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 |
Dentro del libro
Resultados 1-5 de 55
Página x
... Result of substituting the Coordinates of any Point in the Equation of a Conic Diameter of Circle circumscribing Triangle formed by two Tangents and their Chord 241 241 Property of Chords of Intersection of two Conics , each having ...
... Result of substituting the Coordinates of any Point in the Equation of a Conic Diameter of Circle circumscribing Triangle formed by two Tangents and their Chord 241 241 Property of Chords of Intersection of two Conics , each having ...
Página 11
... result of the form x = a , y = b , which , as was proved in the last chapter , represents a point . If the equations be of higher degree , they represent more points than one . For , eliminating y between the equations , we obtain an ...
... result of the form x = a , y = b , which , as was proved in the last chapter , represents a point . If the equations be of higher degree , they represent more points than one . For , eliminating y between the equations , we obtain an ...
Página 24
... result as before . COR . The equation of the line joining the point x'y ' to the origin is y'x = x'y . Ex . 1. Form the equations of the sides of a triangle , the coordinates of whose vertices are ( 2 , 1 ) , ( 3 , − 2 ) , ( — 4 , − 1 ) ...
... result as before . COR . The equation of the line joining the point x'y ' to the origin is y'x = x'y . Ex . 1. Form the equations of the sides of a triangle , the coordinates of whose vertices are ( 2 , 1 ) , ( 3 , − 2 ) , ( — 4 , − 1 ) ...
Página 26
... result shows ( Art . 7 ) that this point divides externally , in the ratio a'b : ab ' , the line joining the two middle points ( a , b ' ) , ( a ' , b ) . 32. To find the equation to rectangular axes of a right line passing through a ...
... result shows ( Art . 7 ) that this point divides externally , in the ratio a'b : ab ' , the line joining the two middle points ( a , b ' ) , ( a ' , b ) . 32. To find the equation to rectangular axes of a right line passing through a ...
Página 28
... result may be obtained geometrically . From the given point draw QR parallel to the given line , and QS perpen- dicular . Then OK = x ' , and OT will be x ' cosa . Again , since SQK = 8 , and QK = y ' , hence = RT = QS = y ' cosß ; x ...
... result may be obtained geometrically . From the given point draw QR parallel to the given line , and QS perpen- dicular . Then OK = x ' , and OT will be x ' cosa . Again , since SQK = 8 , and QK = y ' , hence = RT = QS = y ' cosß ; x ...
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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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