Geometrical conic sections |
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Page 13
... bisected by a diameter will project into chords of an ellipse bisected by the projection of the dia- D Q T d meter . Hence diameters of the circle at right angles to one another project into diameters of the ellipse which bisect each ...
... bisected by a diameter will project into chords of an ellipse bisected by the projection of the dia- D Q T d meter . Hence diameters of the circle at right angles to one another project into diameters of the ellipse which bisect each ...
Page 14
... bisected by a diameter ( as QV by PCp ) is called an ordinate to that diameter . 7. If QT , the tangent to the circle at Q , meet CP pro- duced in T , CV . CT CQ or CP ; or CP is a mean = or = proportional between V and T. The ratios of ...
... bisected by a diameter ( as QV by PCp ) is called an ordinate to that diameter . 7. If QT , the tangent to the circle at Q , meet CP pro- duced in T , CV . CT CQ or CP ; or CP is a mean = or = proportional between V and T. The ratios of ...
Page 15
... bisected at its point of contact . These properties are not affected by pro- jection , and therefore hold true in the ellipse . COR . Hence to draw tangents to an ellipse from any point T , join CT and let it cut the curve in P ; draw ...
... bisected at its point of contact . These properties are not affected by pro- jection , and therefore hold true in the ellipse . COR . Hence to draw tangents to an ellipse from any point T , join CT and let it cut the curve in P ; draw ...
Page 18
... bisected at the points of contact is the projection of one regular polygon , and will project into another . 4. All such rectilinear figures of a given number of 18 CONIC SECTIONS . PF PG= BC2; PF PgAC The ellipse is the projection of a ...
... bisected at the points of contact is the projection of one regular polygon , and will project into another . 4. All such rectilinear figures of a given number of 18 CONIC SECTIONS . PF PG= BC2; PF PgAC The ellipse is the projection of a ...
Page 19
... bisected at V , and CV produced meets the curve in P ; if CV : CP is a constant ratio the same for all the sides ... bisecting supplemental chords are conjugate . 10. Diameters which coincide with the diagonals of the parallelogram on ...
... bisected at V , and CV produced meets the curve in P ; if CV : CP is a constant ratio the same for all the sides ... bisecting supplemental chords are conjugate . 10. Diameters which coincide with the diagonals of the parallelogram on ...
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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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