 | 1860 - 462 pages
...figure must be aliquot parts of the circle or of four right angles. All the angles of any such figure are equal to twice as many right angles as the figure has sides minus four right angles, or if « be the number of sides, the sum of all the angles is (2n —... | |
 | William Schofield Binns - 1861 - 238 pages
...let the required polygon be a pentagon. From Euc. I., 32, Cor. 1, "All the angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides." From this corollary, we can deduce a formula for finding the angle of any polygon. Let x equal... | |
 | Elias Loomis - Conic sections - 1861 - 244 pages
...there are sides of the polygon BCDEF. Also, the anGEOMETRY. gles of the polygon, together with lour right angles, are equal to twice as many right angles as the figure has sides (Prop. XXVIII., BI) ; hence all the angles of the triangles are equal to all the angles of the... | |
 | Euclides - 1862 - 140 pages
...the common vertex of all the triangles, are equal to four right angles. (I. 15, cor. 2.) 6. Therefore all the angles of the figure, together with four right...equal to twice as many right angles as the figure has sides. Corollary. — 2. All the exterior angles of any rectilineal figure are together equal to four... | |
 | Euclides - 1862 - 172 pages
...are equal to twice as many right angles as there are angles or sides. but all the interior angles, together with four right angles, are equal to twice as many right angles as the figure has sides ; (cor. 1) therefore all the interior angles, together with all the exterior angles, are equal... | |
 | University of Oxford - Education, Higher - 1863 - 316 pages
...fall on it from the opposite angle, and the acute angle. 4. All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides. 5. Describe a parallelogram equal to a given rectilineal figure, and having an angle equal to... | |
 | Euclides - 1863 - 122 pages
...point F within the Cor. 1.—All the interior angles (ABC, BCD, &c.) of any rectilineal figure (ABCDE) together with four right angles are equal to twice as many right angles as the figure has sides. ., figure to each of its angles. \ Because the three interior angles of a triangle are equal... | |
 | Henry S. Merrett - 1863 - 428 pages
...sides. It has been proved by the foregoing corollary that all the interior angles, together with the four right angles, are equal to twice as many right angles as the figure has sides. Therefore all the interior angles, together with all the exterior angles, are equal to all the... | |
 | Henry S. Merrett - 1863 - 476 pages
...sides. It has been proved by the foregoing corollary that all the interior angles, together with the four right angles, are equal to twice as many right angles as the figure has sides. Therefore all the interior angles, together with all the exterior angles, are equal to all the... | |
 | Euclides - 1864 - 448 pages
...angles of the triangles are equal to twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right...equal to twice as many right angles as the figure has sides. COR. 2. All the exterior angles of any rectilineal figure, made by producing the sides successively... | |
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F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides. 
