| Euclides - 1846 - 272 pages
...There are as many triangles constructed as the figure has sides, and therefore all these angles will be **equal to twice as many right angles as the figure has sides** (by Prop. 32) ; from these take four right angles, for the angles at the point F (by Cor. 3 Prop. 13),... | |
| Charles William Hackley - 1847 - 248 pages
...Hence it follows that the sum of all the inward angles of the polygon alone, A + B -f- C + D + E, is **equal to twice as many right angles as the figure has sides,** wanting the said four right angles. QED Corol. 1. In any quadrangle, the sum of all the four inward... | |
| Anthony Nesbit - 1847 - 488 pages
...accuracy of the previous work. Moreover, since the sum of all the interior angles of any polygon is **equal to twice as many right angles as the figure has sides,** lessened by four ; as the given figure has five sides, the sum of all its interior angles must be 2x5... | |
| 1847 - 508 pages
...SECTION I. — 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.** 2. Equal triangles, upon equal bases in the same straight line, and towards the same parts, are between... | |
| Euclides - 1848 - 52 pages
...angles. 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.** COB. 2. All the exterior angles of any rectilineal figure, made by producing the sides successively... | |
| Euclid, Thomas Tate - 1849 - 120 pages
...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 ABODE can be divided into as many triangles as the figure has sides, by... | |
| Charles Davies - 1849 - 372 pages
...to two right angles, taken as many times, less two, as the polygon has sides (Prop. XXVI.); that is, **equal to twice as many right angles as the figure has sides,** wanting four right angles. Hence, the interior angles plus four right Let the sides of the polygon... | |
| Elias Loomis - 1849 - 252 pages
...that is, together with four right angles (Prop. V., Cor. 2). Therefore the angles of the polygon are **equal to twice as many right angles as the figure has sides,** wanting four right angles. Cor. 2. All the exterior angles of a polygon are together equal to four... | |
| Charles Davies - 1850 - 218 pages
...triangles is equal to two right angles (Th. xvii) : hence, 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 about the point P is equal to four right angles (Th. ii. Cor. 3) ; and... | |
| Charles Davies - 1850 - 238 pages
...triangles is equal to two right angles (Th. xvii) : hence, 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 about the point P is equal to four right angles (Th. ii. Cor. 3) ; and... | |
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