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" If a pyramid is cut by a plane parallel to its base, the... "
Elements of Geometry - Page 141
by Adrien Marie Legendre - 1819 - 208 pages
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 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...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 276 pages
...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,...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 280 pages
...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...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 294 pages
...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,...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 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...
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Elements of Geometry

Adrien Marie Legendre - 1841 - 288 pages
...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,...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

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...
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Elements of Geometry and Conic Sections

Elias Loomis - 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...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - 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...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 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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