 | 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,... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...two right angles (TI), 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 (T. IV.) ; therefore the sum... | |
 | Charles Hutton - Mathematics - 1860 - 1020 pages
...Ui t »ice as many right angles as the figure has sides. But the sum of all tbr inward angles, with four right angles, is equal to twice as many right angles as ttx figure has sides (th. 19). Therefore the sum of all the inward and all the oetward angles, is equal... | |
 | Charles Davies - 1863 - 436 pages
...twice as many right angles as the polygon has sidesBut the sum of all the interior angles together with four right angles, is equal to twice as many right angles as the polygon nas sides (Th- xxi) : that is, equal to the sum of all the inward and outward angles taken together-... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...similar. For, the corresponding angles in each are equal, because any angle in F( B either polygon is equal to twice as many right angles as the polygon has sides, less four, divided by the number of angles (B. I, P. XXVI, C. 4) ; and further, the corresponding sides... | |
 | 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... | |
 | C. Davies - 1867 - 342 pages
...twice as many right angles as the polygon has sidesBut the sum of all the interior angles together with four right angles, is equal to twice as many right angles as the polygon nas sides (Th- xxi) : that is, equal to the sum of all the inward and outward angles taken togetherFrom... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...to twice as many right angles as the figure has sides. But the sum of all the interior angles, with four right angles, is equal to twice as many right angles as the figure has sides (th. 19) ; therefore the sum of all the interior and all the exterior angles is equal... | |
 | 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.... | |
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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. 
