## A Treatise on Algebra |

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### Common terms and phrases

according added algebraic already arithmetical assumed becomes binomial called cents coefficients complete containing continued cube root denominator derived difference distance Divide dividend divisible divisor employed equal equation example exponent expression factors fifth figure find the values four fraction function geometrical give Given greater Hence hour increased infinite series involving least less letters logarithm manner means method miles multiplied negative obtain operation original perform places polynomial positive preceding principle Prob problem progression proportion proposed PROPOSITION quotient radical raised ratio Reduce remainder represent Required Required the square result RULE second term seen simple solution solved square root substitute subtract successive suppose surd taken term third tion traveled unity unknown quantity variation verified Whence whole

### Popular passages

Page 34 - 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 33 - 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 87 - 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 328 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

Page 29 - 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 134 - The nth root of the product of any number of factors is equal to the product of the nth roots of those factors.

Page 164 - 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 27 - The operation consists in repeating the multiplicand as many times as there are units in the multiplier.

Page 346 - A Grammar of the Greek Language, for the Use of Schools and Colleges. By Charles Anthon, LL.D.

Page 209 - 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.