A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 - Algebra |
From inside the book
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Page 27
... Convergent whose terms perpetually diminish and become ultimately zero , gent series . are called convergent series : whilst those whose terms perpetually increase , and which exclusively belong to Symbolical Algebra , are called ...
... Convergent whose terms perpetually diminish and become ultimately zero , gent series . are called convergent series : whilst those whose terms perpetually increase , and which exclusively belong to Symbolical Algebra , are called ...
Page 28
... convergent or divergent according as a is greater or less than a but if we reverse the order of the symbols , dividing a2 + x2 by a + x , we get the series a − x + 2x2 2x3 2x * + a a2 u3 - & c .... which is convergent or divergent ...
... convergent or divergent according as a is greater or less than a but if we reverse the order of the symbols , dividing a2 + x2 by a + x , we get the series a − x + 2x2 2x3 2x * + a a2 u3 - & c .... which is convergent or divergent ...
Page 71
... Convergent would be recognized in Arithmetical Algebra , is that in which gent series . they follow the order of their magnitude , Art . 646 : thus , if a be greater than x , it is the first ( 1 ) of these series only , which is convergent ...
... Convergent would be recognized in Arithmetical Algebra , is that in which gent series . they follow the order of their magnitude , Art . 646 : thus , if a be greater than x , it is the first ( 1 ) of these series only , which is convergent ...
Page 116
... convergent : if greater than 1 , it is divergent : and the point of change from divergency to convergency , or the contrary , will take place in the ( 1 + r ) th term , where r is that whole number , which is next greater than ( n + 1 ) ...
... convergent : if greater than 1 , it is divergent : and the point of change from divergency to convergency , or the contrary , will take place in the ( 1 + r ) th term , where r is that whole number , which is next greater than ( n + 1 ) ...
Page 117
... convergent 38 from its second term : if n - 3 and x = 11 we find 12 11 ( −3 + 1 ) 12 r = = 22 , 11 1 12 13 and the convergency begins from the 23rd term : if n = and 4 4 we have a point of convergency when r = 3 , and , sub- 3 ...
... convergent 38 from its second term : if n - 3 and x = 11 we find 12 11 ( −3 + 1 ) 12 r = = 22 , 11 1 12 13 and the convergency begins from the 23rd term : if n = and 4 4 we have a point of convergency when r = 3 , and , sub- 3 ...
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.