Geometrical conic sections |
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Page iii
... proved by projection from those connected with the focus and directrix , and thus introduces a valuable simplification into the treat- ment of the subject . It is also a consideration of some importance that we can see at once from the ...
... proved by projection from those connected with the focus and directrix , and thus introduces a valuable simplification into the treat- ment of the subject . It is also a consideration of some importance that we can see at once from the ...
Page 12
... prove that in every case the diameter BB ' of the ellipse at right angles to the plane of the paper is < AA ' in ... proved . 4. In the circle if two diameters are at right 12 CONIC SECTIONS . CP2 + AC2+.
... prove that in every case the diameter BB ' of the ellipse at right angles to the plane of the paper is < AA ' in ... proved . 4. In the circle if two diameters are at right 12 CONIC SECTIONS . CP2 + AC2+.
Page 20
... Prove this , and transfer the property to the ellipse , shewing that if CQT meets the ellipse in P , CQ . CT = CP2 . = 16. If in each of two ellipses the two axes are in the same ratio to one another , shew that radii which are equally ...
... Prove this , and transfer the property to the ellipse , shewing that if CQT meets the ellipse in P , CQ . CT = CP2 . = 16. If in each of two ellipses the two axes are in the same ratio to one another , shew that radii which are equally ...
Page 21
... prove that the area between the chord PQ and the curve will be so also . 27. PD joins the extremities of conjugate diameters , and CIJ makes a constant angle with PD , meeting it in I , and the parallel tangent in J. Shew that I and J ...
... prove that the area between the chord PQ and the curve will be so also . 27. PD joins the extremities of conjugate diameters , and CIJ makes a constant angle with PD , meeting it in I , and the parallel tangent in J. Shew that I and J ...
Page 22
... prove that DQ is parallel to two of the lines joining extremities of the axes of the curve . 39. If NP produced meets the auxiliary circle in Q , prove that GP , CQ produced meet on a circle whose diameter = sum of the axes of the curve ...
... prove that DQ is parallel to two of the lines joining extremities of the axes of the curve . 39. If NP produced meets the auxiliary circle in Q , prove that GP , CQ produced meet on a circle whose diameter = sum of the axes of the curve ...
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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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