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
... Angles it makes with Axes Expression for the Angles a Line makes with Axes 20 Angle between two Lines Equation of Line joining two given Points Condition that three Points shall be on one Right Line Co - ordinates of Intersection of two ...
... Angles it makes with Axes Expression for the Angles a Line makes with Axes 20 Angle between two Lines Equation of Line joining two given Points Condition that three Points shall be on one Right Line Co - ordinates of Intersection of two ...
Страница v
... Angle between two Lines given by a single Equation Equation of Bisectors of Angles between these Lines PAGE 67 68 69 70 71 • 222 72 74 74 Condition that Equation of second Degree should represent Right Lines ( see also pp . 144 , 148 ...
... Angle between two Lines given by a single Equation Equation of Bisectors of Angles between these Lines PAGE 67 68 69 70 71 • 222 72 74 74 Condition that Equation of second Degree should represent Right Lines ( see also pp . 144 , 148 ...
Страница vii
... Angle between Conjugate Diameters 164 Locus of intersection of Tangents which cut at right Angles ( see also pp . 161 , 258 , 339 ) . 166 Supplemental Chords 166 To construct a pair of Conjugate Diameters inclined at a given Angle 166 ...
... Angle between Conjugate Diameters 164 Locus of intersection of Tangents which cut at right Angles ( see also pp . 161 , 258 , 339 ) . 166 Supplemental Chords 166 To construct a pair of Conjugate Diameters inclined at a given Angle 166 ...
Страница viii
... Angles 175 • Tangents at any Point equally inclined to Tangent to Confocal conic through the Point 176 Locus of foot of Focal Perpendicular on Tangent 176 · Angle subtended at the Focus by a Chord , bisected by Line joining Focus to its ...
... Angles 175 • Tangents at any Point equally inclined to Tangent to Confocal conic through the Point 176 Locus of foot of Focal Perpendicular on Tangent 176 · Angle subtended at the Focus by a Chord , bisected by Line joining Focus to its ...
Страница ix
... angle between tangents to ellipse from any point Radii Vectores through Foci have equal difference of Reciprocals Examples on Parabola Three Perpendiculars of Triangle formed by three Tangents intersect on 201 • 201 201 Directrix ( see ...
... angle between tangents to ellipse from any point Radii Vectores through Foci have equal difference of Reciprocals Examples on Parabola Three Perpendiculars of Triangle formed by three Tangents intersect on 201 • 201 201 Directrix ( see ...
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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