| Charles Reiner - Geometry - 1837 - 246 pages
...resolved into as many triangles as the figure has sides ; the sum total of their angles is, therefore, equal to twice as many right angles as the figure has sides. Now, the sum of the angles about the common vertex of these triangles = 4 rt. /.s; therefore, the sum... | |
| Euclides - 1838 - 264 pages
...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. COB. 2. — All the exterior angles of any rectilineal figure are together equal to four right angles.... | |
| Euclides - 1840 - 192 pages
...two right angles. All the angles, therefore, of the triangles into which the AE figure is divided, are equal to twice as many right angles as the figure has sides. But of these, the angles round the point F are equal to four right angles (Prop. 13, cor.) : if these... | |
| Dionysius Lardner - Curves, Plane - 1840 - 386 pages
...supplement of its adjacent external angle, the internal and external angles, taken together, will be equal to twice as many right angles as the figure has sides ; but, from what has been already shown, the external angles alone are equal to four right angles.... | |
| Euclides - Geometry - 1841 - 378 pages
...&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. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...to two right angles ; therefore also the angles CBA, BAC, ACB are equal to two right angles. COR. 1. All the interior angles of any rectilineal figure...twice as many right angles as the figure has sides, wanting four right angles. For any rectilineal figure ABCDE can be divided into as many triangles as... | |
| Euclides - 1842 - 316 pages
...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. COR. 2. All the exterior angles of any rectilineal figure are together equal to four right angles.... | |
| Nicholas Tillinghast - Geometry, Plane - 1844 - 110 pages
...two regular polygons, having the same number of sides. The sum of all the angles in each figure is equal to twice as many right angles as the figure has sides, less four right angles (BI A{ Prop. 13), and as the number of sides is the same in each figure, the sum of all the angles... | |
| Euclides - 1845 - 546 pages
...right angles, (i. 13.) therefore all the interior angles, together with all the exterior angles of the figure, are equal to twice as many right angles as the figure has sides ; but it has been proved by the foregoing corollary, that all the interior angles together with four... | |
| Euclid - Geometry - 1845 - 218 pages
...&c. QED COB. 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. the angles of these triangles are equal to twice as many right angles as there are triangles, that... | |
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