 | Adrien Marie Legendre - 1819 - 574 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... | |
 | Adrien Marie Legendre - 1822 - 394 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... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 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.... | |
 | Adrien Marie Legendre - 1825 - 276 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... | |
 | Timothy Walker - 1829 - 156 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... | |
 | Adrien Marie Legendre - 1836 - 394 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,... | |
 | Adrien Marie Legendre - 1841 - 288 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.... | |
 | Nathan Scholfield - 1845 - 894 pages
...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... | |
 | George Roberts Perkins - 1847 - 326 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... | |
 | Charles William Hackley - 1847 - 248 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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Also, similar pyramids are to each other as the cubes of their homologous edges (Geom., Prop. 
