Solid geometry Volume 1

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Solid geometry Volume 1

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RareBooksClub. Paperback. Book Condition: New. This item is printed on demand. Paperback. 98 pages. Dimensions: 9.7in. x 7.4in. x 0.2in.This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1875 Excerpt: . . . and greater than b. These conies are called the focal ellipse and hyperbola of any of the confocals; they pass through the foci of the two principal sections containing respectively the least and the mean axes of the ellipsoids of the system. The focal hyperbola also passes through the umbilici of the ellipsoids, for which (a-k) (a-V) (c1-k) (b-c) a-c But there are other properties which make the term focal conies peculiarly appropriate, and which we shall discuss in the next chapter. 300. To find the confocal hyperboloids which pass through a point in the principal plane section of an ellipsoid which contains the primary and least axes. Let the equation of the ellipsoid be x y z I Jz 1 i a a--p a--y and let (f, 0, h) be the point in the plane of zx. If a be the primary semi-axis of a confocal hyperboloid f 0 h aV (a- and ) (a-ff) (a-) (a-7) 5 therefore cither a 3, or a j-. which is a hyperboloid of one or two sheets according as f a. point is one side or the other of the 7 focal hyperbola. The other solution gives the focal hyperbola, which must be considered as a flat hyperboloid of two sheets or one, according to the position of the point. 301. We may observe here that as these focal conies belong to the group of confocals, many of the propositions given above can be applied to them. For...

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