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 страници |
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Страница iv
... Vertices Area of any Polygon • Condition that three Lines may meet in a Point ( see also Area of Triangle formed by three given Lines Equation of Line through the Intersection of two given Lines 28 29 30 p . 34 ) • Test that three ...
... Vertices Area of any Polygon • Condition that three Lines may meet in a Point ( see also Area of Triangle formed by three given Lines Equation of Line through the Intersection of two given Lines 28 29 30 p . 34 ) • Test that three ...
Страница vi
... vertex Tangential Equation of circumscribing Circle Conditions that general Equation should represent a Circle Radical Axis of two Circles in Trilinear Co - ordinates Equation of Circle inscribed in a Triangle Its Tangential Equation ...
... vertex Tangential Equation of circumscribing Circle Conditions that general Equation should represent a Circle Radical Axis of two Circles in Trilinear Co - ordinates Equation of Circle inscribed in a Triangle Its Tangential Equation ...
Страница x
... Vertex of Triangle whose sides touch a given Conic , and base Angles move on fixed Lines ( see also pp . 307 , 336 ) 239 • To inscribe in a Conic a Triangle whose sides pass through fixed Points ( see also pp . 261 , 269 , 289 ) ...
... Vertex of Triangle whose sides touch a given Conic , and base Angles move on fixed Lines ( see also pp . 307 , 336 ) 239 • To inscribe in a Conic a Triangle whose sides pass through fixed Points ( see also pp . 261 , 269 , 289 ) ...
Страница xi
... Vertex of a Triangle inscribed in one Conic , and whose sides touch one another ( see also p . 336 ) 246 • ENVELOPES , how found 247 Examples of Envelopes 248 · Formation of Trilinear Equation of a Conic from Tangential , and vice versa ...
... Vertex of a Triangle inscribed in one Conic , and whose sides touch one another ( see also p . 336 ) 246 • ENVELOPES , how found 247 Examples of Envelopes 248 · Formation of Trilinear Equation of a Conic from Tangential , and vice versa ...
Страница xii
... Vertices of circumscribing Quadrilateral 275 • Tangential Equation of Reciprocal Conic 374 Trilinear Equation given Focus and either three Points or three Tangents Reciprocation of Anharmonic Properties 276 • 275 Carnot's Theorem ...
... Vertices of circumscribing Quadrilateral 275 • Tangential Equation of Reciprocal Conic 374 Trilinear Equation given Focus and either three Points or three Tangents Reciprocation of Anharmonic Properties 276 • 275 Carnot's Theorem ...
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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