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" The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two. "
Elements of Geometry: With Practical Applications ... - Page 37
by George Roberts Perkins - 1847 - 308 pages
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New Series of The Mathematical Repository, Volume 3

Thomas Leybourn - Mathematics - 1814
...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,...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 208 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...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 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...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

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,...
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Plane Trigonometry and Mensuration for the Use of the Royal Military College

William Scott - Measurement - 1845 - 290 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...
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Practical Geodesy: Comprising Chain Surveying, and the Use of Surveying ...

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...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 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,...
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Elements of Geometry and Conic Sections

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,...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...divided by producing either of the sides CD or FD. This polygon is said to have a re-entering angle at D. PROPOSITION XXIV. THEOREM. In any convex polygon,...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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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 236 pages
...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 angles as the polygon has sides (Th. xxi) : that is, equal to the sum of all the inward and outward angles taken together. From each...
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