A Treatise on Conic SectionsAmerican Mathematical Soc., 2005 - 399 pages This is the classic book on the subject, covering the whole ground and full of touches of genius. |
Table des matières
THE POINT | 1 |
Polar Coordinates | 9 |
Meaning of the Constants in Equation of a Right Line | 17 |
Discussion of Quadratic which determines Points where Line meets a Conic | 22 |
EXAMPLES ON THE RIGHT LINE | 23 |
Coordinates of Intersection of two Right Lines | 25 |
Problems where it is proved that a Moveable Line always passes through | 35 |
CHAPTER IV | 53 |
Focal properties of Conics see also pp 267 277 281 321 339 | 236 |
If three Conics have each double contact with a fourth their Chords | 243 |
Corresponding Chords of two Conics intersect on one of their Chords of Intersec | 249 |
Subnormal Constant | 257 |
Equation of a Conic having double contact with two given Conics | 262 |
Equation of pair of Tangents through a given Point see also p 149 | 269 |
To inscribe in a Conic a Triangle whose sides pass through fixed Points see | 273 |
Locus of foot of Perpendicular from Focus on Tangent | 274 |
THE METHOD OF INFINITESIMALS | 57 |
Centre and Axis of Homology | 60 |
Middle Points of Diagonals of a Quadrilateral are in a Right Line see also p | 62 |
RIGHT LINES | 67 |
Equation of Circle | 75 |
All Circles have imaginary common Points at infinity see also p 325 | 96 |
PROPERTIES OF TWO OR MORE CIRCLES | 98 |
Coordinates of intersection of two Normals | 99 |
Conjugate Diameters | 103 |
To draw a Normal through a given Point see also p 335 | 106 |
Axis of Similitude | 108 |
Method of finding Coordinates of Foci of given Conic see also p 353 | 113 |
CHAPTER IX | 116 |
Equation of inscribed Circle derived from that of circumscribing | 127 |
CHAPTER X | 136 |
Condition that a given Line should touch a Conic see also pp 267 340 | 153 |
Equation of Perpendicular on a given Line | 157 |
Sum of Squares of Reciprocals of Semidiameters at right Angles is constant | 159 |
Locus of intersection of Normals at extremities of a Focal Chord see also p 335 211 | 166 |
Geometrical construction for the Axes see also p 173 | 173 |
Rectangle under Focal Perpendiculars on Tangent is constant | 181 |
If two Chords meet in a Point Lines joining their extremities transversely meet | 184 |
how found | 190 |
Figure of Hyperbola | 199 |
of Perpendiculars at Middle Points of Sides | 205 |
Radii Vectores through Foci have equal difference of Reciprocals | 209 |
ditto given lengths of two Tangents and contained Angle see also | 214 |
Conjugate Hyperbola | 222 |
Anharmonic Property of Conics proved see also pp 252 288 318 | 226 |
RECIPROCAL POLARS | 276 |
Polar of one Circle with regard to another | 283 |
207 | 285 |
Carnots Theorem respecting Triangle cut by Conic see also p 319 | 289 |
CHAPTER XIII | 295 |
Generalizations of Mac Laurins Method of generating Conics see also p 300 | 300 |
Anharmonic proof of Pascals Theorem | 301 |
Analytic condition that four Points should form a Harmonic System | 305 |
System of Conics through four Points cut any Transversal in Involution | 311 |
Projective Properties of a Quadrilateral | 317 |
Anharmonic Properties of Points and Tangents of a Conic see also pp 240 288 | 318 |
The six Vertices of two selfconjugate Triangles lie on same Conic see also p 341 | 323 |
Every Parabola has a Tangent at an infinite Distance | 329 |
Locus of Intersection of Normals to a Conic at the extremities of Chords passing | 335 |
Criterion whether Conics intersect in two real and two imaginary Points or not | 337 |
Anharmonic ratio of four Points on a Conic abcd abcd if the Lines | 342 |
Loci | 343 |
Equation of four common Tangents | 344 |
Four Conics having double contact with S and passing through three Points | 359 |
Tangent to any Conic cuts off constant Area from similar and concentric Conic | 373 |
NOTES | 379 |
Expression of the Coordinates of a Point on a Conic by a single Parameter | 386 |
| 393 | |
| 394 | |
| 395 | |
| 396 | |
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| 399 | |
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Expressions et termes fréquents
asymptotes ax² axes bisected bisector chord of contact circumscribing coefficients common tangents condition conic section conjugate diameters constant corresponding cos² denote determine directrix double contact drawn ellipse equal find the equation find the locus fixed line fixed point foci focus four points geometrically given circles given line given point Hence hyperbola imaginary points infinite distance inscribed intercept last article length line at infinity line joining line meets meet the curve middle points origin parabola parallel 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 right angles right line second degree sides sin² square substituting tangential equation theorem transform trilinear coordinates values vanish vertex vertices