A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic Andgeometric MethodsLongmans, Green and Company, 1879 - 399 páginas |
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Página iv
... Section proved Algebraic Expression for Anharmonic Ratio of a Pencil Homographic Systems of Lines 55 55 56 57 Expression of Equation of any Right Line in terms of three given ones 57 Harmonic Properties of a Quadrilateral proved ( see ...
... Section proved Algebraic Expression for Anharmonic Ratio of a Pencil Homographic Systems of Lines 55 55 56 57 Expression of Equation of any Right Line in terms of three given ones 57 Harmonic Properties of a Quadrilateral proved ( see ...
Página xiii
... Conic , lie on the same Conic , ( see also p . 343 ) 320 Projections of Properties concerning Right Angles 321 Locus ... Section is Ellipse , Hyperbola , or Parabola 327 + Origin of these Names 328 Every Parabola has a Tangent at an infinite ...
... Conic , lie on the same Conic , ( see also p . 343 ) 320 Projections of Properties concerning Right Angles 321 Locus ... Section is Ellipse , Hyperbola , or Parabola 327 + Origin of these Names 328 Every Parabola has a Tangent at an infinite ...
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 " l + m + n Ans . x = , y ly ' + my " + ny " " l + m + n TRANSFORMATION OF COORDINATES . 8. When we know the coordinates of a point referred to one pair of axes , it is frequently necessary to find its co ...
... section . lx ' + mx " + nx " l + m + n Ans . x = , y ly ' + my " + ny " " l + m + n TRANSFORMATION OF COORDINATES . 8. When we know the coordinates of a point referred to one pair of axes , it is frequently necessary to find its co ...
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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Otras ediciones - Ver todas
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Sin vista previa disponible - 2015 |
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Sin vista previa disponible - 2016 |
Términos y frases comunes
anharmonic ratio asymptotes ax² axes bisected bisector by² centre chord of contact circumscribing coefficients common tangents condition conic having double conic section conic touching conjugate diameters corresponding cos² denote determine directrix double contact drawn ellipse equal find the equation find the locus fixed line fixed point foci focus four points given line given point Hence hyperbola imaginary points infinite distance inscribed intercept last Article 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 reciprocal rectangle represents right angles right line second degree sides sin² square substituting tangential equation theorem transform values vanish vertex vertices µß
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