A Course of Pure Geometry: Containing a Complete Geometrical Treatment of the Properties of the Conic SectionsUniversity Press, 1917 - 295 páginas |
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Términos y frases comunes
A₁ ABCD asymptotes axes B₁ BC² bisects C₁ CA² CD² centre of similitude circle of curvature circular points circumcircle circumscribing coaxal circles collinear concurrent confocal conjugate diameters conjugate hyperbola conjugate lines constant corresponding points CP² cross-ratio diagonals diameter parallel directrix double lines drawn ellipse equal figure F fixed point focal chord foci focus and directrix four points given circles given point harmonic conjugates incircle involution pencil latus rectum Let the tangent line at infinity line joining locus meets the curve middle point Newton's theorem nine-points circle ordinate orthocentre orthogonal projection pair of conjugate parabola perpendicular perspective plane PN² points of contact points of intersection polar pole Prop proposition Prove quadrilateral radical axis ratio rectangular hyperbola right angles self-conjugate shew straight line subtends tangents triangle ABC vanishing line vertex vertices
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Página 106 - To prove that the locus of the middle points of a system of parallel chords of a parabola is a straight line parallel to the axis of the parabola.
Página 24 - It may also be defined as the locus of a point which moves in a plane so that its distance from a fixed point, called the focus.
Página 258 - Thus the inverse of the circle is another circle. COR. 1. The inverse of a straight line is a circle passing through the centre of inversion. COR. 2. If two circles be inverse each to the other, the centre of inversion is a centre of similitude (§ 25); and the radii of the circles are to one another in the ratio of the distances of their centres from 0. The student should observe that, if we call the two circles S and $', and if OPQ meet S' again in Q', Q
Página 156 - deviation' or angle between the load- and flexureplanes is a maximum when the former has for trace on the crosssection a diagonal of the rectangle formed by the tangents at the extremities of the principal axes of the ellipse of inertia. A good illustration of a simple kind shewing the deviation is given in § 7, p. 57. [172.] The notes on pp. 73 — 85 deal with the elastic line when the flexure is not so small that we may neglect the square of the slope which the elastic line makes with the...
Página 38 - The lines joining the vertices of a triangle to the points of contact with the opposite sides of the incircle and ecircles are respectively concurrent.
Página 130 - Tangents to a parabola at the extremities of a focal chord intersect at right angles in the directrix.
Página ii - PUTNAM'S SONS BOMBAY, CALCUTTA, MADRAS : MACMILLAN AND CO., LTD. TORONTO : JM DENT AND SONS, LTD. TOKYO: THE MARUZEN-KABUSHIKI-KAISHA [All rights reserved] SIX LECTURES ON POLITICAL PHILOSOPHY BY W.
Página 114 - The semi-latus rectum is a harmonic mean between the segments of any focal chord. Let a focal chord PSQ meet the directrix in R} and let PM, SX, QN be perpendiculars to the directrix.
Página 188 - CO' of a, hyperbola to meet CO' and CO in PI and 7f, then [Use § 183.] 7. The tangent to a hyperbola at P meets an asymptote in T and TQ is drawn parallel to the other asymptote to meet the curve in Q. PQ meets the asymptote in L and M. Prove that LM is trisected at P and Q. 8. From any point R on an asymptote of a hyperbola...
Página 110 - FSP' when P' approaches P = a right angle. It should be observed that this second proof yields also the result that tangents at the extremities of a focal chord intersect in the directrix...