An Elementary Treatise On Solid Geometry ..
An Elementary Treatise On Solid Geometry ..
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In our eReader you can find the full English version of the book. Read An Elementary Treatise On Solid Geometry .. Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book An Elementary Treatise On Solid Geometry ..
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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.
What to read after An Elementary Treatise On Solid Geometry ..?
You can find similar books in the "Read Also" column, or choose other free books by W Steadman William Steadman Aldis to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
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.
What to read after An Elementary Treatise On Solid Geometry ..?
You can find similar books in the "Read Also" column, or choose other free books by W Steadman William Steadman Aldis to read onlineMoreLess
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