Solid Geometry

Cover Solid Geometry
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If two prola.te surfaces of revo- lution have a common focus, their planes of intersection will pass through the line of intersection of their directrix planes.
xi. If two tetrahedrons be such that each angular point of one is the pole of a face of the other with respect to a given conicoid, the lines joining corresponding angular points will be generators of one conicoid circumscribing both tetra- hedrons.
xii. If a paraboloid of revolution be described passing through a given ellipse, and a r
...ight circular cylin- der be described also passing through the ellipse, the axis of the cylinder will be parallel to that of the paraboloid, and will pass through the pole of the plane of the ellipse.
If three conicoids have one com- mon plane section, the second planes of intersection of the surfaces, taken two and two, will intersect in the same straight line.
Two conicoids, each touching another along a plane curve, will themselves intersect in two plane curves, whose planes pass through the line of intersection of the planes of contact.


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