A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 |
Fra bogen
Resultater 1-5 af 37
Side 96
... cubic and biquadratic equations would be as follows . ( 1 ) x - p = 0 , ( 2 ) ... equation may be solved , by processes which have tion may be solved already ... equation : factors . and it is merely necessary to solve the several equations ...
... cubic and biquadratic equations would be as follows . ( 1 ) x - p = 0 , ( 2 ) ... equation may be solved , by processes which have tion may be solved already ... equation : factors . and it is merely necessary to solve the several equations ...
Side 102
... equation ) , as follows : xa + px3 + q x2 + rx + s 12 { 22 + 2 - 3 ( 22 - 9 ) 212 + pr3 + p2x2 4 212+ px -q - -q 4 ) ... cubic equation to determine the value of d . 9x2 And 16 + 24x + 256 is a complete 102.
... equation ) , as follows : xa + px3 + q x2 + rx + s 12 { 22 + 2 - 3 ( 22 - 9 ) 212 + pr3 + p2x2 4 212+ px -q - -q 4 ) ... cubic equation to determine the value of d . 9x2 And 16 + 24x + 256 is a complete 102.
Side 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 ... equation - 1 ...
... 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 ... equation - 1 ...
Side 179
... formula in Art . 774 , that = sin 0 = 2 cos sin = 4 cos2 sin sin 20 3 3 - sin 3 ( replacing sin 20 by 2 cos -4 ( 1 - six ) sin - in = sin2 3 sin 5 ) a cubic equation , whose roots are sin 3 where is the least angle whose sine is of the ...
... formula in Art . 774 , that = sin 0 = 2 cos sin = 4 cos2 sin sin 20 3 3 - sin 3 ( replacing sin 20 by 2 cos -4 ( 1 - six ) sin - in = sin2 3 sin 5 ) a cubic equation , whose roots are sin 3 where is the least angle whose sine is of the ...
Side 326
... , if we make x = a 3 y + we get x3 = y3 + ay2 + a2y + 3 27 ' - a x2 = - ay3 — 2ay a3 3 ab + bx = + by + 3 - C C. Adding together the several terms on each side of the CHAPTER XLI On the solution and theory of cubic equations.
... , if we make x = a 3 y + we get x3 = y3 + ay2 + a2y + 3 27 ' - a x2 = - ay3 — 2ay a3 3 ab + bx = + by + 3 - C C. Adding together the several terms on each side of the CHAPTER XLI On the solution and theory of cubic equations.
Almindelige termer og sætninger
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
Populære passager
Side 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.
Side 235 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Side 235 - The logarithm of a product is the sum of the logarithms of its factors.
Side 248 - The sides of a triangle are proportional to the sines of the opposite angles.
Side 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.
Side 359 - HAMILTON. A publication which is justly distinguished for the originality and elegance of its contributions to every department of analysis.
Side 21 - The coefficient of the quotient must be, found by dividing the coefficient of the dividend by that of the divisor ; and 2.
Side 166 - Given the sines and cosines of two angles, to find the sine and cosine of their sum or difference.
Side 395 - ... and it is in this sense, and in this sense only, that...
Side 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.