 | Adrien Marie Legendre - 1819 - 574 pagina’s
...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.... | |
 | Adrien Marie Legendre - 1822 - 394 pagina’s
...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... | |
 | Adrien Marie Legendre - 1825 - 570 pagina’s
...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... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 pagina’s
...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.... | |
 | Adrien Marie Legendre - 1828 - 346 pagina’s
...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... | |
 | Timothy Walker - 1829 - 138 pagina’s
...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... | |
 | Adrien Marie Legendre - 1830 - 344 pagina’s
...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... | |
 | Adrien Marie Legendre - 1836 - 394 pagina’s
...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... | |
 | Adrien Marie Legendre - 1841 - 288 pagina’s
...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.... | |
 | Benjamin Peirce - 1841 - 186 pagina’s
...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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XVII.) ; hence two similar pyramids are to each other as the cubes of their homologous sides. 
