A Treatise on Algebra |
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Common terms and phrases
a²-b² according to Art algebraic expression Arithmetic arithmetical progression ax² binomial called cents Charles Anthon coefficient Completing the square cube root denotes Divide the number dividend divisible dollars equation x² example extracting the square factors find the values following RULE fourth power fourth root fraction geometrical geometrical progression gives greater greatest common divisor Hence inequality infinite series last term less letters taken LL.D method miles monomial multiplicand multiplied nth root number of permutations number of terms obtain operation order of differences original equation polynomial positive preceding principles Prob problem proportion quadratic equations quotient radical quantities ratio Reduce remainder represent Required the number Required the square required to divide Resolve result second degree second term Sheep extra signifies solved square root subtract suppose surd theorem unity unknown quantity Whence whole number
Popular passages
Page 38 - 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 37 - THEOREM I. The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 91 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Page 332 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 33 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
Page 138 - The nth root of the product of any number of factors is equal to the product of the nth roots of those factors.
Page 168 - 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 31 - The operation consists in repeating the multiplicand as many times as there are units in the multiplier.
Page 4 - A Grammar of the Greek Language, for the Use of Schools and Colleges. By Charles Anthon, LL.D.
Page 213 - When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c., increasing the denomination still by unity, in any number of proportionals.