Geometrical conic sections |
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Page vi
... FOCAL PROPERTIES OF THE ELLIPSE . PAGE 14 15 16 16 17 18 1,2 . Preliminary . 3-5 . Foci and directrices 6. Secant and tangent 7. Tangent equally inclined to the focal distances 8. Auxiliary circle 2328 24 25 29 30 31 9. SY . HZ = BC2 32 ...
... FOCAL PROPERTIES OF THE ELLIPSE . PAGE 14 15 16 16 17 18 1,2 . Preliminary . 3-5 . Foci and directrices 6. Secant and tangent 7. Tangent equally inclined to the focal distances 8. Auxiliary circle 2328 24 25 29 30 31 9. SY . HZ = BC2 32 ...
Page vii
... focal distance and the axis of the curve 12. Tangents at the extremities of a focal chord · 13. Perpendicular from the focus on the tangent . 14-18 . Intersecting tangents 85585 96 97 97 98 19. Tangents at the extremities of a chord ...
... focal distance and the axis of the curve 12. Tangents at the extremities of a focal chord · 13. Perpendicular from the focus on the tangent . 14-18 . Intersecting tangents 85585 96 97 97 98 19. Tangents at the extremities of a chord ...
Page 23
... . 45. Prove that PG . Pg = CD3 . 46. If CR be the perpendicular from the centre on the tan- gent at P , and BR , AD be joined ; prove that the triangles ACD , RCB are similar . CHAPTER IV . Focal Properties of the Ellipse . 1. EXAMPLES .
... . 45. Prove that PG . Pg = CD3 . 46. If CR be the perpendicular from the centre on the tan- gent at P , and BR , AD be joined ; prove that the triangles ACD , RCB are similar . CHAPTER IV . Focal Properties of the Ellipse . 1. EXAMPLES .
Page 24
John Stuart Jackson. CHAPTER IV . Focal Properties of the Ellipse . 1. We have now to shew that there are two points within the ellipse which , regarding the curve in its relation to the circle , are as it ... FOCAL PROPERTIES OF THE ELLIPSE.
John Stuart Jackson. CHAPTER IV . Focal Properties of the Ellipse . 1. We have now to shew that there are two points within the ellipse which , regarding the curve in its relation to the circle , are as it ... FOCAL PROPERTIES OF THE ELLIPSE.
Page 25
... cone will be invariable . Also OS , O'H will be at right angles to the cutting plane , which will therefore touch the spheres in S and H , Let P be any point of the elliptic section , FOCAL PROPERTIES OF THE ELLIPSE . 25.
... cone will be invariable . Also OS , O'H will be at right angles to the cutting plane , which will therefore touch the spheres in S and H , Let P be any point of the elliptic section , FOCAL PROPERTIES OF THE ELLIPSE . 25.
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Common terms and phrases
AC² Algebra ARITHMETIC asymptotes auxiliary circle axis major BC² BEGINNERS bisects the angle Cambridge CD² centre Chap Christ's College cloth Conic Sections conjugate diameters conjugate hyperbola CP² Crown 8vo cutting plane directrix draw drawn parallel ELEMENTARY TREATISE ellipse English equal angles equally inclined Examination Papers Extra fcap extremities fcap focal chord foci focus GEOMETRY given Grammar Greek Hence intersect John's College Latin latus rectum line joining manual Mathematical meet the curve method Metric System middle point MIXED MATHEMATICS parabola parallelogram perpendicular point of contact produced meet Professor projection proposition prove quadrilateral rectangle rectangular hyperbola render revised right angles Schools Second Edition semi-diameters shew sphere straight line subtend tangent touch transverse axis triangles Trigonometry University of Cambridge vertex
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