 | Edward Olney - Geometry - 1877 - 272 pages
...one re-entrant angle. PROPOSITION XV. 233. TJieorem, — The sum of the interior angles of a polygon is equal to twice as many right angles as the polygon has sides, less four right angles. FIo. 187. DEM. — Let n be the, number of sides of any polygon; then the sum... | |
 | William Chauvenet - Geometry - 1879 - 380 pages
...two right angles (11); therefore, the sum of all the angles, both interior and exterior, is twice aa many right angles as the polygon has sides. But the sum of the interior angles alone is twice as many right angles as the polygon has sides, less four right angles... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...the sum of the angles of all the triangles, that is, the sum of the interior angles of the polygon, is equal to twice as many right angles as the polygon has sides minus two. \ DEFINITIONS. 126.. Every proposition has an hypothesis (19), and a conclusion. Thus in... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...if, etc. QUERY. THEOREM XXVI. The sum of the interior angles of a polygon, plus four right angles, is equal to twice as many right angles as the polygon has sides. For, take any polygon, as ABCD E. If from any point within it, as F, lines be drawn to the vertices... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...equal, each to each. PROPOSITION XV. 264. Theorem. — The sum of the interior angles of a polygon is equal to twice as many right angles as the polygon has sides, less four right angles. DEMONSTRATION. Let n be the number of aides of any polygon. We are to prove... | |
 | Mathematical association - 1883 - 86 pages
...complementary. THEOR. 26. All the interior angles of any convex polygon together with four right angles are equal to twice as many right angles as the polygon has sides. THEOR. 27. The exterior angles of any convex polygon made by producing the sides in order are together... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...any convex polygon : A then shall all the interior angles of ABCDE together with four right angles be equal to twice as many right angles as the polygon has sides. Take any point O within the polygon ABCDE, and join O to each of the angular points of the polygon.... | |
 | Mathematical association - 1884 - 146 pages
...any convex polygon : A then shall all the interior angles of ABCDE together with four right angles be equal to twice as many right angles as the polygon has sides. Take any point O within the polygon ABCDE, and join O to each of the angular points of the polygon.... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...they are similar. For, the corresponding angles in each are equal, because any angle in either polygon is equal to twice as many right angles as the polygon has sides, less four right angles, divided PROPOSITION II. THEOREM. The circumference of a circle may be circumscribed... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...at any one vertex is two right angles (§ 31). Hence the sum of all the interior and exterior angles is equal to twice as many right angles as the polygon has sides. But the sum of the interior angles alone is equal to twice as many right angles as the polygon has sides, less four right... | |
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... therefore the sum of the angles of all the triangles is equal to twice as many right angles as the figure has sides. But the sum of all the angles... 
