A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 - Algebra |
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Page v
... give it with unusual fulness and detail : such roots may be considered as forming the connecting link between Arithmetical and Symbolical Algebra , without whose aid the two sciences could be very imperfectly separated from each other ...
... give it with unusual fulness and detail : such roots may be considered as forming the connecting link between Arithmetical and Symbolical Algebra , without whose aid the two sciences could be very imperfectly separated from each other ...
Page 25
... 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 _ ( a − b ) b2 _ & c . - x -b Ꮖ All the terms of this series , after the first , are negative . ( 6 ) VOL ...
... 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 _ ( a − b ) b2 _ & c . - x -b Ꮖ All the terms of this series , after the first , are negative . ( 6 ) VOL ...
Page 33
... give the interpretation Products of of the meaning of the product of four or more symbols repre- more sym- senting lines , or of two or more symbols representing areas , or of any other combinations of symbols representing lines , areas ...
... give the interpretation Products of of the meaning of the product of four or more symbols repre- more sym- senting lines , or of two or more symbols representing areas , or of any other combinations of symbols representing lines , areas ...
Page 45
... give 135 for the coefficient of the first term , which is the least common multiple of 27 and 15 . ( 5 ) x + 2x2 + 9 x2 + 2x + 3 7x311x + 15x + 9 7x + 3 the common divisor is x2- 2x + 3 . ( 6 ) 12x2 + 55x + 63 = = 4x + 9 : : 63 x3 ...
... give 135 for the coefficient of the first term , which is the least common multiple of 27 and 15 . ( 5 ) x + 2x2 + 9 x2 + 2x + 3 7x311x + 15x + 9 7x + 3 the common divisor is x2- 2x + 3 . ( 6 ) 12x2 + 55x + 63 = = 4x + 9 : : 63 x3 ...
Page 59
... give to those extended operations and to their results , such an interpretation as was consistent with the conditions which they were required to satisfy . In the further developement of this science we shall continue to be guided by ...
... give to those extended operations and to their results , such an interpretation as was consistent with the conditions which they were required to satisfy . In the further developement of this science we shall continue to be guided by ...
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.