## A Treatise on Algebra |

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### Common terms and phrases

algebraic arithmetical progression binomial binomial theorem cent coefficient common denominator common difference compound interest continued fraction cube root decimal denote digits Divide the number dividend divisible dollars equa equal equation whose roots EXAMPLES exponent expression Extract the square factors figure Find the cube Find the fifth Find the fourth Find the number Find the square Find the sum find the values following RULE fourth power geometrical progression Given greatest common divisor Hence indicates infinite series last term least common multiple less logarithm miles monomial Multiply negative nth root number of terms obtain polynomial positive preceding Prob problem quotient radical sign ratio real roots Reduce remainder represent Resolve result second degree second term Solve the equation square root Sturm's Theorem subtract suppose surd third tion unity unknown quantity whence whole number zero

### Popular passages

Page 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.

Page 141 - 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 39 - ... the square of the second. In the second case, (ab)2 = a?-2ab + bi. (2) That is, the square of the difference of two numbers 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 54 - Divide the less number by the remainder, the last divisor by the last remainder, and so on, till nothing remains. The last divisor will be the greatest common divisor sought.

Page 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.

Page 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.

Page 227 - In arithmetical progression there are five parts to be considered, viz : the first term, the last term, the number of terms, the common difference, and the sum of all the terms.

Page 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.

Page 220 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.

Page 202 - A , where m=c 9. Find two numbers such that their sum, their product, and the difference of their squares may be all equal to one another.