 | George Roberts Perkins - Geometry - 1860 - 472 pages
...exterior angles is equal to four right angles (T. IV.) ; therefore the sum of all the interior angles is equal to twice as many right angles as the polygon has sides, wanting four right angles. Cor. I. In any triangle, the sum of the three angles is equal to two right... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...they be similar. For, the corresponding angles in each are equal, because any angle in F( B either polygon is equal to twice as many right angles as the polygon has sides, less four, divided by the number of angles (B. I, P. XXVI, C. 4) ; and further, the corresponding sides... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...the polygon. The sum of the angles of each triangle is two right angles. Therefore, the sum of the angles of the polygon is equal to twice as many right angles as it has sides, less two. The remark in Article 346 applies as well to this theorem. 424. Let R represent... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...three be among the equal parts. SUM OF THE ANGLES. 433. Theorem. — The gum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two. For the polygon may be divided into as many triangles as it has sides, less two (417); and... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...the polygon. The sum of the angles of each triangle is two right angles. Therefore, the sum of the angles of the polygon is equal to twice as many right angles as it has sides, less two. The remark in Article 346 applies as well to this theorem. 434. Let R represent... | |
 | Sir Norman Lockyer - Science - 1901 - 1076 pages
...(Grynaeus-Bale, 1533 AD ) these two corollaries are given : — (1) The sum of the interior angles of any polygon is equal to twice as many right angles as the polygon has sides less two. (2) The sum of the exterior angles of any polygon is equal to four right angles. STAM. EUMORFOPOULOS.... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...equal to two right angles (Prop. II.) ; therefore the sum of all the interior and exterior angles, is equal to twice as many right angles as the polygon has sides ; that is, they are equal to all the interior angles of the polygon, together with four right angles.... | |
 | Hippolyte Taine - Knowledge - 1871 - 606 pages
...the polygon ; so that the angles of the polygon, if we add to them the angles at the vertices, are equal to twice as many right angles as the polygon has sides. Now we know independently that the angles at the vertices are together equal to four right angles ;... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...many right angles as the figure has sides minus two. For if from any vertex A, diagonals AC, AD,AE, are drawn, the polygon will be divided into as many...meet form an angle with each other ? Two lines not iu the same plane ? 2. Does the magnitude of an angle depend upon the length of its sides ? 8. If a... | |
 | Edward Olney - 1872 - 270 pages
...at least one re-entrant angle. PROPOSITION XV. 253. Theorem,—The sum of the interior angles of a polygon is equal to twice as many right angles as the polygon has sides, less four right angles. Fio. 187. DEM.—Let n be the number of sides of any polygon; then the sum... | |
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... polygon, is equal to twice as many right angles as the polygon has sides minus two. 
