 | Adrien Marie Legendre - Geometry - 1822 - 394 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... | |
 | Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...Draw from the vertex A the arcs AC, AD, which divide it into as many triangles as it has sides minus two. By the preceding theorem (891), the sum of the...as it has sides minus two, which agrees with (903). 4" "" '"•*"' -, с V \ МдЯ Я13.8 в V , y • -*«Г --• / ! 1 >v2--V / \ • ST * т i. Ы... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...their angles diminished by as many times two right angles as there are triangles ; that is, the surface of the polygon is equal to the sum of all its angles...times two right angles, as it has sides minus two. 470. Theorem. If a portion ABCD (fig. 192) of a regular polygon, situated entirely upon the same side... | |
 | Adrien Marie Legendre - Geometry - 1837 - 372 pages
...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 two, into the tri-rectangular triangle. Scholium. Let... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 pages
...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 two, into the tri-rectangular triangle. Scholium.... | |
 | Nathan Scholfield - 1845 - 894 pages
...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 two, into the tri-rectangular triangle. Scholium.... | |
 | Nathan Scholfield - Geometry - 1845 - 506 pages
...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 two, into the tri-rectangular triangle. Scholium.... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...their angles diminished by as many times two right angles as there are triangles ; that is, the surface of the polygon is equal to the sum of all its angles...times two right angles, as it has sides minus two. Surface described by t!ie revolution of a regular portion of a Polygon. 471. Theorem. If a portion... | |
 | George Roberts Perkins - Geometry - 1847 - 326 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. Schol. Let s be the sum of all the angles in... | |
 | Elias Loomis - Conic sections - 1849 - 252 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... | |
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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... 
