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" This pulyedrun may be considered as formed of pyramids, each having for its vertex the centre of the sphere, and for its base one of the faces of the polyedron. "
Elementary Geometry: With Applications in Mensuration - Page 149
by Charles Davies - 1850 - 216 pages
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 394 pages
...their surfaces. Scholium. Conceive a polyedron, all of whose faces touch the sphere ; this polyedron may be considered as formed of pyramids, each having...centre of the sphere, and for its base one of the polyedron's faces. Now it is evident that all these pyramids will have the radius of the sphere for...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...their surf&%?s. Scholium. Conceive a polyedron, all of whose faces touch the sphere ; this polyedron may be considered as formed of pyramids, each having...centre of the sphere, and for its base one of the polyedron's faces. Now it is evident that all these pyramids will have the radius of the sphere for...
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A Practical Treatise on Arithmetic: Wherein Every Principle Taught is ...

George Leonard (Jr.) - Arithmetic - 1839 - 362 pages
...the product of the surface of one end by the length, the quantity contained in a pyramid, or cone, is equal to One third of the product of its base by its height. What is called the frustnim of a pyramid or cone ? What is said of pyramids and cones which...
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A Practical Treatise on Arithmetic, [etc.].

George Leonard - Arithmetic - 1841 - 356 pages
...the product of the surface of one end by the length, The quantity contained in a pyramid, or cone, is equal to One third of the product of its base by its height. . Figure 20. The surface of a sphere, globe, or ball, like figure 20, has been found by calculation...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 268 pages
...their surfaces. Scholium. Conceive a polyedron, all of whose faces touch the sphere ; this polyedron may be considered as formed of pyramids, each having...centre of the sphere, and for its base one of the polyedron's faces. Now it is evident that all these pyramids will have the radius of the sphere for...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...1. Conceive also a polyedron, all of whose faces touch the sphere; this polyedron may be considerd as formed of Pyramids, each having for its vertex...centre of the sphere, and for its base one of the polyedrons faces. Now, it is evident l"at all these pyramids will have the radius of the sphere for...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Geometry - 1845 - 506 pages
...1. Conceive also a polyedron, all of whose faces touch the sphere; this polyedron may be considerd as formed of pyramids, each having for its vertex...centre of the sphere, and for its base one of the polyedrons faces. Now, it is evident that all these pyramids will have the radius of the sphere for...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845 - 542 pages
...1. Conceive also a polyedron, all of whose faces touch the sphere; this polyedron may be considerd as formed of pyramids, each having for its vertex...centre of the sphere, and for its base one of the polyedrons faces. Now, it is evident that all these pyramids will have the radius of the sphere for...
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The Cambridge and Dublin Mathematical Journal, Volumes 7-9

Duncan Farquharson Gregory, Robert Leslie Ellis, William Thomson Baron Kelvin, Norman Macleod Ferrers - Mathematics - 1848 - 1002 pages
...that the sphere and cone intersect in a circle which lies in the plane. The cone is one of revolution having for its vertex the centre of the sphere, and for its axis the line whose equations are x = y = z. Each of the coordinate .axes is a generating line of the...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 372 pages
...Conceive a polyedron, all of whose faces touch the sphere ; this polyedron may be considered as formed ot pyramids, each having for its vertex the centre of the sphere, and for its base one of the polyedron's faces. Now it is evident that all these pyramids will have the radius of the sphere for...
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