 | 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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... and the sum of the angles in all the triangles is evidently 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... 
