The Geometry of Conics, Part 1 |
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Page 3
... passes through the focus is said to be a Focal Chord . The focal chord perpen- dicular to the axis is called the Latus Rectum . 4. COR . The square of the focal ordinate or semi - latus rectum is equal to 4AS . AS . Hence the latus ...
... passes through the focus is said to be a Focal Chord . The focal chord perpen- dicular to the axis is called the Latus Rectum . 4. COR . The square of the focal ordinate or semi - latus rectum is equal to 4AS . AS . Hence the latus ...
Page 5
... passes through the focus . 6. Shew that QOQ ' = MYM ' . [ 6 . 7. The perpendicular to a chord of a parabola from its middle point V meets the axis at a distance equal to SX from the foot of the ordinate of V. 10. PROP . III . To find ...
... passes through the focus . 6. Shew that QOQ ' = MYM ' . [ 6 . 7. The perpendicular to a chord of a parabola from its middle point V meets the axis at a distance equal to SX from the foot of the ordinate of V. 10. PROP . III . To find ...
Page 10
... passes through a fixed point , and AN . AM - PN . PM = 16AS2 . 25. If PQ be a focal chord , AP , AQ meet the latus rectum at distances from S equal to the ordinates Q , P. [ Ex . 13 . 26. If the diameter at P meets the latus rectum in L ...
... passes through a fixed point , and AN . AM - PN . PM = 16AS2 . 25. If PQ be a focal chord , AP , AQ meet the latus rectum at distances from S equal to the ordinates Q , P. [ Ex . 13 . 26. If the diameter at P meets the latus rectum in L ...
Page 22
... passes through S. 65. If a circle through S touches the parabola in P , Q , then SP is equal to the latus rectum . 66. The normal at any point is equal to twice the focal per- pendicular upon the tangent , and is also a mean ...
... passes through S. 65. If a circle through S touches the parabola in P , Q , then SP is equal to the latus rectum . 66. The normal at any point is equal to twice the focal per- pendicular upon the tangent , and is also a mean ...
Page 23
... passes through S. 74. If from the foot of the normal at P a perpendicular PK be drawn to SP , then PK = 2AS . 75. Determine the position of P so that the triangle SPG may be equilateral . 76. The tangent at any point meets the directrix ...
... passes through S. 74. If from the foot of the normal at P a perpendicular PK be drawn to SP , then PK = 2AS . 75. Determine the position of P so that the triangle SPG may be equilateral . 76. The tangent at any point meets the directrix ...
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Common terms and phrases
abscissa auxiliary circle bisects the angle Bishop of Carlisle CA² Cambridge CB² CD² centre CN² concyclic Conic Sections conjugate diameters conjugate radii constant ratio CP² CS² CV² draw drawn ellipse equally inclined Fellow of Trinity fixed point focal chord focal perpendicular focal radii focus Geometry Hence intersect J. W. DONALDSON late Fellow latus rectum locus meet the asymptotes meet the curve meet the directrix meets the axis middle point minor axis normal parabola parallel chords parallelogram Pembroke College PN² point Q principal ordinate PROP QV² radius rectangular hyperbola right angles right-angled triangles Second Edition Shew shewn sides SP² St John's College straight line joining subtends a right supplementary angles tangent Third Edition Treatise Trinity College vertex
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