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 iii
... Transformation of Co - ordinates does not change Degree of an Equation Polar Co - ordinates PAGE 2 8 5 10 CHAPTER II . THE RIGHT LINE . Two Equations represent Points . A single Equation represents a Locus [ Geometric representation of ...
... Transformation of Co - ordinates does not change Degree of an Equation Polar Co - ordinates PAGE 2 8 5 10 CHAPTER II . THE RIGHT LINE . Two Equations represent Points . A single Equation represents a Locus [ Geometric representation of ...
Página vi
... X. GENERAL EQUATION OF SECOND DEGREE . Number of conditions which determine a Conic Transformation to Parallel Axes of Equation of second Degree 131 132 Discussion of Quadratic which determines Points where Line meets a vi CONTENTS .
... X. GENERAL EQUATION OF SECOND DEGREE . Number of conditions which determine a Conic Transformation to Parallel Axes of Equation of second Degree 131 132 Discussion of Quadratic which determines Points where Line meets a vi CONTENTS .
Página vii
... Transformation of general Equation to the centre Condition that it should represent right Lines Centre , the Pole of the Line at infinity ( see also p . 284 ) 149 150 150 Asymptotes of Curve 150 · · Equation of the Axes , how found 151 ...
... Transformation of general Equation to the centre Condition that it should represent right Lines Centre , the Pole of the Line at infinity ( see also p . 284 ) 149 150 150 Asymptotes of Curve 150 · · Equation of the Axes , how found 151 ...
Página viii
... Transformation of the Equation to the form y2 = px 184 Expression for Parameter of Parabola given by general Equation ditto , given lengths of two Tangents and contained Angle ( see also p . 203 ) 186 188 • • Parabola the limit of the ...
... Transformation of the Equation to the form y2 = px 184 Expression for Parameter of Parabola given by general Equation ditto , given lengths of two Tangents and contained Angle ( see also p . 203 ) 186 188 • • Parabola the limit of the ...
Página xii
... transformed from one origin to another Reciprocals with regard to a Parabola 280 281 • CHAPTER XVI . HARMONIC AND ANHARMONIC PROPERTIES . Anharmonic Ratio , when one Point infinitely distant 283 Centre the Pole of the Line at infinity ...
... transformed from one origin to another Reciprocals with regard to a Parabola 280 281 • CHAPTER XVI . HARMONIC AND ANHARMONIC PROPERTIES . Anharmonic Ratio , when one Point infinitely distant 283 Centre the Pole of the Line at infinity ...
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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