain polynomial positive pounds preceding Prob problem quotient radical sign ratio real roots Reduce remainder represent Resolve result second degree second term simultaneous equations Solve the equation square root Sturm's Theorem subtract suppose surd third three numbers tion unity unknown quantity whence whole number zero
Pasajes populares
Página 72 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Página 46 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Página 294 - Hence, to involve a number by logarithms, we have the following RULE. Multiply the logarithm of the number by the exponent of the power required.
Página 181 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left. How much wine did he draw each time ? 50.
Página 148 - 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.
Página 284 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Página 258 - We may obtain the sixth root by extracting the cube root of the square root, or the square root of the cube root. It is, however, best to extract the roots of the lowest degrees first, because the operation is less laborious. We may obtain the eighth root by extracting the square root three times successively.
Página 371 - The conception of a force acting directly as the quantity of matter, and inversely as the square of the distance...
Página 204 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Página 139 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.