The sum of the face angles of any polyhedron is equal to four right angles taken as many times, less two, as the polyhedron has vertices. Solid Geometry - Page 338by William Betz, Harrison Emmett Webb - 1916 - 178 pagesFull view - About this book
| George Albert Wentworth - Geometry - 1877 - 416 pages
...+ F — 2. .-.E+2=V+ F, QED PROPOSITION XXVI. THEOREM. 595. The sum of all tha angles of the faces of any polyhedron is equal to four right angles taken as many times as the polyhedron has vertices less two. Let E denote the number of edges, V the number oí vertices,... | |
| William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...number of solid angles formed by 3, 5, 7, &c., plane angles, must be even. XI.* Theorem. The sum of all the face angles of any polyhedron is equal to four right angles, taken as many times as the polyhedron has vertices, less two. To BE PROVED. The sum of the face angles S = 4R (w-2). PROOF.... | |
| Webster Wells - Geometry - 1886 - 392 pages
...Or, E + 2=V+F. PROPOSITION XXXIII. THEOREM. 591. In any polyedron the sum of the angles of the faces is equal to four right angles taken as many times, less two, as the polyedron has vertices. Let E denote the number of edges, V the number of vertices, F the number of... | |
| George Albert Wentworth - Geometry - 1892 - 468 pages
...increase the number of edges or vertices. Hence, for F faces -2, or PROPOSITION XXIX. THEOREM. 628. The sum of the face angles of any polyhedron is equal...angles taken as many times, less two, as the polyhedron JMS vertices. S BC Let E denote the number of edges, V the number oi vertices, F the number of faces,... | |
| Arthur Latham Baker - Geometry, Solid - 1893 - 154 pages
...holds for the given polyhedron. QED PROPOSITION XXIII. THEOREM. 212.*** The sum of the face-angles of any polyhedron is equal to four right angles taken as many times as the polygon has vertices less two. Notation. Let E, F and V denote the number of edges, faces and... | |
| George Albert Wentworth - Geometry - 1894 - 456 pages
...increase the number of edges or vertices. Hence, for F faces -2, or PROPOSITION XXIX. THEOREM. 628. The sum of the face angles of any polyhedron is equal...taken as many times, less two, as the polyhedron has verticesi BC Let E denote the number of edges, V the number of vertices, F the number of faces, and... | |
| George Albert Wentworth - Geometry - 1895 - 468 pages
...number of edges or vertices. Hence, for F faces —2, or PROPOSITION XXIX. THEOREM. 628. The sum of tJie face angles of any polyhedron is equal to four right...many times, less two, as the polyhedron has vertices. 8 B c Let E denote the number of edges, V the number of vertices, F the number of faces, and S the... | |
| George Albert Wentworth - Mathematics - 1896 - 68 pages
...of edges increased by two is equal to the number of vertices increased by the number of faces. 628. The sum of the face angles of any polyhedron is equal...many times, less two, as the polyhedron has vertices. THEOREMS. 641. Every section of a cylinder made by a plane passing through an element is a parallelogram.... | |
| Henry Dallas Thompson - Geometry, Solid - 1896 - 226 pages
...triangular, the number of faces is even and is four less than twice the number of the vertices. 15. The sum of the face angles of any polyhedron is equal to four right angles taken as many times as the polyhedron has vertices less two. 1 6. A regular polyhedron may be divided into as many regular... | |
| George Albert Wentworth - Geometry - 1899 - 496 pages
...will not increase the number of edges or vertices. Hence, for F faces PROPOSITION XXV. THEOREM. 663. The sum of the face angles of any polyhedron is equal...many times, less two, as the polyhedron has vertices. Let E denote the number of edges, V the number of vertices, F the number of faces, and S the sum of... | |
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