 | John Radford Young - Conic sections - 1830 - 342 pages
...the faces of the parallelopiped whose edges are any system of semi-conjugate diameters, is equal to the sum of the squares of the faces of the rectangular parallelopiped whose edges are the semiprincipal diameters ; also the volume of the former is equal to the volume... | |
 | John Radford Young - Conic sections - 1830 - 390 pages
...the [faces of the parallelopiped whose edges are any system of serai-conjugate diameters, is equal to the sum of the squares of the faces of the rectangular parallelopiped whose edges are the semiprincipal diameters ; also the volume of the former is equal to the volume... | |
 | Thomas Leybourn - Mathematics - 1830 - 630 pages
...Class. i. Prove that 2. In any surface of the second order which has a centre, the sum of the squares of any system of conjugate diameter» is equal to the sum of the squares of the principal diameter». 3. Shew under what condition the equation Pdx ; (¿dy+Rdz - о... | |
 | John Radford Young - Geometry, Analytic - 1835 - 298 pages
...the faces of the parallelopiped whose edges are any system of semi-conjugate diameters, is equal to the sum of the squares of the faces of the rectangular parallelopiped whose edges are the semi-prinoipal diameters ; also the volume oi' the former is equal to the volume... | |
 | Michel Chasles - Cone - 1837 - 564 pages
...parallelopiped constructed on any system of conjugate diameters, are respectively equal to the volume, and the sum of the squares of the faces, of the rectangular parallelopiped constructed on the axes. a?2 y1 ¡g2 Let -ю + 775 + -7; = 1 be the equation to ,a surface of а o с then the equation to the... | |
 | John Hymers - Geometry, Analytic - 1848 - 368 pages
...parallelopiped constructed on any system of conjugate diameters, are respectively equal to the volume, and the sum of the squares of the faces, of the rectangular parallelopiped constructed on the axes. ****** Let -77 + -r + — r = 1 be the equation to a surface of a2 62 e2 the second order, referred... | |
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... the former is equal to the volume of the latter. Since the conditions furnished by the equations of the surface and by the equations of the tangent planes at the extremities of the conjugate diameters, as exhibited in last proposition... 