A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric MethodsLongmans, Green, and Company, 1879 - 399 страници |
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Страница ix
... Contact having double contact 226 Osculating Circle defined 227 Expressions and construction for Radius of Curvature ( see also pp . 234 , 242 , 374 ) 228 If a Circle intersect a Conic , chords of intersectioa nre equally inclined to ...
... Contact having double contact 226 Osculating Circle defined 227 Expressions and construction for Radius of Curvature ( see also pp . 234 , 242 , 374 ) 228 If a Circle intersect a Conic , chords of intersectioa nre equally inclined to ...
Страница x
... double contact with each other 234 234 Every Parabola has a Tangent at infinity ( see also p . 329 ) Similar and ... double contact with a third 242 Diagonals of inscribed and circumscribed Quadrilateral pass through the same Point 242 ...
... double contact with each other 234 234 Every Parabola has a Tangent at infinity ( see also p . 329 ) Similar and ... double contact with a third 242 Diagonals of inscribed and circumscribed Quadrilateral pass through the same Point 242 ...
Страница xi
... double contact with a third , its Chord of contact passes through one or two fixed Points 262 · touching four Lines Equation of a Conic having double contact with two given Conics · 262 262 · Locus of a Point whence sum or difference of ...
... double contact with a third , its Chord of contact passes through one or two fixed Points 262 · touching four Lines Equation of a Conic having double contact with two given Conics · 262 262 · Locus of a Point whence sum or difference of ...
Страница xii
... double contact with a given one 282 Polar of one Circle with regard to another 283 · Reciprocation of Theorems concerning Angles at Focus 284 · Envelope of Asymptotes of Hyperbolas having same Focus and Directrix Reciprocals of equal ...
... double contact with a given one 282 Polar of one Circle with regard to another 283 · Reciprocation of Theorems concerning Angles at Focus 284 · Envelope of Asymptotes of Hyperbolas having same Focus and Directrix Reciprocals of equal ...
Страница xiv
... double contact Condition that they should touch each other 356 356 To draw a Conic having double contact with a given one , and touching three other such Conics 356 • Four Conics having double contact with S , and passing through three ...
... double contact Condition that they should touch each other 356 356 To draw a Conic having double contact with a given one , and touching three other such Conics 356 • Four Conics having double contact with S , and passing through three ...
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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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