 | Education - 1840 - 468 pages
...the coefficient of friction when the whole pressure upon the axis takes place at the upper ring. 21. The sum of the squares of the projections of any three conjugate diameters of an ellipsoid (whose sepii-axes are a, b, c) upon a given principal diameter is (•(instanti and... | |
 | English literature - 1840 - 528 pages
...the coefficient of friction when the whole pressure upon the axis takes place at the upper ring. 21. The sum of the squares of the projections of any three conjugate diameters of an ellipsoid (whose semi-axes are a, b, c) upon a given principal diameter is constant ; and the... | |
 | John Adams Coombe - 1841 - 220 pages
...sin/, v/3 " This gives the value of /и, that there may be no pressure on the lower ring. PnOBLEM XXI. The sum of the squares of the projections of any three conjugate diameters of an ellipsoid (whose semiaxes are a, b, c) upon a given principal diameter is constant: and the tangent... | |
 | Duncan Farquharson Gregory - 1845 - 364 pages
...reader is referred to a memoir by M. Brassine, in Liouville's Journal de Mathimatiques, Av. 1842. PEOB. 2. The sum of the squares of the projections of any...extremities of each diameter, and add them. Now if X, ju, v, be the direction-cosines of the given line, the sum of the projections of the co-ordinates of... | |
 | Mathematics - 1850 - 318 pages
...(т,) and (т„). It is also a well-known theorem, that in any central surface of the second order, the sum of the squares of the projections of any three conjugate semidiameters upon the normal to any given central section, is constant. From the principles which... | |
 | Duncan Farquharson Gregory - 1852 - 352 pages
...referred to a memoir by M. Brassine, in Liouville's Journal de Mathe_ matiques, Av. 1842. PEOB. 3. The sum of the squares of the projections of any three...extremities of each diameter, and add them. Now, if X, /A, v, be the direction_ cosines of the given line, the sum of the projections of the coordinates of... | |
 | Great Britain. Education Department. Department of Science and Art - 1877 - 562 pages
...Find the locus of the middle points of a system of parallel chords of a central conicoid. Prove that the sum of the squares of the projections of any three conjugate diameters, on an axis of the eonicoid, is equal to the square of that axis. SUBJECT V. PURE MATHEMATICS, STAGES 6... | |
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... the coefficient of friction when the whole pressure upon the axis takes place at the upper ring. 21. The sum of the squares of the projections of any three conjugate diameters of an ellipsoid (whose semi-axes are a, b, c) upon a given principal diameter... 