A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric MethodsLongmans, Green, and Company, 1879 - 399 páginas |
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Página vi
... Quantities unchanged by Inversion • CHAPTER IX . THE CIRCLE - ABRIDGED NOTATION . Equation of Circle circumscribing a Quadrilateral Equation of Circle circumscribing Triangle a , ß , y Geometrical meaning of the Equation Locus of Point ...
... Quantities unchanged by Inversion • CHAPTER IX . THE CIRCLE - ABRIDGED NOTATION . Equation of Circle circumscribing a Quadrilateral Equation of Circle circumscribing Triangle a , ß , y Geometrical meaning of the Equation Locus of Point ...
Página 4
... quantities x , y . Ans . x = , y , and the common distance is √ ( 50 ) • 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 . Ans . x = , y , and the common distance is √ ( 50 ) • 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 coordinates of any point taken at random will not satisfy it . The assemblage then of points ...
... 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 coordinates of any point taken at random will not satisfy it . The assemblage then of points ...
Página 18
... quantities a and b For example , the equation x y a + = 1 , which cuts off positive intercepts on both axes , re- presents the line MN on the preceding figure ; x y α b = 1 , cutting off a positive intercept on the axis of x , and a ...
... quantities a and b For example , the equation x y a + = 1 , which cuts off positive intercepts on both axes , re- presents the line MN on the preceding figure ; x y α b = 1 , cutting off a positive intercept on the axis of x , and a ...
Página 20
... quantities = 1 . Hence we learn that A and B are re- √ ( 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 that ...
... quantities = 1 . Hence we learn that A and B are re- √ ( 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 that ...
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Otras ediciones - Ver todas
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Sin vista previa disponible - 2015 |
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Sin vista previa disponible - 2016 |
Términos y frases comunes
anharmonic ratio asymptotes ax² axes bisected bisectors by² centre chord of contact circumscribing coefficients common tangents condition conic having double conic section conjugate diameters corresponding cos² denote determine directrix double contact drawn ellipse equal find the equation find the locus fixed line fixed point foci focus four points geometrically given conic given line given point Hence hyperbola imaginary points infinite distance inscribed intercept last Article 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 reciprocal rectangle right angles right line second degree sides sin² square substituting tangential equation theorem values vanish vertex vertices
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