 | Elias Loomis - Conic sections - 1858 - 256 pages
...is equal to tw» 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,... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...among the equal parts. SUM OF THE ANGLES. 433. Theorem. — The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two. For the polygon may be divided into as many triangles as it has sides, less two (417); and... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...of every triangle are acute, or each less than a right angle. THEOREM XIX. In any figure whatever, the sum of all the interior angles, taken together, is equal to twice as many right angles, wanting four, as the figure /MS sides. Let ABCDE be any figure ; then the sum of all its interior angles,... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...among the equal parts. SUM OF THE ANGLES. 433. Theorem. — The gum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two. For the polygon may be divided into as many triangles as it has sides, less two (417); and... | |
 | Sir Norman Lockyer - Science - 1901 - 1076 pages
...(Grynaeus-Bale, 1533 AD ) these two corollaries are given : — (1) The sum of the interior angles of any polygon is equal to twice as many right angles as the polygon has sides less two. (2) The sum of the exterior angles of any polygon is equal to four right angles. STAM. EUMORFOPOULOS.... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...equal to two right angles (Prop. II.) ; therefore the sum of all the interior and exterior angles, is equal to twice as many right angles as the polygon has sides ; that is, they are equal to all the interior angles of the polygon, together with four right angles.... | |
 | Hippolyte Taine - Knowledge - 1871 - 606 pages
...the polygon ; so that the angles of the polygon, if we add to them the angles at the vertices, are equal to twice as many right angles as the polygon has sides. Now we know independently that the angles at the vertices are together equal to four right angles ;... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 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. PRACTICAL QUESTIONS. 1. Do two lines that do not meet form an angle with each other ? Two... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...among the equal parts. SUM OF THE ANGLES. 423. Theorem. — The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two. For the polygon may be divided into as many triangles as it has sides, less two (417); and... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...one re-entrant angle. PROPOSITION XT. 253. TJieorem. — Tlie sum of the inferior angles of a polygon is equal to twice as many right angles as the polygon has sides, less four right angles. DEM. — Let n he the number of sides of any polygon ; then the sum of its... | |
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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. 
