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 vii
... Figure of Ellipse investigated 156 Geometrical construction for the Axes ( see also p . 168 ) 156 Ordinates of Ellipse in given ratio to those of concentric Circle 157 Figure of Hyperbola 158 Conjugate Hyperbola 159 Asymptotes defined ...
... Figure of Ellipse investigated 156 Geometrical construction for the Axes ( see also p . 168 ) 156 Ordinates of Ellipse in given ratio to those of concentric Circle 157 Figure of Hyperbola 158 Conjugate Hyperbola 159 Asymptotes defined ...
Страница xv
... Figure formed by six Points on a Conic On systems of Tangential Co - ordinates • On Mr. Casey's form of the Equation of a Conic having double contact with a given one and touching three others On the Problem to describe a Conic under ...
... Figure formed by six Points on a Conic On systems of Tangential Co - ordinates • On Mr. Casey's form of the Equation of a Conic having double contact with a given one and touching three others On the Problem to describe a Conic under ...
Страница 2
... figure are x = a , y = 0 ; that those of the point N are x = 0 , y = b ; and of the origin itself are x = 0 , y = 0 . 3. In order that the equations x = a , y = b should only be satisfied by one point , it is necessary to pay attention ...
... figure are x = a , y = 0 ; that those of the point N are x = 0 , y = b ; and of the origin itself are x = 0 , y = 0 . 3. In order that the equations x = a , y = b should only be satisfied by one point , it is necessary to pay attention ...
Страница 3
... figure , the angle YOX oblique and = w , then and or , PSQ = 180 ° - w , PQ * = PS " + QS2-2PS.QS.cos PSQ , - PQ2 = ( y ' —y " ) " + ( x ' — x ' ) 2 + 2 ( y ' - y " ) ( x - x " ) cosw . - Similarly , the square of the distance of a ...
... figure , the angle YOX oblique and = w , then and or , PSQ = 180 ° - w , PQ * = PS " + QS2-2PS.QS.cos PSQ , - PQ2 = ( y ' —y " ) " + ( x ' — x ' ) 2 + 2 ( y ' - y " ) ( x - x " ) cosw . - Similarly , the square of the distance of a ...
Страница 7
... figure the angles a , B , w are all measured on the same side of Ox ; and a ' , B ' , w , all on the same side of Oy . If any of these angles lie on the opposite side it must be given a negative sign . Thus , if OY lie to the left of Oy ...
... figure the angles a , B , w are all measured on the same side of Ox ; and a ' , B ' , w , all on the same side of Oy . If any of these angles lie on the opposite side it must be given a negative sign . Thus , if OY lie to the left of Oy ...
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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