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" From this it is manifest that the side of the hexagon is equal to the radius of the circle. "
Recreations in mathematics and natural philosophy, recomposed by m. Montucla ... - Page 138
by Jacques Ozanam - 1840
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Recreations in Mathematics and Natural Philosophy ...

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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

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...
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Mechanics Magazine, Volume 2

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...
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American Mechanics' Magazine, Volume 1

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...
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Elements of Plane Geometry According to Euclid

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...
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Elements of geometry and mensuration

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...
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The Elements of Euclid, with many additional propositions, and explanatory ...

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...
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A Treatise on Arithmetic ...

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...
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A Treatise on Arithmetic: Through which the Entire Science Can be Most ...

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...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

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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