A Treatise on Algebra |
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Common terms and phrases
according to Art Algebra arithmetical progression binomial cent coefficients College Completing the square continued fraction contrary sign cube root denotes Divide the number dividend divisible dollars equa EXAMPLES exponent expression extracting the square factors figure Find the square find the values following RULE fourth power fourth root geometrical progression given equation greatest common divisor Hence inequality infinite series last term least common multiple less letters taken Loomis method monomial multiplied negative nth root number of terms obtain polynomial preceding principles Prob problem Professor of Mathematics proportional quadratic equations quotient radical quantities ratio real roots Reduce remainder Required the cube Required the number Required the square Required the sum result second degree second term solved square root substitute subtract surd THEOREM third three numbers tion tities unity unknown quantity values of x Whence whole number zero
Popular passages
Page 28 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Page 236 - 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 308 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 196 - Multiply the last term by the ratio, from the product subtract the first term, and divide the remainder by the ratio, less 1 ; the quotient will be the sum of the series required.
Page 200 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.
Page 142 - 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.
Page 38 - 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.
Page 50 - Reduce the fractions, if necessary, to a common denominator; add the numerators together, and place their sum over the common denominator.
Page 38 - ... the first term of the quotient ; multiply the divisor by this term, and subtract the product from the dividend. II. Then divide the first term of the remainder by the first term of the divisor...
Page 48 - To reduce fractions to a common denominator. RULE. Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.