Geometrical conic sections |
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Page iv
... intersecting chords in constant directions ( Chap . v . § 15 ) , given by Dean Hamilton in his treatise published in 1773 , as an improving and interesting study and one that is in harmony with the scheme of this work . I have to ...
... intersecting chords in constant directions ( Chap . v . § 15 ) , given by Dean Hamilton in his treatise published in 1773 , as an improving and interesting study and one that is in harmony with the scheme of this work . I have to ...
Page vi
... Intersecting tangents 15. SG : SP :: SA : AX 33 33 34 36 CHAPTER V. ON THE HYPERBOLA . 1. Definition 2. Projection of the rectangular hyperbola 3. Magnitude of the axes · Properties of the rectangular hyperbola : - 4. Asymptotes . • 42 ...
... Intersecting tangents 15. SG : SP :: SA : AX 33 33 34 36 CHAPTER V. ON THE HYPERBOLA . 1. Definition 2. Projection of the rectangular hyperbola 3. Magnitude of the axes · Properties of the rectangular hyperbola : - 4. Asymptotes . • 42 ...
Page vii
... Intersecting tangents 85585 96 97 97 98 19. Tangents at the extremities of a chord intersect on its diameter 20. PT PV . 21. QV2 = 4SP . PV 99 • 99 • · 100 22. Length of focal chord 23. Ratio of the rectangles under segments of intersecting ...
... Intersecting tangents 85585 96 97 97 98 19. Tangents at the extremities of a chord intersect on its diameter 20. PT PV . 21. QV2 = 4SP . PV 99 • 99 • · 100 22. Length of focal chord 23. Ratio of the rectangles under segments of intersecting ...
Page 4
... intersecting lines , that which is subtended by the line of intersection and the vertical opposite angle will be increased , the other two di- minished by projection ; and these angles may be increased and diminished to any extent by ...
... intersecting lines , that which is subtended by the line of intersection and the vertical opposite angle will be increased , the other two di- minished by projection ; and these angles may be increased and diminished to any extent by ...
Page 10
... intersecting it in the line AA ' such that A , A ′ are points in the generating line on oppo- site sides of the axis VO ; then the section APA ' is call- ed an Ellipse . It is manifest that the ellipse will be a closed curve , and ...
... intersecting it in the line AA ' such that A , A ′ are points in the generating line on oppo- site sides of the axis VO ; then the section APA ' is call- ed an Ellipse . It is manifest that the ellipse will be a closed curve , and ...
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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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