Geometrical conic sections |
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Page 8
... containing the axis cuts the cone in two right lines inclined to each other at a constant angle . 3. From the definition of a sphere it is evident that every point in the sphere is equidistant from the centre of the generating circle ...
... containing the axis cuts the cone in two right lines inclined to each other at a constant angle . 3. From the definition of a sphere it is evident that every point in the sphere is equidistant from the centre of the generating circle ...
Page 14
... containing it meet therefore when projected these chords are parallel to conjugate diameters of the ellipse : such chords when projected are called supplemental chords ; they form two sides of a triangle the base of which is a diameter ...
... containing it meet therefore when projected these chords are parallel to conjugate diameters of the ellipse : such chords when projected are called supplemental chords ; they form two sides of a triangle the base of which is a diameter ...
Page 41
... contains the vertex of an ellipse cut from it intercepted between the vertex and a line through C at right angles to the axis of the cone ; shew that AD = CS . 52. To cut an ellipse of given axes from a given cone . CHAPTER V. On the ...
... contains the vertex of an ellipse cut from it intercepted between the vertex and a line through C at right angles to the axis of the cone ; shew that AD = CS . 52. To cut an ellipse of given axes from a given cone . CHAPTER V. On the ...
Page 61
... contain the transverse axis will be obtuse instead of acute . 14. Supplemental Chords . P If any point Q in an hyperbola be joined with the ex- tremities PP ' of any diameter , PQ , P'Q are called sup- plemental chords , and are ...
... contain the transverse axis will be obtuse instead of acute . 14. Supplemental Chords . P If any point Q in an hyperbola be joined with the ex- tremities PP ' of any diameter , PQ , P'Q are called sup- plemental chords , and are ...
Page 67
... containing the asymptotes , are parallel to them . EXAMPLES . 1. Or all hyperbolas that can be cut from a given cone , the ratio BC AC is greatest in that cut by a plane parallel to the axis . : Give a construction for determining , if ...
... containing the asymptotes , are parallel to them . EXAMPLES . 1. Or all hyperbolas that can be cut from a given cone , the ratio BC AC is greatest in that cut by a plane parallel to the axis . : Give a construction for determining , if ...
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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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