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

Adrien Marie Legendre - 1822 - 367 σελίδες
...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...

Elements of Geometry

Adrien Marie Legendre - 1825 - 224 σελίδες
...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,...

Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 224 σελίδες
...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...

Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre - 1825 - 224 σελίδες
...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,...

Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1828 - 316 σελίδες
...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...

Elements of geometry

Adrien Marie Legendre - 1841 - 235 σελίδες
...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,...

Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

1845
...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...

Elements of Geometry and Conic Sections

Elias Loomis - 1849 - 226 σελίδες
...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...

ELEMENTS OF GEOMETRY AND TRIGONOMETRY

A. M. LEGENDRE - 1852
...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...

Elements of Geometry and Trigonometry: From the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - 1854 - 432 σελίδες
...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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