| 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... | |
| 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... | |
| 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.... | |
| 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... | |
| 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... | |
| 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,... | |
| 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.... | |
| 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... | |
| 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... | |
| 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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