| Euclides - 1838
...a side of a triangle, &c. o. E. i,. COn. 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 - 1840
...two right angles. All the angles, therefore, of the triangles into which the AE figure is divided, **are equal to twice as many right angles as the figure has sides.** But of these, the angles round the point F are equal to four right angles (Prop. 13, cor.) : if these... | |
| Dionysius Lardner - Curves, Plane - 1840 - 314 pages
...supplement of its adjacent external angle, the internal and external angles, taken together, will be **equal to twice as many right angles as the figure has sides** ; but, from what has been already shown, the external angles alone are equal to four right angles.... | |
| Euclides - Geometry - 1841 - 351 pages
...Wherefore, if a side of a triangle, &c. 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 ABCDE can be divided into as many triangles as the figure has sides, by... | |
| Euclides - 1842
...each of them is a right angle (10. Def.). 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... | |
| John Playfair - Euclid's Elements - 1842 - 317 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... | |
| John Playfair - Euclid's Elements - 1844 - 317 pages
...angles of the figure are equal to twice as many right angles as the figure has sides, wanting four. **COR. 2. All the exterior angles of any rectilineal figure are together equal to four right angles.** ABC, with its adjacent exterior Because every interior angle ABD, is equal (13. 1.) to two right angles... | |
| Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...two regular polygons, having the same number of sides. The sum of all the angles in each figure is **equal to twice as many right angles as the figure has sides,** less four right angles (BI A{ Prop. 13), and as the number of sides is the same in each figure, the... | |
| Euclides - 1845
...then «6 is the sum of all the interior 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 - 199 pages
...Wherefore, if a side of a triangle, &c. 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... | |
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