Geometrical conic sections |
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Page 5
... proportional between DA and DB . 7. The area of any figure will be reduced by projection in the maximum ratio of the planes . For every triangle may be divided by a line through one of the angular points parallel to the line of ...
... proportional between DA and DB . 7. The area of any figure will be reduced by projection in the maximum ratio of the planes . For every triangle may be divided by a line through one of the angular points parallel to the line of ...
Page 14
... proportional between V and T. The ratios of these lines are not altered by projection ; therefore also in the ellipse CV . CT = CP As a particular case of this proposition , if the tangent at P meets the axis major in T , and PN be the ...
... proportional between V and T. The ratios of these lines are not altered by projection ; therefore also in the ellipse CV . CT = CP As a particular case of this proposition , if the tangent at P meets the axis major in T , and PN be the ...
Page 15
... proportional to CT , CP . Through V draw an ordinate QVq parallel to the tangent at P : join TQ , Tq , then by the proposition of the last Art . these will be the tangents required . 9. The above propositions might equally have been ...
... proportional to CT , CP . Through V draw an ordinate QVq parallel to the tangent at P : join TQ , Tq , then by the proposition of the last Art . these will be the tangents required . 9. The above propositions might equally have been ...
Page 17
... proportional to the parallel semi - diameters . Hence if a circle intersect an ellipse in four points and the common chords be drawn , it will easily appear that the J. C. S. 2 semi - diameters to which these chords are parallel must ON ...
... proportional to the parallel semi - diameters . Hence if a circle intersect an ellipse in four points and the common chords be drawn , it will easily appear that the J. C. S. 2 semi - diameters to which these chords are parallel must ON ...
Page 19
... proportional to the diameters parallel to them . 8. All triangles circumscribing an ellipse which have the line joining each angular point with the point of contact of the opposite side passing through the centre , are equal and are ...
... proportional to the diameters parallel to them . 8. All triangles circumscribing an ellipse which have the line joining each angular point with the point of contact of the opposite side passing through the centre , are equal and are ...
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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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