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 iii
... Polar Co - ordinates PAGE 2 8 5 10 CHAPTER II . THE RIGHT LINE . Two Equations represent Points . A single Equation represents a Locus [ Geometric representation of Equations Equation of a Right Line parallel to an Axis through the ...
... Polar Co - ordinates PAGE 2 8 5 10 CHAPTER II . THE RIGHT LINE . Two Equations represent Points . A single Equation represents a Locus [ Geometric representation of Equations Equation of a Right Line parallel to an Axis through the ...
Страница iv
... Polar Equation of a Right Line 2221888 31 32 32 33 34 36 36 CHAPTER III . EXAMPLES ON THE RIGHT LINE . Investigation of rectilinear Loci of Loci leading to Equations of Higher Degree Problems where it is proved that a Moveable Line ...
... Polar Equation of a Right Line 2221888 31 32 32 33 34 36 36 CHAPTER III . EXAMPLES ON THE RIGHT LINE . Investigation of rectilinear Loci of Loci leading to Equations of Higher Degree Problems where it is proved that a Moveable Line ...
Страница v
... Polar Equation of a Circle 86 87 CHAPTER VII . EXAMPLES ON CIRCLE . Circular Loci 88 Condition that intercept by Circle on a given Line may subtend a right Angle at a given Point If a Point A lie on the polar of B , B lies on the polar ...
... Polar Equation of a Circle 86 87 CHAPTER VII . EXAMPLES ON CIRCLE . Circular Loci 88 Condition that intercept by Circle on a given Line may subtend a right Angle at a given Point If a Point A lie on the polar of B , B lies on the polar ...
Страница vii
... Polar Class of a Curve , defined Harmonic Property of Polars ( see also p . 284 ) Polar properties of inscribed Quadrilateral ( see also p . 307 ) Equation of pair of Tangents from given Point to a Conic ( see also p . 257 ) Rectangles ...
... Polar Class of a Curve , defined Harmonic Property of Polars ( see also p . 284 ) Polar properties of inscribed Quadrilateral ( see also p . 307 ) Equation of pair of Tangents from given Point to a Conic ( see also p . 257 ) Rectangles ...
Страница viii
... Polar Equation , Focus being Pole ( see p . 309 ) . 177 · 178 Segments of Focal Chord have constant Harmonic Mean 179 • Origin of names Parabola , Hyperbola , and Ellipse ( see also p . 316 ) 180 ASYMPTOTES : how found 180 Intercepts on ...
... Polar Equation , Focus being Pole ( see p . 309 ) . 177 · 178 Segments of Focal Chord have constant Harmonic Mean 179 • Origin of names Parabola , Hyperbola , and Ellipse ( see also p . 316 ) 180 ASYMPTOTES : how found 180 Intercepts on ...
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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