| Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...as the figure has sides ; but the exterior are equal to four right angles ; therefore the interior **are equal to twice as many right angles as the figure has sides,** wanting four. PROP. II. Two straight lines, which make with a third line the interior angles on the... | |
| Euclides - 1846 - 272 pages
...internal, are equal to twice as many right angles, as there are sides of the figure ; but the internal **with four right angles, are equal to twice as many right angles as** there are sides of the figure (by Cor. 6) ; take away from both the internal angles, and the external... | |
| Education - 1847 - 508 pages
...liquidation of it. In how many years will the debt be paid off? OEOMETBY AND TRIGOSO1IETBY. SECTION I. — **1. All the interior angles of any rectilineal figure,...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... | |
| Great Britain. Committee on Education - School buildings - 1847 - 606 pages
...liquidation of it. In how many years will the debt be paid off? GEOMETRY AND TRIGONOMETRY. SECTION I. **1. All the interior angles of any rectilineal figure,...equal to twice as many right angles as the figure** hag sides. 2. Equal triangles, upon equal bases in the same straight line, and towards the same parts,... | |
| Anthony Nesbit - Plane trigonometry - 1847 - 492 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 - 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... | |
| Euclides - 1848 - 52 pages
...opposite angles ; and the three ulterior angles of every triangle are together equal to two right angles. **COR. 1. All the interior angles of any rectilineal...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
...triangles ; that is (Cor. 2. i. 15.), together with four right angles. Therefore all the angles of the **figure, together with four right angles, are equal...twice as many right angles as the figure has sides.** COR. 2. All the exterior angles of any rectilineal figuro, are together equal to four right angles.... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...(Prop. XXVII., BI), that is, as 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,... | |
| Charles Davies - Trigonometry - 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... | |
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