 | Adrien Marie Legendre - 1822 - 394 pagina’s
...necessary, notwithstanding, to demonstrate this truth in a rigorous manner. PROPOSITION XXI. THEOREM. If a pyramid is cut by a plane parallel to its base, the frustum that remains when the little pyramid is taken away, is equal to the sum of three pyramids having... | |
 | Adrien Marie Legendre - 1825 - 276 pagina’s
...equal in solidity. 421. Scholium. This proposition seems to result immediately from a former (386), in which it was shown that, with respect to two symmetrical...pyramid is cut by a plane parallel to its base, the frustum which remains, after taking away the smaller pyramid, is equal to the sum of three pyramids,... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 pagina’s
...equal in solidity. 421. Scholium. This proposition seems to result immediately from a former (386), in which it was shown that, with respect to two symmetrical...rigorous manner. THEOREM. 422. If a pyramid is cut by n plane parallel to its base, the frustum which remains, afier taking away the smaller pyramid, is... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 294 pagina’s
...equal in solidity. 421. Scholium. This proposition seems to result immediately from a former (386), in which it was shown that, with respect to two symmetrical...necessary to demonstrate it in a rigorous manner. j THEOREM. — 422. If a pyramid is cut by a plane parallel to its base, the frustum which remains,... | |
 | Adrien Marie Legendre - 1828 - 346 pagina’s
...bases. For a like reason, two prisms of the same base are to each other as their altitudes. LEMMA. 408. If a pyramid is cut by a plane parallel to its base, First, The edges and the altitude will be divided proportionally. Secondly, The section will be a polygon... | |
 | Adrien Marie Legendre - 1841 - 288 pagina’s
...equal in solidity. 421. Scholium. This proposition seems to result immedi ately from a former (386), in which it was shown that, with respect to two symmetrical...pyramid is cut by a plane parallel to its base, the frustum which remains, after taking away the smaller pyramid, is equal to the sum of three pyramids,... | |
 | Nathan Scholfield - 1845 - 894 pagina’s
...prisms, so divided, will bo the elementary prisms of the prism so divided. PROPOSITION XIX. THEOEEM. If a pyramid is cut by a plane parallel to its base, First, The edges and the altitudes will be divided proportionally. And thirdly, These two surfaces... | |
 | Elias Loomis - 1849 - 252 pagina’s
...Solid FD : solid fd : : AB': ab': : AF': af. Therefore, similar prisms, &c. PROPOSITION XIII. THEOREM. If a pyramid is cut by a plane parallel to its base, 2d. The section will be a polygon similar to the base. 1st. The edges and the altitude will be divided... | |
 | Adrien Marie Legendre - 1852 - 436 pagina’s
...the perpendicular let fall from the vertex to either side of the polygon which forms the base. 13. If a pyramid is cut by a plane parallel to its base, forming a second base, the part lying between the bases, is called a truncated pyramid, or frustum... | |
 | Charles Davies - 1854 - 436 pagina’s
...the perpendicular let fall from the vertex to either side of the polygon which forms the base. 13. If a pyramid is cut by a plane parallel to its base, forming a second base, the part • lying between the bases, is called a truncated pyramid, or frustum... | |
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If a pyramid is cut by a plane parallel to its base, the... 
