 | Charles Davies - 1849 - 372 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 - 1852 - 436 pages
...solidity of the pyramid S-ABCDE, and abcdex^So measures that of the pyramid S-abcde (p. 17) ; hence, two similar pyramids are to each other as the cubes of their homologous edges. GENERAL SCHOLIUMS. 1. The chief propositions of this Book relating to the solidity of polyedrons, may... | |
 | Charles Davies - 1854 - 436 pages
...of the pyramid S•ABCDE, and abcdex^So measures that of the pyramid S•abcde (p. 17) ; hence, two similar pyramids are to each other as the cubes of their homologous edges. GENERAL SCHOLIUMS. 1. The chief propositions. of this Book relating to the solidity of polyedrons,... | |
 | George Roberts Perkins - 1856 - 460 pages
...V=(A + # + A^ a*) x^h — A x ±h +.ax + ^ A xaxi A, which establishes the Theorem. THEOREM XX. 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 angle... | |
 | Elias Loomis - 1857 - 242 pages
...and pyramids generally are to each other as the products of their bases by their altitudes. Cor. 3. Similar pyramids are to each other as the cubes of their homologous edges. Scholium. The solidity of any polyedron may be found by dividing it into pyramids, by planes passing... | |
 | Adrien Marie Legendre, Charles Davies - 1857 - 442 pages
...of the pyramid S• ABCDE, and abcdexySo measures that of the pyramid S•abcde (p. 17) ; hence, two similar pyramids are to each other as the cubes of their homologous edges. GENERAL SCHOLIUMS. 1. The chief propositions of this Book relating to the solidity of polyedrons, may... | |
 | Elias Loomis - 1858 - 256 pages
...and pyramids generally are to each other as the products of their bases by their altitudes. Cor. 3. Similar pyramids are to each other as the cubes of their homologous edges. Scholium. The solidity of any polyedron may be found by dividing it into pyramids, by planes passing... | |
 | Elias Loomis - 1859 - 372 pages
...multiplied by one third of this perpendicular. Also, similar pyramids are to each other as the cubes oi their homologous edges (Geom., Prop. 17, Cor. 3, B....unity, may be computed in the following manner : Let C — ABD be a tetraedron. From one angle, C, let fall a perpendicular, CE, on the opposite face; c... | |
 | Horatio Nelson Robinson - 1860 - 470 pages
...to those of the other, each to each, and similarly placed. Now, any two of these similar triangular pyramids are to each other as the cubes of their homologous edges ; and being like parts of their respective polyedrous, it follows that the polyedrous are to each other... | |
 | George Roberts Perkins - 1860 - 472 pages
...+ a + A? a') x i7t =A x £A + ax £A + ^ A xax £ A, which establishes the Theorem. THEOREM XX. 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 angle... | |
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Also, similar pyramids are to each other as the cubes of their homologous edges (Geom., Prop. 
