| Thomas Leybourn - Mathematics - 1814 - 420 pages
...Hence, by adopting the notation in the question, we have But the sum of the angles of any polygon being **equal to twice as many right angles as the polygon has sides,** less four; the sum of all the angles of the polygon will be equal to an even number of right angles,... | |
| John Radford Young - Euclid's Elements - 1827 - 228 pages
...to say, the sum of the angles of the polygon, together with those about the point within . it, are **equal to twice as many right angles as the polygon has sides** ; but those angles which are' about the point, amount to four right angles, (Prop. VI. Cor. 2.) deducting... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...figure has sides, wanting four right angles. Hence, the interior angles plus four right .. -i angles, **is equal to twice as many right angles as the polygon has** aides, and consequently, equal to the sum of the interior angles plus the exterior angles. Taking from... | |
| Nathan Scholfield - 1845 - 894 pages
...of each as there arc 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 the interior angles is equal to two right angles, taken as many times, less two,... | |
| 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 angles... | |
| George Roberts Perkins - Geometry - 1847 - 326 pages
...(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
...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,... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...the sides CD or FD. This polygon is said to have a re-entering angle at D. PROPOSITION XXIV. THEOREM. **In any convex polygon, the sum of all the interior angles, taken together, is equal to twice as many** right-angles as the polygon has sides, wanting four right-angles. Let ABCDFG be a convex polygon. Conceive... | |
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