A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 - Algebra |
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Page 127
... period of n terms may be formed , which is de- pendent upon those roots of 1 different from 1 , which are , severally denominated by the prime factors of n . 711. The roots of the equation XPq 1 = 0 ( 1 ) period and their number . The ...
... period of n terms may be formed , which is de- pendent upon those roots of 1 different from 1 , which are , severally denominated by the prime factors of n . 711. The roots of the equation XPq 1 = 0 ( 1 ) period and their number . The ...
Page 128
... period of - the base of pq terms of the roots of the equation x2 . 1 = 0 . complete period of the roots of r " - 1 = 0 . The roots of 16 - 1 = 0 . In the first place every term of the period aß , ( aß ) , ( aß ) 3 ...... . ( a ß3 ) o1 ...
... period of - the base of pq terms of the roots of the equation x2 . 1 = 0 . complete period of the roots of r " - 1 = 0 . The roots of 16 - 1 = 0 . In the first place every term of the period aß , ( aß ) , ( aß ) 3 ...... . ( a ß3 ) o1 ...
Page 129
... period which they -10 , which is different from 1 , and ẞ one of the ph roots form . of a , we shall find that the p roots of the equation a13 - 1 = 0 may be represented by the terms of the period whose base is aß . For the terms of this ...
... period which they -10 , which is different from 1 , and ẞ one of the ph roots form . of a , we shall find that the p roots of the equation a13 - 1 = 0 may be represented by the terms of the period whose base is aß . For the terms of this ...
Page 130
... period of 2n terms will a , a2 , a3 , 2n - 1 2n a express the whole series of its roots . For a " = - 1 , ( a3 ) ... period a , a3 , a3 ... ... asn are different from each other : and since they are n in number , they form all the roots of ...
... period of 2n terms will a , a2 , a3 , 2n - 1 2n a express the whole series of its roots . For a " = - 1 , ( a3 ) ... period a , a3 , a3 ... ... asn are different from each other : and since they are n in number , they form all the roots of ...
Page 131
... period is terms of the period , the last or nth term being 1 : but it will altered by likewise be found that the terms of all these periods follow different order : thus , if in the period a , a2 , a3 , a ' , a3 , ao , 1 ( 1 ) , a ...
... period is terms of the period , the last or nth term being 1 : but it will altered by likewise be found that the terms of all these periods follow different order : thus , if in the period a , a2 , a3 , a ' , a3 , ao , 1 ( 1 ) , a ...
Common terms and phrases
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
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.