 | Nathan Scholfield - 1845 - 894 pages
...many right angles as the figure has sides, wanting four right angles. Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the exterior angles. Taking from each... | |
 | William Scott - Measurement - 1845 - 288 pages
...end ought to coincide. Also, the sum of all the angles, together with four right angles, ought to be equal to twice as many right angles as the polygon has sides (Eue. i. 32. cor.). To find the angle contained by two straight lines conceived to be drawn from a... | |
 | Sir J. Butler Williams - Geodesy - 1846 - 368 pages
...of all the interior angles of the polygon formed by joining the stations by straight lines will be equal to twice as many right angles as the polygon has sides, wanting 4 right angles (Euc. Cor. 32, I.) Thus, if the figure have 3 sides, the sum of the interior... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...angles (Prop. i) ; •therefore the sum of all the interior angles, together with all the exterior angles, is equal to twice as many right angles as the polygon has sides ; but the sum of all the exterior angles is equal to four right angles (Prop. xxm) ; therefore the... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...as many of each as there are sides of the polygon : hence, the sum of all the interior and exterior angles is equal to twice as many right angles as the polygon has sides. Again, the sum of all tho interior angles is equal to two right angles, taken as many times, less two,... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...is equal to two right angles (Prop. XXVII.); therefore the sum of the angles of all the triangles, is equal to twice as many right angles as the polygon has sides. But the same angles are equal to the angles of the polygon, together with the angles at the point F,... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...each as there are sides of the polygon: hence, the sum of all the interior and exterior angles will be equal to twice as many right angles as the polygon has sides. But the sum of all the interior angles together with four right angles, is equal to twice as many right... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...as there are sides of the polygon : hence, the sum of all the interior and exterior angles will be equal to twice as many right angles as the polygon has sides. But the sum of all the interior angles together with four right angles, is equal to twice as many right... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...right angles as the figure has sides, less four right angles (P. 26). Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the exterior angles. Taking from each... | |
 | Euclides - Geometry - 1853 - 334 pages
...are similar. For if there be two regular polygons of the same number of sides, all the angles of each together with four right angles is equal to twice as many right angles as the polygon has sides ; and things that are equal to the same thing are equal to one another (Ax. i) : therefore the sum... | |
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Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the exterior angles. 
