| John Playfair - Euclid's Elements - 1846 - 317 pages
...from a point F within the figure to each of its angles. And, by the preceding proposition, all the **angles of these triangles are equal to twice as many right angles as** there are triangles, that is, as there are sides of the figure ; and the same angles are equal to the... | |
| Euclides - 1846
...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),... | |
| George Moody - 1847
...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... | |
| Anthony Nesbit - Plane trigonometry - 1847 - 426 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... | |
| Charles William Hackley - Geometry - 1847 - 103 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... | |
| Euclides - 1848
...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... | |
| Elias Loomis - Conic sections - 1849 - 226 pages
...there are sides of the polygon BCDEF. Also, the angles of the polygon, together with four right angles, **are equal to twice as many right angles as the figure has sides** (Prop. XXVIII., BI); hence all the angles of the triangles are equal to all the angles of the polygon,... | |
| Euclides - 1849
...from a point r within the figure to each of its angles. And, by the preceding proposition, all the **angles of these triangles are equal to twice as many right angles as** there are triangles, that is, as there are sides of the figure ; and the same angles are equal to the... | |
| Charles Davies - Trigonometry - 1849 - 359 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... | |
| Great Britain. Committee on Education - 1850
...Section.) 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. If the square described upon one side of a triangle be equal to the sum of the squares described... | |
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