A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric MethodsLongmans, Green, Reader, and Dyer, 1869 - 377 páginas |
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Página vi
... Quantities unchanged by Inversion Equation of Circle cutting three at right Angles ( see pp . 128 , 347 ) 113 114 114 · 115 CHAPTER IX . THE CIRCLE - ABRIDGED NOTATION . Equation of Circle circumscribing a Quadrilateral • Equation of ...
... Quantities unchanged by Inversion Equation of Circle cutting three at right Angles ( see pp . 128 , 347 ) 113 114 114 · 115 CHAPTER IX . THE CIRCLE - ABRIDGED NOTATION . Equation of Circle circumscribing a Quadrilateral • Equation of ...
Página 4
... quantities x , y . √ ( 50 ) Ans . x = , y , and the common distance is 3 6. The distance between two points , being expressed in the form of a square root , is necessarily susceptible of a double sign . If the distance PQ , measured ...
... quantities x , y . √ ( 50 ) Ans . x = , y , and the common distance is 3 6. The distance between two points , being expressed in the form of a square root , is necessarily susceptible of a double sign . If the distance PQ , measured ...
Página 12
... quantities x , y ; and an inde- finite number of systems of values of x and y can be found which will satisfy the given equation . And yet the co - ordinates of any point taken at random will not satisfy it . The assemblage then of ...
... quantities x , y ; and an inde- finite number of systems of values of x and y can be found which will satisfy the given equation . And yet the co - ordinates of any point taken at random will not satisfy it . The assemblage then of ...
Página 18
... quantities a and b . For example , the equation х + 2 = 1 , which cuts off positive intercepts on both axes , re- - a b X presents the line MN on the preceding figure ; - = 1 , cutting α off a positive intercept on the axis of x , and a ...
... quantities a and b . For example , the equation х + 2 = 1 , which cuts off positive intercepts on both axes , re- - a b X presents the line MN on the preceding figure ; - = 1 , cutting α off a positive intercept on the axis of x , and a ...
Página 20
... quantities = 1 . Hence we learn , that B are re- A and √ ( A2 + B2 ) √ ( A2 + B2 ) spectively the cosine and sine of the angle which the per- pendicular from the origin on the line ( Ax + By + C = 0 ) makes with the axis of x , and ...
... quantities = 1 . Hence we learn , that B are re- A and √ ( A2 + B2 ) √ ( A2 + B2 ) spectively the cosine and sine of the angle which the per- pendicular from the origin on the line ( Ax + By + C = 0 ) makes with the axis of x , and ...
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Términos y frases comunes
anharmonic ratio asymptotes ax² axes bisected bisectors chord of contact circumscribing coefficients common tangents condition conic section conjugate diameters corresponding cos² denote determine directrix double contact drawn ellipse equal find the co-ordinates find the equation find the locus fixed lines fixed point foci focus four points given circles given line given point Hence hyperbola imaginary points infinite distance inscribed intercept joining the points last Article length line at infinity line joining line meets meet the curve middle points origin parabola parallel Pascal's theorem perpendicular point of contact point x'y points at infinity points of intersection polar polar equation pole proved quadratic quadrilateral radical axis radius vector rectangle right angles right line second degree sides sin² square substituting tangential equation theorem values vanish vertex vertices