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" XVII.) ; hence two similar pyramids are to each other as the cubes of their homologous sides. "
Elements of Geometry - Page 153
by Adrien Marie Legendre - 1825 - 224 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...solidity of the pyramid SABCDE (4 I3), and abcde x -j So is the solidity of the pyramid Sabcde ; therefore two similar pyramids are to each other as the cubes of their homologous sides. 20 THEOREM. 435. Two similar polyedrons are to each other as the cubes of their homologous sides. Demonstration....
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 394 pages
...the 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

Adrien Marie Legendre - 1825 - 570 pages
...A ; it is evident that the pyramid, which connects four vertices of one polyedron, will be similar to the pyramid which connects the four homologous...are to each other as the cubes of their homologous sides,rt Di'mnn.etraiion. Two pyramids being similar, the less may be placed in the greater so that...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...of 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. Demonstration....
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...which joins the four homologous vertices of the other polyedron. Hence two similar polyedrons, 8tc. THEOREM. 434. Two similar pyramids are to each other as the cubes of their homologous sides. For two pyramids being similar, the smaller may be placed within the greater, so that the solid angle...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 138 pages
...cylinders are similar, when their altitudes are to each other as the radii of their bases — . 166. — Two similar pyramids are to each other as the cubes of their homologous sides — . Since by the definition the homologous solid angles are equal, the less pyramid may be placed...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1830 - 344 pages
...four homologous vertices of the other polyedron. Hence two similar polyedrons, ike. THEOREM. 434. Ttco similar pyramids are to each other as the cubes of their homologous sides. For two pyramids being similar, the smaller may be placed within the greater, so that the solid angle...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 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, may be...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 288 pages
...of 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. Demonstration....
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1841 - 186 pages
...altitudes by their altitudes, or as the cubes of their altitudes. 412. Corollary. Similar prisms or pyramids are to each other as the cubes of their homologous sides. Ratio of Similar Solids. 413. Corollary. Similar cylinders or ct>nes are to each other as the cubes...
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