PAGE . 2. Projection of the rectangular hyperbola Properties of the rectangular hyperbola :-- 5. Intercepts between asymptotes and curve equal. Locus of the middle points of parallel chords 7,8. CV.CT = CP?; CN.CT = CAP. 9. Conjugate hyperbola, conjugate diameters. . 52 12, 13. These properties transferred to the general hyperbola 58 15, 16. Ratio of rectangles on the segments of intersecting chord 61 . 92 96 1. Definition. 87 2. Limiting form of semi-ellipse or semi-hyperbola 5. Locus of middle points of parallel chords 11. Tangent equally inclined to the focal distance and the axis of 12. Tangents at the extremities of a focal chord 13. Perpendicular from the focus on the tangent . 19. Tangents at the extremities of a chord intersect on its 23. Ratio of the rectangles under segments of intersecting chords 101 . . . ERRATA. Two lines from the bottom of p. 61, after rectangles insert under the segments. p. 72, for Chap. VII. read Chap. VI. CONIC SECTIONS. ERRATA. p. 4, § 6, line 2, for except those contained, &c. read except those right angles contained by lines parallel and perpendicular to the line of intersection. p. 14, § 7, line 3, for V and T read CV and CT. p. 46, line 12 from the bottom, for diminishes the more read increases the more. p. 55, line 4, for asymptotes read asymptote. References in Chap. VI. to Chap. V. should be to Chap. IV. p. 61, line 3 from the bottom, after rectangles insert under the segments. p. 72, for Chap. VII. read Chap. VI. p. 81, line 10 from the bottom, for SQP read SQP'. p. 82, line 8 from the bottom, for CR' read CR?. p. 87, for Chap. VIII. read Chap. VII. p. 91, line 4, for Chap. VI. read Chap. V. If a straight line be drawn through two adjacent points of a curve, and the two points move towards one another on the curve until they coincide, the straight line in its final position is said to be a tangent to the curve at the point which it has finally in common with it. 2. In order to project a straight line AB (fig. $ 5) on a plane abc, we must draw the perpendicular Aa from some 1 J. C. S. |
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