 | Euclid, John Playfair - 1846 - 334 σελίδες
...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 - 272 σελίδες
...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),... | |
 | 1847 - 508 σελίδες
...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 - 1847 - 492 σελίδες
...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 - 1847 - 248 σελίδες
...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 σελίδες
...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 - 1849 - 252 σελίδες
...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,... | |
 | Euclid, Thomas Tate - 1849 - 120 σελίδες
...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 - 1849 - 372 σελίδες
...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 - 942 σελίδες
...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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... figure, together with four right angles, are equal to twice as many right angles as the figure has be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles. 
