| Nathan Scholfield - 1845 - 896 pages
...BAE is equal to the angle B, and the part DAE is equal to the angle C. PROPOSITION XXVIII. THEOREM. **The sum of all the interior angles of a polygon is equal to** tvire as many ri^ht angles as ike figure has sides, less four right angles. Let ABCDEFG he the proposed... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...&c. 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... | |
| Euclides - 1845 - 544 pages
...angles. But all the interior angles of any rectilinear figure together with four right angles, are **equal to twice as many right angles as the figure has sides,** that is, if we agree to assume IT to designate two right angles, .-. nS + 27T = ntr, and «6 = »ir... | |
| Euclid - Geometry - 1845 - 218 pages
...QED COB. 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.** the angles of these triangles are equal to twice as many right angles as there are triangles, that... | |
| Dennis M'Curdy - Geometry - 1846 - 168 pages
...p. 13. (e)p.29; Cor. 1. All the interior angles of any rectilineal figure and four right angles, are **equal to twice as many right angles as the figure has sides.** For, about a point within the figure, as many triangles may be formed as the figure has sides, each... | |
| Euclides - 1846 - 292 pages
...QEU 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... | |
| 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),... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 332 pages
...many right angles as the figure has sides, wanting four. For all the angles exterior and interior are **equal to twice as many right angles as the figure has sides** ; but the exterior are equal to four right angles ; therefore the interior are equal to twice as many... | |
| Anthony Nesbit - Plane trigonometry - 1847 - 492 pages
...prove the 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... | |
| Benjamin Peirce - Geometry - 1847 - 204 pages
...the exterior angle BCD is equal to the sum of the two opposite interior angles A and B. 72. Theorem. **The sum of all the interior angles of a polygon is equal to** as many times two right angles as it has sides minus two. Proof. Let ABCDE, &c. (fig. 37), be the given... | |
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