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 páginas |
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Página iv
... Pencil Homographic Systems of Lines Expression of Equation of any Right Line in terms of three given ones Harmonic Properties of a Quadrilateral proved ( see also p . 305 ) Homologous triangles : Centre and Axis of Homology Condition ...
... Pencil Homographic Systems of Lines Expression of Equation of any Right Line in terms of three given ones Harmonic Properties of a Quadrilateral proved ( see also p . 305 ) Homologous triangles : Centre and Axis of Homology Condition ...
Página xi
... pencils Envelope of Pole of a given Point with regard to a Conic having double contact with two given ones 259 260 260 260 Equation of Asymptotes of a Conic given by general Equation ( see also p . 328 ) Given three Points on Conic ...
... pencils Envelope of Pole of a given Point with regard to a Conic having double contact with two given ones 259 260 260 260 Equation of Asymptotes of a Conic given by general Equation ( see also p . 328 ) Given three Points on Conic ...
Página xii
... Pencil Lines from two fixed Points to a variable Point , how cut any Parallel to Asymptote 284 285 • · Parallels to Asymptotes through any Point on Curve , how cut any Diameter Anharmonic property of Tangents to Parabola 286 287 How any ...
... Pencil Lines from two fixed Points to a variable Point , how cut any Parallel to Asymptote 284 285 • · Parallels to Asymptotes through any Point on Curve , how cut any Diameter Anharmonic property of Tangents to Parabola 286 287 How any ...
Página 55
... pencil of four right lines meeting in a point O be intersected by any transverse right line in the four points A , P , P ' , B , then the ratio AP.P'B AP'.PB is constant , no matter how B P ' P A = p : the transverse line be drawn ...
... pencil of four right lines meeting in a point O be intersected by any transverse right line in the four points A , P , P ' , B , then the ratio AP.P'B AP'.PB is constant , no matter how B P ' P A = p : the transverse line be drawn ...
Página 56
... pencil . The pencil is a harmonic pencil when k = - 1 , for then the T angle AOB is divided internally and externally into parts whose sines are in the same ratio . Hence we have the important theo- rem , two lines whose equations are a ...
... pencil . The pencil is a harmonic pencil when k = - 1 , for then the T angle AOB is divided internally and externally into parts whose sines are in the same ratio . Hence we have the important theo- rem , two lines whose equations are a ...
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Términos y frases comunes
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