 | George Washington Hull - Geometry - 1807 - 408 pages
...equilateral and equiangular. Therefore ^4D and FK are equal polygons. §215. QED 442. COR. — Any section of a prism made by a plane parallel to the base is equal to the base. PROPOSITION II. THEOREM. 443. The lateral area of a prism is equal to the product of the perimeter... | |
 | Euclides - 1842 - 316 pages
...SECTION of a pyramid made by a plane parallel t° the base is a figure similar to the base : and a section of a prism made by a plane parallel to the base is a figure similar and equal to the base. Let the pyramid K-ABCD be cut by a plane parallel to the baseABCD:... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...polygons are both mutually equilateral and mutually equiangular, and consequently are equal. Cor. A section of a prism made by a plane parallel to the base of the prism, is a polygon equal to the base. THEOREM V. Two parallelopipedons, the one rectangular... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...perpendicular to the bases. A REGULAR PRISM is a right prism whose base is a regular polygon. 673. Corollary — The altitude of a right prism is equal...solid between^ the two secant planes is also a prism. 228 HOW DIVI8IBLE. 673. Problem. — Every prism can be divided into (tie tame number of triangular... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...sides of a right prism are rectangles. The sides of a regular prism are equal. 673. Theorem — If tivo parallel planes pass through a prism, so that each...solid between the two secant planes is also a prism. 228 HOW DIVISIBLE. 675. Problem — Every prism can be divided into the same number of triangular prisms... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...two sections, being both mutually equilateral and mutually equiangular, are equal. 15. Corollary. Any section of a prism, made by a plane parallel to the base, is equal to the base. PROPOSITION II.— THEOREM. 16. The lateral area of a prism is equal to the product of the perimeter... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...plane parallel to their bases, the areas of the sections are proportional to the areas of the PKISMS. 669. A PRISM is a polyedron which has two of its faces...solid between the two secant planes is also a prism. 228 HOW DIVISIBLE. 673. Problem — Every prism can be divided into the tame number of triangular prisms... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...two sections, being both mutually equilateral and mutually equiangular, are equal. 15. Corollary. Any section of a prism, made by a plane parallel to the base, is equal to the base. PROPOSITION II.—THEOREM. 16. The lateral area of a prism is equal to the product of the perimeter... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...the polygons, being mutually equiangular and equilateral, are equal (II. G). 171 Cor. 1. A section made by a plane parallel to the base is equal to the base. • 181 Cor. 2. A section of a cylinder made by a plane parallel to the base is a circle equal to the... | |
 | William Frothingham Bradbury - Geometry - 1873 - 288 pages
...the polygons, being mutually equiangular and equilateral, are equal (II. 6). 17« Cor. 1. A section made by a plane parallel to the base is equal to the base. 18, Cor. 2. A section of a cylinder made by a plane parallel to the base is a circle equal to the base.... | |
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... the two planes are equal polygons. Each side of one of the sections is parallel to the corresponding side of the other section, since they are the intersections of two parallel planes by a third. Hence, that portion of each side of the prism which... 
