| George Roberts Perkins - Geometry - 1850 - 332 pages
...all the triangles is evidently the same as that of all the angles in the polygon: hence the surface **of the polygon is equal to the sum of all its angles, diminished by** twice as many right-angles as it has sides minus two. ScTiol. Let s be the sum of all the angles in... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...angles of all the triangles is the sattne as that of all the angles of the polygon ; hence, the surface **of the polygon is equal to the sum of all its angles, diminished by** twice as many right angles as it has Asides less two, into the tri-rectangular triangle. APPENDIX.... | |
| Charles Davies - Geometry - 1854 - 436 pages
...angles of all the triangles is the same as that of all the angles of the polygon ; hence, the surface **of the polygon is equal to the sum of all its angles, diminished by** twice as many right angles as it has sides less two, into the tri•rectangular triangle. Scholium.... | |
| George Roberts Perkins - Geometry - 1856 - 460 pages
...all the triangles is evidently the same as that of all the angles in the polygon ; hence the surface **of the polygon is equal to the sum of all its angles, diminished by** twice as many right angles as it has sides minus two. Scholium. Let s be the sum of all the angles... | |
| Elias Loomis - Conic sections - 1858 - 256 pages
...triangles, etc. PROPOSITION XXI. THEOREM. Tfte surface, of a spherical polygon is measured by the sum of **its angles, diminished by as many times two right angles as it has sides** less two, multiplied by the quadrantal triangle. Let ABCDE be any spherical polygon. From the vertex... | |
| George Roberts Perkins - Geometry - 1860 - 470 pages
...all the triangles is evidently the same as that of all the angles in the polygon ; hence the surface **of the polygon is equal to the sum of all its angles,** dimir ished by twice as many right angles as it has sides minus two. Scliolium. Let s be the sum of... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...the sum of all the angles of the polygon ; hence the surface of the polygon is measured by the sum of **its angles, diminished by as many times two right angles as it has sides** less two, multiplied by the quadrantal triangle. Cor. If the polygon has five sides, and the sum of... | |
| John Reynell Morell - Geometry - 1871 - 156 pages
...polygon, to all its vertices. (Fig. 68.) Pig. 68. 81. The sum of the angles of every polygon amounts to **as many times two right angles as it has sides minus two.** For the angles of the triangles of the first decomposition noticed above composed the angles of the... | |
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