 | Samuel Hunter Christie - 1847 - 172 pages
...the cubes of the diameters of their bases, or as the cubes of their altitudes. PROP. LXXIV. THEOR. If a sphere be cut by a plane, the section will be a circle. Let ABC (fig. 81) be a sphere, and let it be cut by the plane BDC : the section BDC is a circle. From E,... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...of the frustum, its volume would be expressed by (th. 73, schol.) 7r(r' + r'S + rr')h. PROP. XIII. If a sphere be cut by a plane, the section will be a circle. Because the radii of the sphere are all equal, each of them being equal to the radius of the describing... | |
 | Olinthus Gregory - 1863 - 482 pages
...equal to one another. 11. Every pyramid is a third part of a prism of the same base and altitude. 12. If a sphere be cut by a plane, the section will be a circle. 13. Every sphere is two-thirds of its circumscribing cylinder. 14. A cone hemisphere, and cylinder... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...or cones are as the cubes of their like linear sides, or diameters, or altitudes, &e PROPOSITION XI. If a sphere be cut by a plane, the section will be a circle. Because the radii of the sphere are all equal, each of them being equal to the radius of the describing... | |
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... pyramids or cones are as the cubes of their like linear sides, or diameters, or altitudes, &c. And the same for all similar solids whatever, viz. that they are in proportion to each other, as the cubes of their like linear dimensions, since they are... 
