A Treatise on Algebra

Harper & brothers, 1846 - Algebra - 346 pages
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Contents

 Solution of Problems 79 SECTION VIII 93 By Comparison By Addition and Subtraction 108 Inequalities 116 SECTION X 122 Involution of Monomials Sign of the Result 133 To reduce a Rational Quantity to the Form of a Surd 140 To reduce Surds to a common Index 156 Solution of Pure Quadratics 163 Solution of Complete Quadratics 169 Solution of the Equation x2n + pxn 185 Discussion of the general Equation of the Second Degree 193 Discussion of particular Problems 200 Definitions Ratios compared with each other 214
 36 263 SECTION XVIII 265 To find the nth Term of a Series 271 SECTION XIX 278 203 295 SECTION XX 301 207 304 40 313 To find the Integral Roots of an Equation 314 210 316 Newtons Method of Approximation 321 212 336 45 340 242 5

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.