A Treatise on Algebra |
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Common terms and phrases
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
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 216 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion. Let ad— be.
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 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 282 - 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.
Page 192 - In a parcel which contains 24 coins of silver and copper, each silver coin is worth as many cents as there are copper coins, and each copper coin is worth as many cents as there are silver coins ; and the whole are worth 2 dollars and 16 cents.
Page 293 - To find any root of a given number, divide the logarithm of the number by the index of the root. The quotient is the logarithm of the root.
Page 220 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
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.