# Ellipsoids Sentence Examples

Legendre, in 1783, extended Maclaurin's theorem concerning

**ellipsoids**of revolution to the case of any spheroid of revolution where the attracted point, instead of being limited to the axis or equator, occupied any position in space; and Laplace, in his treatise Theorie du mouvement et de la figure elliptique des planetes (published in 1784), effected a still further generalization by proving, what had been suspected by Legendre, that the theorem was equally true for any confocal**ellipsoids**.The continuity is secured if the liquid between two

**ellipsoids**X and X 11 moving with the velocity U and 15 1 of equation (II), is squeezed out or sucked in across the plane x=o at a rate equal to the integral flow of the velocity I across the annular area a l.The potential of such a shell at any internal point is constant, and the equi-potential surfaces for external space are

**ellipsoids**confocal with the ellipsoidal shell.Legendre shows that Maclaurin's theorem with respect to confocal

**ellipsoids**is true for any position of the external point when the**ellipsoids**are solids of revolution.During forty years the resources of analysis, even in the hands of d'Alembert, Lagrange and Laplace, had not carried the theory of the attraction of

**ellipsoids**beyond the point which the geometry of Maclaurin had reached.The third memoir relates to Laplace's theorem respecting confocal

**ellipsoids**.The problem is identical with that of finding the common conjugate diameters of the

**ellipsoids**T(x, y, I) =const., V(x, y, 1) =const.For example, all

**ellipsoids**referred to co-ordinates parallel to any three conjugate diameters are parallel projections of each other and of a sphere referred to rectangular co-ordinates.Among his most remarkable works may be mentioned his ten memoirs on quantics, commenced in 1854 and completed in 1878; his creation of the theory of matrices; his researches on the theory of groups; his memoir on abstract geometry, a subject which he created; his introduction into geometry of the "absolute"; his researches on the higher singularities of curves and surfaces; the classification of cubic curves; additions to the theories of rational transformation and correspondence; the theory of the twenty-seven lines that lie on a cubic surface; the theory of elliptic functions; the attraction of

**ellipsoids**; the British Association Reports, 1857 and 1862, on recent progress in general and special theoretical dynamics, and on the secular acceleration of the moon's mean motion.Add the error

**ellipsoids**of each shot to get an error ellipsoid for the entire loop.AdvertisementIf the structure was refined anisotropically, the orientations and the magnitudes of vibrational

**ellipsoids**should be displayed.