 | Jacques Ozanam - 1803 - 548 pages
...triangle and a square, and that the side of the hexagon is equal to the radius of the circumscriptible circle. THIS problem is, in some measure, the reverse...may be easily solved for the same polygons. We shall begin therefore with the pentagon. Let A 13 (fig. 42 pi. 5) be the side of the required pentagon l... | |
 | John Playfair - 1806 - 320 pages
...inscribed in the given circle ABCDEF. Which was to be done. COR. It appears from the demonstration that the side of the hexagon is equal to the radius of the circle. For the triangle EGD is equilateral. If through the points A, B, C, D, E, F there be drawn... | |
 | 1824 - 726 pages
...circle, and the converse. —If .our readers will turn to the figure there given, they will perceive that the side of the hexagon :is equal to the radius of the circumscribed circle; and that three radii, one til which must be vertical, drawn from the angles of... | |
 | 1825 - 428 pages
...a circle, and the converse. If our readers will turn to the figure there given, they will perceive that the side of the hexagon is equal to the radius of the circumscribed circle ; and that three radii, one of which must be vertical, drawn from the angles of... | |
 | Andrew Bell - 1837 - 290 pages
...equilateral, as was shown j and it is inscribed in the given circle ABCDEF. COB. — From this it is manifest, that the side of the hexagon is equal to the radius of the circle. drawn straight lines touching the circle, an equilateral and equiangular hexagon shall be described... | |
 | Thomas Lund - 1854 - 520 pages
...shew that ir lies between 3 and 4. In any circle inscribe a regular hexagon : then it is easily shewn that the side of the hexagon is equal to the radius of the circle, and therefore its whole perimeter = 6 times the radius = 3 diameters. Again, circumscribe a... | |
 | Euclides - 1855 - 230 pages
...Def. 15. I. 32 n, cor. 5. 1.13. e) I. 15. V) ill. 26. III. 29. IV. 11. cor. COROLLARY. It is evident that the side of the hexagon is equal to the radius of the circumscribing circle. PROPOSITION XVI. PROBLEM. — To inscribe an equilateral and equiangular quindecagon... | |
 | Noble Heath - 1855 - 468 pages
...triangles are equiangular, But equiangular triangles are also equilateral, (Euc. cor. 6, I;j therefore, the side of the hexagon is equal to the radius of the circle in which it is inscribed. Hence we see that the radius of a circle is the chord of an arc of... | |
 | Noble Heath - 1856 - 472 pages
...triangles are equiangular, But equiangular triangles are also equilateral, (Euc. cor. 6, 1;) therefore, the side of the hexagon is equal to the radius of the circle in which it is inscribed. Hence we see that the radius of a circle is the chord of an arc of... | |
 | Euclides - 1860 - 288 pages
...be equilateral ; and it is inscribed in the given circle ABCDEF. COR. — From this it is manifest, that the side of the hexagon is equal to the radius of the circle. And if through the points A, B, C, D, E, and F there be drawn straight lines touching the circle,... | |
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From this it is manifest that the side of the hexagon is equal to the radius of the circle. 
