 | Benjamin Greenleaf - 1862 - 518 pages
...the solidity of the pyramid ABC-S, and DEFX i SP that of the pyramid DEF-S (Prop. XX.) ; hence two similar pyramids are to each other as the cubes of their homologous edges. DE2. PROPOSITION XXIII. — THEOREM. 495. There can be no more than five regular polyedrons. For, since... | |
 | Benjamin Greenleaf - 1861 - 638 pages
...the solidity of the pyramid ABC-S, and DEFX £ SP that of the pyramid DEF-S (Prop. XX.) ; hence two similar pyramids are to each other as the cubes of their homologous edges. PROPOSITION XXIII. — THKOREM. • 495. There can be no more than five regular polyedrons. For, since... | |
 | Benjamin Greenleaf - 1863 - 504 pages
...the solidity of the pyramid ABC-S, and DEFX i SP that of the pyramid DEF-S (Prop. XX.) ; hence two similar pyramids are to each other as the cubes of their homologous edges. PROPOSITION XXIII. — THEOREM. 495. There can be no more than five regular polyedrons. For, since... | |
 | Edward Brooks - 1868 - 284 pages
...found by dividing it into triangular pyramids, by passing planes through its vertices. THEOREM XIV. Similar pyramids are to each other as the cubes of their homologous edges. - Let S—ABCDE and S—FGH1K be two similar pyramids ; then will they be to each other as the cubes... | |
 | Benjamin Greenleaf - 1868 - 340 pages
...1.7320508 6.0000000 3.4641016 8.6602540 0.1178511 1.0000000 0.4714045 7.6631189 2.1816950 Also, since similar pyramids are to each other as the cubes of their homologous edges (Prop. XX II. Ek. VIII.), two polyedrons containing the same number of similar pyramids are to each... | |
 | Isaac Stone - 1869 - 272 pages
...having equivalent hases and equal altitudes, are equivalent, or equal in value. P. XV. B. VH. 12. Two similar pyramids are to each other as the cubes of their homologous edges. P. XX. B. VH. Give the general Scholiums to this Theorem. BOOK VHI. 1. Define a Cylinder, Cone, Sphere,... | |
 | Elias Loomis - 1871 - 302 pages
...and pyramids generally are to each othei »s the products of their bases by their altitudes. Cot 3. Similar pyramids are to each other as the cubes of their homologous edges. Scholium. The solidity of any polyedron may be found ly dividing it into pyramids, by planes passing... | |
 | Charles Davies - 1872 - 464 pages
...the cubes of their altitudes, or as the cubes of any other homologous lines. PROPOSITION XX. THEOREM. Similar pyramids are to each other as the cubes of their homologous edges. Let S-ABCDE, and S-abcde, be two similar pyramids, so placed that their homologous angles at the vertex... | |
 | Edward Olney - 1872 - 472 pages
...consequently *RH' : яrh' : : R' : Ia : : H" : Ae. PROPOSITION XI. 330. Theorem. — The volumes of similar pyramids are to each other as the cubes of their homologous dimensions. DEM. — Letting A and a be homologous sides of the bases of two similar pyramids, В and... | |
 | Edward Olney - 1872 - 562 pages
...consequently *RH' : nrh' : : R' : r1 : : H1 : A'. PROPOSITION XI. 530, TJieorem. — The volumes of similar pyramids are to each other as the cubes of their homologous dimensions. DEM.— Letting A and a be homologous sides of the bases of two similar pyramids, B and... | |
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Also, similar pyramids are to each other as the cubes of their homologous edges (Geom., Prop. 
