An Elementary Treatise on Conic Sections |
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Page vii
... AXES . ANHARMONIC RATIOS OR CROSS RATIOS . INVOLUTION CHAPTER IV . THE CIRCLE Examples on Chapter IV CHAPTER V. THE PARABOLA Examples on Chapter V CHAPTER VI . THE ELLIPSE Examples on Chapter VI CHAPTER VII . THE HYPERBOLA Examples on ...
... AXES . ANHARMONIC RATIOS OR CROSS RATIOS . INVOLUTION CHAPTER IV . THE CIRCLE Examples on Chapter IV CHAPTER V. THE PARABOLA Examples on Chapter V CHAPTER VI . THE ELLIPSE Examples on Chapter VI CHAPTER VII . THE HYPERBOLA Examples on ...
Page viii
... axes of the conic 199 · Meaning of S - λS ' = 0 , S - λuv = 0 and S - λu2 = 0 200 Equation of a pair of tangents 202 Equation of the director - circle Four foci of a coņic 203 204 Eccentricities of a conic 205 Equations giving the foci ...
... axes of the conic 199 · Meaning of S - λS ' = 0 , S - λuv = 0 and S - λu2 = 0 200 Equation of a pair of tangents 202 Equation of the director - circle Four foci of a coņic 203 204 Eccentricities of a conic 205 Equations giving the foci ...
Page 2
... axes OX , OY . The point of inter- section of the axes is called the origin . When the angle between the axes is a right angle the axes are said to be rectangular ; when the angle between the axes is not a right angle the axes are said ...
... axes OX , OY . The point of inter- section of the axes is called the origin . When the angle between the axes is a right angle the axes are said to be rectangular ; when the angle between the axes is not a right angle the axes are said ...
Page 3
... axes be inclined at an angle w . W Ο L Y R M X Draw PM , QL parallel to OY , and QR parallel to OX , as in the figure . But .. Then OL = x " , LQ = y " , OM = x ' , MP = y ' . By trigonometry PQ2 = QR2 + RP - 2 QR . RP cos QRP . QR = LM ...
... axes be inclined at an angle w . W Ο L Y R M X Draw PM , QL parallel to OY , and QR parallel to OX , as in the figure . But .. Then OL = x " , LQ = y " , OM = x ' , MP = y ' . By trigonometry PQ2 = QR2 + RP - 2 QR . RP cos QRP . QR = LM ...
Page 4
... axes be rectangular , TOP = ± √ { x2 + y " } . Except in the case of straight lines parallel to one of the axes , no convention is made with regard to the direction which is to be considered positive . We may therefore suppose either ...
... axes be rectangular , TOP = ± √ { x2 + y " } . Except in the case of straight lines parallel to one of the axes , no convention is made with regard to the direction which is to be considered positive . We may therefore suppose either ...
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Common terms and phrases
2hxy a² b2 angular points asymptotes ax² axes bisect by² Cambridge centre coincident common confocal conics conic touching conjugate diameters constant corresponding Crown 8vo curve diagonals director-circle directrix distance eccentric angles Edition ellipse equal angles Extra fcap fcap find the equation find the locus fixed point fixed straight line foci focus four given points four points given conic given straight line imaginary inscribed latus rectum Let the equation line at infinity line joining line whose equation locus meet middle point nine-point circle normals original conic parabola Pascal's Theorem perpendicular point of intersection points at infinity points of contact polar pole Professor prove quadrilateral radical axis radius ratio rectangular hyperbola right angles second degree self-polar shew sides square tangential equation tangents triangle formed triangle of reference Trinity College values vertex vß² x² y² zero
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