The elements of astronomy; a textbook . as EF). In thiscase, the plane of the section cuts completely across the ellipse formed will vary in shape and size according tothe position of the plane, — the circle being simply a specialcase when the cutting plane is perpendicular to the axis. (6) When the cutting plane makes with the axis an angleless than BVC (the semi-angle of the cone), it plunges contin-ually deeper into the cone and never comes out on the other side,the cone being supposed to be indefinitely prolonged. Thesection in this case is a hyperbola, GHK. If the plane ofthe sec
The elements of astronomy; a textbook . as EF). In thiscase, the plane of the section cuts completely across the ellipse formed will vary in shape and size according tothe position of the plane, — the circle being simply a specialcase when the cutting plane is perpendicular to the axis. (6) When the cutting plane makes with the axis an angleless than BVC (the semi-angle of the cone), it plunges contin-ually deeper into the cone and never comes out on the other side,the cone being supposed to be indefinitely prolonged. Thesection in this case is a hyperbola, GHK. If the plane ofthe section be produced upward, however, it encounters thecone produced, cutting out from it a second hyperbola,GHK, exactly like the original one, but turned in the oppo-site direction. The axis of the hyperbola is always reckonedas negative, lying outside of the curve itself (in the figure itis the line HE1). The centre of the hyperbola is the middlepoint of this axis, a point also outside the curve. 506] ELEMENTS OF A PLANET S ORBIT. 377. Fig. 133. — The Conies. (c) When the angle madeby the cutting plane with theaxis is exactly equal to thecones semi-angle, the planewill be parallel to a planewhich is tangent to the coni-cal surface, and we then getthe special case of the parab-ola, which is, so to speak,the boundary or partition be-tween the infinite variety ofellipses and hyperbolas whichcan be cut from a given parabolas are of the sameshape, just as all circles are,differing only in size. This fact is by no meansself-evident, and we cannotstop to prove it; but it is does not mean, of course,that an arc of a parabola hasthe same shape as an arc ofanother parabola taken from adifferent part of the curve, butthat the complete parabolas,cut from infinitely extendedcones, are similar, whateverthe angle of the cone. 507. Elements of a Planets Orbit (supplementary to Art. 296).— In order to describe a planets orbit intelligibly, andto supply the data required fo
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