An Elementary Treatise On Solid Geometry ..

Cover An Elementary Treatise On Solid Geometry ..
An Elementary Treatise On Solid Geometry ..
W Steadman William Steadman Aldis
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The two values oi h in (9) of Art. 169 must be equal and of opposite sign ; . -. U'(v+w)+V'{w + u) + W'{u+v)-2u'VW-2v'WU-2iv'UV=0.
The points of intersection of the surface with the sphere 111 ^ ABC 6. Take the general equation of a quadric and determine the conditions that it may touch the plane of xij at the origin, and that sections by planes parallel to that plane may be circles.
IS 7. Using the equation in the last question the locus required ex + hy + h (z — a) — z = 0.
8. See Ex. 4, Chap
.... Xii. The surface in the question and the two surfaces 2 2 *> 9 X y z X y ^ ^ can be shewn to cut always at right angles, where /3 and y are any constants. Hence the intersections of these surfaces with the given one are its lines of curvature.
At the points of intersection of the first with the given surface we have ax = /5?/ + 6' a plane ; and by combining this with tlie given equation, that can be written - {ax - c") + o {(^U + ^' - c^) + z'' = ax - c", which is the equation of a sphere.


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