 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...to those Of the other ; still it was necessary to demonstrate it in a rigorous manner. THEOREM. 422. If a pyramid is cut by a plane parallel to its base, the fruttum which remains, after taking au.ay the smaller pyramid, is equal to the sum of . three pyramids,... | |
 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...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 - Geometry - 1825 - 276 pages
...to those of the other ; still it was necessary to demonstrate it in a rigorous manner. THEOREM. 422. If a 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 - Geometry - 1828 - 346 pages
...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... | |
 | Dionysius Lardner - Curves, Plane - 1840 - 386 pages
....172 (357.) Numerical Calculation of the Volumes of all Solids - 172 (359.) If a triangular Pyramid be cut by *a Plane parallel to its Base, the Pyramid cut off will be similar to the whole - - - - - 173 (362.) The Volumes of similar Pyramids as the Cubes of their... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...those of the other ; still it was necessary to demonstrate it in a rigorous manner. • THEOREM. 422. If a 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 pages
...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 - Conic sections - 1849 - 252 pages
...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 - Geometry - 1852 - 436 pages
...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 - Geometry - 1854 - 436 pages
...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... 
