The Geometry of Conics, Part 1 |
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Page 3
... touch a given straight line on the same side at a given point . If to each circle a tangent parallel to the given line be drawn , it will cut the circle next larger in points lying on a parabola . 6. PROP . II . The locus of the middle ...
... touch a given straight line on the same side at a given point . If to each circle a tangent parallel to the given line be drawn , it will cut the circle next larger in points lying on a parabola . 6. PROP . II . The locus of the middle ...
Page 9
... touches the directrix . 15. Shew that SO2 = SX . Ov≈ 4AS . SP . 16. Also that QD2 = 4AS . PV . [ 12 . [ 12 . 17. Deduce from Ex . 9 , that the ratio of the rectangles in Art . 15 is the same for all similarly situated parabolas . 18. A ...
... touches the directrix . 15. Shew that SO2 = SX . Ov≈ 4AS . SP . 16. Also that QD2 = 4AS . PV . [ 12 . [ 12 . 17. Deduce from Ex . 9 , that the ratio of the rectangles in Art . 15 is the same for all similarly situated parabolas . 18. A ...
Page 10
... touches a given straight line . 34. A point moves in such a way that its perpendicular distance from a fixed straight line is less by a constant quantity than its distance from a fixed point . Shew that the point de- scribes a parabola ...
... touches a given straight line . 34. A point moves in such a way that its perpendicular distance from a fixed straight line is less by a constant quantity than its distance from a fixed point . Shew that the point de- scribes a parabola ...
Page 21
... touches a parabola . 50. Shew how to draw tangents to a parabola from any given external point . 51. If PQ be the chord of contact of tangents from O , then SO2 = SP . SQ . 52. The tangent at diameter through P in T. meets the tangent ...
... touches a parabola . 50. Shew how to draw tangents to a parabola from any given external point . 51. If PQ be the chord of contact of tangents from O , then SO2 = SP . SQ . 52. The tangent at diameter through P in T. meets the tangent ...
Page 22
... touches the parabola in P , Q , then SP is equal to the latus rectum . 66. The normal at any point is equal to twice ... touches a given straight line is a circle . 69. The circle on a focal radius touches the tangent at A. 70. The ...
... touches the parabola in P , Q , then SP is equal to the latus rectum . 66. The normal at any point is equal to twice ... touches a given straight line is a circle . 69. The circle on a focal radius touches the tangent at A. 70. The ...
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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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