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" 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 338
by William Betz, Harrison Emmett Webb - 1916 - 178 pages
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Elements of Plane and Solid Geometry

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,...
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Elements of Geometry: And the First Principles of Modern Geometry

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....
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The Elements of Geometry

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...
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A Text-book of Geometry

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,...
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The Elements of Solid Geometry: With Numerous Exercises

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...
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A Text-book of Geometry

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...
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A Text-book of Geometry

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...
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Syllabus of Geometry

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....
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Elementary Solid Geometry and Mensuration

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...
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Plane and Solid Geometry

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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