...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...

...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,...

...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...

...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,...

...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...

...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,...

...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...

...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...

...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...

...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...