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CONOID (Gr. KWvor, cone, and el os, f...

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Originally appearing in Volume V06, Page 964 of the 1911 Encyclopedia Britannica.
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CONOID (Gr. KWvor, cone, and el os, form), in geometry, the solids (or surfaces) formed by the revolution of a conic section about one of its principal axes. If the conic be a circle the conoid is a sphere (q.v.); if an ellipse a spheroid (q.v.); if a parabola a paraboloid; if a hyperbola the surface is a hyperboloid of either one or two sheets according as the revolution takes place about the conjugate or transverse axis, and the surface generated by the asymptotes is called the " asymptotic cone." If two intersecting straight lines be regarded as a conic, then the principal axes are the bisectors of the angles between the lines; consequently the corresponding conoid is a right circular cone. It is to be noted that all these surfaces are surfaces of revolution; and they, therefore, differ from the surfaces discussed under the same names in the article GEOMETRY: Analytical. The spheroid has for its cartesian equation(x2+y2)/a2+z2/b2 = 1; the hyperboloid of one sheet(of revolution)is(x2+y2)/a2-z2/b2=1; the hyperboloid of two sheets is z2/c2-(x2+y2)/a2=1; and the paraboloid of revolution is x2+y2=4az.
End of Article: CONOID (Gr. KWvor, cone, and el os, form)
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JOHN CONOLLY (1794-1866)

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