A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 - Algebra |
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Page ix
... fractions with compound deno- minators into partial fractions 294 308 CHAPTER XL . On the assumption and determination of series 316 CHAPTER XLI . On the solution and theory of cubic equations . 326 CHAPTER XLII . On the solution and ...
... fractions with compound deno- minators into partial fractions 294 308 CHAPTER XL . On the assumption and determination of series 316 CHAPTER XLI . On the solution and theory of cubic equations . 326 CHAPTER XLII . On the solution and ...
Page 25
... fraction from 1 or from its equivalent ō ' having a b . a the same denominator with , ( Art . 128 ) , which gives us Б or its equivalent ( a - b ) b for the coefficient of x in the re- mainder . x - a ( a - b ) ( 5 ) = 1 - - ( a - b ) b ...
... fraction from 1 or from its equivalent ō ' having a b . a the same denominator with , ( Art . 128 ) , which gives us Б or its equivalent ( a - b ) b for the coefficient of x in the re- mainder . x - a ( a - b ) ( 5 ) = 1 - - ( a - b ) b ...
Page 27
... fraction in which it origi- nates : but the corresponding aggregates of such terms , in the The transi- divergent series , will bear no such relation to it , being always convergent different in sign and more and more different in ...
... fraction in which it origi- nates : but the corresponding aggregates of such terms , in the The transi- divergent series , will bear no such relation to it , being always convergent different in sign and more and more different in ...
Page 28
... fraction a2 + x2 a + x > x2 + a2 x + a is identical in value with we must adopt , in Arithmetical Algebra , in dividing its numerator by the denominator , that form of the fraction which secures the arrangement of its terms in the order ...
... fraction a2 + x2 a + x > x2 + a2 x + a is identical in value with we must adopt , in Arithmetical Algebra , in dividing its numerator by the denominator , that form of the fraction which secures the arrangement of its terms in the order ...
Page 35
... fraction ( Art . 92 ) . If the dividend be concrete and the divisor an abstract number or numerical fraction , the quotient is a concrete quantity of the same kind with the dividend ( Art . 590 ) . If the dividend and divisor be ...
... fraction ( Art . 92 ) . If the dividend be concrete and the divisor an abstract number or numerical fraction , the quotient is a concrete quantity of the same kind with the dividend ( Art . 590 ) . If the dividend and divisor be ...
Common terms and phrases
A₁ angle of transfer application arith Arithmetical Algebra assumed becomes biquadratic equation Chapter coefficients common divisor considered corresponding cosē cosecant cotangent cube roots cubic equation denote determined divergent series divisor equa equal equisinal equivalent forms examples expression factors figure follows formula fraction geometrical angle given in Art goniometrical angle greater identical inasmuch indeterminate infinity involve last Article less likewise logarithms magnitude and position metical multiple negative nth roots operations period primitive equation primitive line problem proposition quadratic quotient radius ratio replace represent right angles shewn sides similar manner sinē sine and cosine solution square root subtraction successive Symbolical Algebra tangent tion triangle unknown quantities values whole number zero
Popular passages
Page 88 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 235 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Page 235 - The logarithm of a product is the sum of the logarithms of its factors.
Page 248 - The sides of a triangle are proportional to the sines of the opposite angles.
Page 455 - Inquiry into the Validity of a Method recently proposed by George B. Jerrard, Esq., for Transforming and Resolving Equations of Elevated Degrees: undertaken at the request of the Association by Professor Sir WR Hamilton.
Page 359 - HAMILTON. A publication which is justly distinguished for the originality and elegance of its contributions to every department of analysis.
Page 21 - The coefficient of the quotient must be, found by dividing the coefficient of the dividend by that of the divisor ; and 2.
Page 166 - Given the sines and cosines of two angles, to find the sine and cosine of their sum or difference.
Page 395 - ... and it is in this sense, and in this sense only, that...
Page 262 - Fink not only discovered the law of tangents, but pointed out its principal application; namely, to aid in solving a triangle when two sides and the included angle are given.