 | Euclid - Geometry - 1853 - 176 pages
...Polygons. HYPOTHESES. If a figure be rectilinear. Idem • . CONSEQUENCES. The sum of all the internal {angles, together with four right angles, is equal to twice as many right angles as the figure has sides. {All its external angles are together equal to four right angles. L. Relative to... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...right angles as the figure has sides, less four right angles (P. 26). 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 sum of the exterior angles. Taking... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...But the angles at 0 are equal to four right angles (30 Cor.); .'. all the angles of the polygon are equal to twice as many right angles as the polygon has sides, diminished by four right angles. COR. 1 . Hence, all the angles of a pentagon = 6 right angles ; hexagon... | |
 | George Roberts Perkins - Geometry - 1856 - 460 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... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...ABD, is 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.... | |
 | Education - 1857 - 1266 pages
...alternate sides, also produced, the angles formed by these lines, together with eight right angles are equal to twice as many right angles as the polygon has sides. 4. If two chords intersect in a circle, the difference of their squares is equal to the difference... | |
 | British and foreign school society - 1857 - 548 pages
...alternate sides, also produced, the angles formed by these lines, together with eight right angles, are equal to twice as many right angles as the polygon has sides. 4. If two chords intersect in a circle, the difference of their squares is equal to the difference... | |
 | 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
...equal 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... | |
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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. 
