A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 |
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Σελίδα ix
... assumption and determination of series 316 CHAPTER XLI . On the solution and theory of cubic equations . 326 CHAPTER XLII . On the solution and theory of biquadratic equations 346 CHAPTER XLIII . On the solution and reduction of recurring.
... assumption and determination of series 316 CHAPTER XLI . On the solution and theory of cubic equations . 326 CHAPTER XLII . On the solution and theory of biquadratic equations 346 CHAPTER XLIII . On the solution and reduction of recurring.
Σελίδα 73
... cubic , biquadratic and higher roots , will admit of a corresponding generalization , by the use of the cubic , biquadratic and higher roots of 1 and -1 : the further consideration of such signs , and of their symbolical properties ...
... cubic , biquadratic and higher roots , will admit of a corresponding generalization , by the use of the cubic , biquadratic and higher roots of 1 and -1 : the further consideration of such signs , and of their symbolical properties ...
Σελίδα 96
... cubic and biquadratic equations would be as follows . ( 1 ) x - p = 0 , ( 2 ) x2 - px + q = 0 , ( 3 ) x3 - px2 + qx − r = 0 , ( 4 ) x1- px3 + qx2 − r x + s = 0 : - and similarly for equations of the fifth , sixth and higher orders ...
... cubic and biquadratic equations would be as follows . ( 1 ) x - p = 0 , ( 2 ) x2 - px + q = 0 , ( 3 ) x3 - px2 + qx − r = 0 , ( 4 ) x1- px3 + qx2 − r x + s = 0 : - and similarly for equations of the fifth , sixth and higher orders ...
Σελίδα 102
... ax + b and c : but not necessarily when they are of the form x2 + ax + d and bx + c , inasmuch as it will generally require the solution of a cubic equation to determine the value of d . 9x2 And 16 + 24x + 256 is a complete 102.
... ax + b and c : but not necessarily when they are of the form x2 + ax + d and bx + c , inasmuch as it will generally require the solution of a cubic equation to determine the value of d . 9x2 And 16 + 24x + 256 is a complete 102.
Σελίδα 120
... cubic and higher roots , and which , like those we have already considered , are capable , as we shall pro- Evolution . ceed to shew , of being correctly expressed or symbolized by the multiple symbolical values of the cubic and higher ...
... cubic and higher roots , and which , like those we have already considered , are capable , as we shall pro- Evolution . ceed to shew , of being correctly expressed or symbolized by the multiple symbolical values of the cubic and higher ...
Συχνά εμφανιζόμενοι όροι και φράσεις
A₁ angle of transfer application arith Arithmetical Algebra assumed becomes biquadratic equation Chapter coefficients common divisor considered corresponding cos² 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 sin² sine and cosine solution square root subtraction successive Symbolical Algebra tangent tion triangle unknown quantities values whole number zero
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 235 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Σελίδα 235 - The logarithm of a product is the sum of the logarithms of its factors.
Σελίδα 248 - The sides of a triangle are proportional to the sines of the opposite angles.
Σελίδα 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.
Σελίδα 359 - HAMILTON. A publication which is justly distinguished for the originality and elegance of its contributions to every department of analysis.
Σελίδα 21 - The coefficient of the quotient must be, found by dividing the coefficient of the dividend by that of the divisor ; and 2.
Σελίδα 166 - Given the sines and cosines of two angles, to find the sine and cosine of their sum or difference.
Σελίδα 395 - ... and it is in this sense, and in this sense only, that...
Σελίδα 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.