| 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 - 376 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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