 | Ferdinand Rudolph Hassler - 1828 - 180 pagina’s
...angles, as AGD, GDE, and so on, standing in equal segments, are equal to one another; and their sum being equal to twice as many right angles as the figure has sides wanting four: that is, eight right angles, each of these angles of the hexagon is equal eight sixths... | |
 | Thomas Curtis - 1829 - 814 pagina’s
...BE. THEOREM XX. — All the interior angles of any rectilineal figure, А В С DE (fig. 43, p. I.), are together equal to twice as many right angles as the figure has sides wanting four right angles. For from any point, as F, within the figure, let lines be drawn to its angular... | |
 | John Playfair - 1829 - 210 pagina’s
...= (2n — 4) xr = (n— 2) x 2r, that is, all the interior angles of any convex rectilineal figure are together equal to twice as many right angles as the figure has sides less two sides. " Es. PROPOSITION M. THEOREM. All the exterior angles of any convex rectilineal figure,... | |
 | Pierce Morton - 1830 - 584 pagina’s
...many, in number, as the sides of the figure, the angles [IV. § s. of these triangles are (I. 19.) together equal to twice as many right angles as the figure has sides. But the angles of these triangles are those which contain the solid angle at A, together with the pairs... | |
 | Thomas Perronet Thompson - 1833 - 168 pagina’s
...equal to twice as many right angles as the figure has sides. But (by Cor. 1 .) all the interior angles are together equal to twice as many right angles as the figure' has sides, diminished by four right angles ; and (by adding four right angles to each), all the interior angles... | |
 | Euclid - 1833 - 216 pagina’s
...formed as many triangles as the figure has sides, and therefore all their angles taken together are equal to twice as many right angles as the figure has sides (1): but the angles at the point F are equal to four right angles (2); and therefore the angles of... | |
 | Charles Bonnycastle - 1834 - 678 pagina’s
...we may refer to the proposition which asserts the interior angles of a plane figure to be equivalent to twice as many right angles as the figure has sides, minus two, art. 205. And as conditions exist involving merely the directions of the points, so also we have... | |
 | 1835 - 684 pagina’s
...has as many angles as sides : therefore all the interior angles together with four right angles are equal to twice as many right angles as the figure has sides. Therefore, &c. Cor. The four angles of a quadrilateral are together equal to four right angles. SECTION... | |
 | Euclid - 1835 - 540 pagina’s
...QED COR. 1. All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by... | |
 | John Playfair - 1836 - 148 pagina’s
...with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides. COR. II. All the exterior angles of any rectilineal figure are together equal to four right angles.... | |
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Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides. 
