| John Daniel Runkle - Mathematics - 1860
...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 (2 n —... | |
| William Schofield Binns - 1861
...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, LL.D. - 1861
...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
...all the triangles, are equal to four right angles, (i. 15, cor. 2) 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. Cor. 2. Att the exterior angles of any rectilineal figure are together equal to four right angles.... | |
| Euclides - 1862
...with its adjacent exterior angle ABD, are equal to two right angles. (I. 13.) angles of the figure, **are equal to twice as many right angles as the figure has** sides. 3. But all the interior angles, together with four right angles, are equal to twice as many... | |
| University of Oxford - Education, Higher - 1863
...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
...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 - Surveying - 1863 - 317 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
...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
...Wherefore, if a side of any triangle be produced, &c. QED COR. 1. 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. D For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides,... | |
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