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" Also, similar pyramids are to each other as the cubes of their homologous edges (Geom., Prop. "
Elements of Plane and Spherical Trigonometry: With Their Applications to ... - Page 83
de Elias Loomis - 1855 - 178 pages
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Elements of Geometry

Adrien Marie Legendre - 1819 - 208 pages
...homologous vertices of the other polyedron : therefore two similar polyedrons, &c. THEOREM. 434. Two similar pyramids are to each other as the cubes of their homologous sides. Demonstration. Two pyramids being similar, the less may be placed in the greater so that they...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1822 - 367 pages
...solidity of the pyramid SABCDE, and abcde x £So is that of the pyramid Sabcde (18. VI.) ; hence two similar pyramids are to each other as the cubes of their homologous sides. PROPOSITION XXVII. THEOREM. Two similar polyedrons are to each other as the cubes of their homologous...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 224 pages
...the pyramid S ABCDE (4 1 3), and abcdexi S o is the solidity of the pyramid S abcde ; therefore two similar pyramids are to each other as the cubes of their homologous sides. THEOREM. 435. Two similar polyedrons are to each other as the cubes of their homologous sides....
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 pages
...homologous vertices of the other polyedron ; therefore two similar polyedrons, &c. THEOREM. 434. Two similar pyramids are to each other as the cubes of their homologous sides. Demonstration. Two pyramids being similar, the less may be placed in the greater so that they...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - 1829 - 129 pages
...homologous faces are to each other as the squares of their homologous sides. 166. THEOREM. — Two similar pyramids are to each other as the cubes of their homologous sides. DEM. — Since by the definition the homologous solid angles are equal, the less pyramid may...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 359 pages
...solidity of the pyramid S-ABCDE, and abcde x^So is that of the pyramid S-abcde (Prop. XVII.) ; hence two similar pyramids are to each other as the cubes of their homologous sides. General Scholium. The chief propositions of this Book relating to the solidity ol polyedrons,...
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Elements of geometry

Adrien Marie Legendre - 1841 - 235 pages
...the' pyramid SAB CDE (41 3), and abcde x \ So is the solidity of the pyramid Sab cde; therefore two similar pyramids are to each other as the cubes of their homologous sides. THEOREM. 435. Two similar polyedrons are to each other as the cubes of their homologous sides....
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

1845
...solidity of the pyramid S ABCDE ando&cdeXiSo is that of the pyramid Sabcde (Prop. XXV. Cor.) ; hence two similar pyramids are to each other as the cubes of their homologous sides. And since two similar polyedrons may be conceived to be made up of the same number of triangular...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - 1847 - 308 pages
...faces which form the solid angle whence the planes of division proceed. PROPOSITION XVIII. THEOREM. Two similar pyramids are to each other as the cubes of their homologous sides. For, two pyramids being similar, the smaller maybe placed within the greater, so that the solid...
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Elementary Course of Geometry ...

Charles William Hackley - 1847 - 103 pages
...pyramids are equal when their base and an edge of the one are equal to the same in the other. 21. That similar pyramids are to each other as the cubes of their homologous sides. 22. That similar polyhedrons are as the cubes of their homologous sides. 23. That the surfaces...
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