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
... Section proved Algebraic Expression for Anharmonic Ratio of a 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 ) ...
... Section proved Algebraic Expression for Anharmonic Ratio of a 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 ) ...
Página xiii
... Conics The six Vertices of two self - conjugate Triangles lie on same Conic ( see also p . 329 ) Chord of a Conic passes through a fixed . Point , if the Angle it subtends at a fixed Point in Curve , has fixed Bisector Projections of ...
... Conics The six Vertices of two self - conjugate Triangles lie on same Conic ( see also p . 329 ) Chord of a Conic passes through a fixed . Point , if the Angle it subtends at a fixed Point in Curve , has fixed Bisector Projections of ...
Página 5
... section are obtained from those for internal section by changing the sign of the ratio : that is , by changing m : + n into m : -n . In fact , in the case of internal section , PR and RQ are measured in the same direction , and their ...
... section are obtained from those for internal section by changing the sign of the ratio : that is , by changing m : + n into m : -n . In fact , in the case of internal section , PR and RQ are measured in the same direction , and their ...
Página 6
... section . lx ' + mx " + nx " Ans . x = 1 + m + n , y = ly ' + my " + ny " " l + m + n TRANSFORMATION OF CO - ORDINATES . * 8. When we know the co - ordinates of a point referred to one pair of axes , it is frequently necessary to find ...
... section . lx ' + mx " + nx " Ans . x = 1 + m + n , y = ly ' + my " + ny " " l + m + n TRANSFORMATION OF CO - ORDINATES . * 8. When we know the co - ordinates of a point referred to one pair of axes , it is frequently necessary to find ...
Página 33
... section by Art . 31 , and then to substitute these values for x'y ' in the equation of Art . 28 , viz . , y — y ' = m ( x − x ' ) . The question , however , admits of an easier solution by the help of the following important principle ...
... section by Art . 31 , and then to substitute these values for x'y ' in the equation of Art . 28 , viz . , y — y ' = m ( x − x ' ) . The question , however , admits of an easier solution by the help of the following important principle ...
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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