A Treatise on Algebra: Symbolical algebra and its applications to the geometry of positionsJ. & J. J. Deighton, 1845 - Algebra |
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Page 89
... circle produced A geome- from whence the tangent drawn to the circle shall be equal blem . to a given line . Let AB ( 2c ) be the given chord , and CD ( 1 ) the given line : assume P to be the point in the chord BA pro- duced , from ...
... circle produced A geome- from whence the tangent drawn to the circle shall be equal blem . to a given line . Let AB ( 2c ) be the given chord , and CD ( 1 ) the given line : assume P to be the point in the chord BA pro- duced , from ...
Page 90
... circle , is equal in length to the given line CD ( 1 ) , and we denote PA , the assumed distance of P from A , by x : the conditions of the problem , which are involved in the general property of the tangent of a circle , shew that a ...
... circle , is equal in length to the given line CD ( 1 ) , and we denote PA , the assumed distance of P from A , by x : the conditions of the problem , which are involved in the general property of the tangent of a circle , shew that a ...
Page 91
... circle from the point P thus determined , is equal to the given line CD . We then subjoin the proof , by which the correctness of this construction , or synthesis , is established . : cesses of The processes of exposition in Geometry ...
... circle from the point P thus determined , is equal to the given line CD . We then subjoin the proof , by which the correctness of this construction , or synthesis , is established . : cesses of The processes of exposition in Geometry ...
Page 132
... circle r times , having marked every term of the period once , and once only , before we return to the first term : thus , if n = 7 and r = 2 , and if we arrange the terms of the period ment of the 0 , roots of a " — 1 where n is a ...
... circle r times , having marked every term of the period once , and once only , before we return to the first term : thus , if n = 7 and r = 2 , and if we arrange the terms of the period ment of the 0 , roots of a " — 1 where n is a ...
Page 134
... circle , where no regard is paid to the initial term : they will be found hereafter to be connected with the most important analytical theories * , and therefore deserve the most careful attention of the student . They form the basis of ...
... circle , where no regard is paid to the initial term : they will be found hereafter to be connected with the most important analytical theories * , and therefore deserve the most careful attention of the student . They form the basis of ...
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.