| John Mason Good - 1819
...the circle to the area of the ellipse, or any corresponding segments. Also the area of the elli|>se **is a mean proportional between the areas of the inscribed and circumscribed** circle*. J'or other properties, with their démonstrations, we refer to the best treatises on conies,... | |
| James Hann - Plane trigonometry - 1854 - 119 pages
....: АО' + OB' +OC' = ab + ac + bc- IZRr. (] 0) The area of a regular hexagon inscribed in a circle **is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.** л г г. пт* . Sir Area of hexagon = — sm — 6r" . 360° =Tsm-6= 3r* sin 60" , „ . ., i •... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...sides is odd. 258. An equiangular polygon circumscribed about a circle is regular. 259. The area of the **regular inscribed hexagon is three-fourths of that of the regular circumscribed hexagon.** 260. The area of the regular inscribed hexagon is a mean proportional between the areas of the inscribed... | |
| William Chauvenet - Geometry - 1872 - 368 pages
...sides is odd. 258. An equiangular polygon circumscribed about a circle is regular. 259. The area of the **regular inscribed hexagon is three-fourths of that of the regular circumscribed hexagon.** 260. The area of the regular inscribed hexagon is a mean proportional between the areas of the inscribed... | |
| David Munn - 1873
...reduced £ ; find the diameter of the hole. 60. The area of the regular hexagon inscribed in a circle **is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.** 6 1. If a spherical shell, when formed into a solid sphere, be equal in volume to its own cavity, shew... | |
| Harvard University - 1874
...quadrilateral form another quadrilateral which is capable of being inscribed hi a circle. 10. Prove **that the area of a regular inscribed hexagon is a...inscribed and circumscribed equilateral triangles.** 11. On a line are taken any points A, B, C On a parallel line fax taken points A', B', C', . . . .... | |
| David Munn - Measurement - 1874 - 157 pages
...reduced -]• ; find the diameter of the hole. 60. The area of the regular hexagon inscribed in a circle **is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.** 6 1. If a spherical shell, when formed into a solid sphere, be equal in volume to its own cavity, shew... | |
| Aaron Schuyler - Geometry - 1876 - 384 pages
...the regular inscribed hexagon is threefourths of the area of the regular circumscribed hexagon. 8. **The area of a regular inscribed hexagon is a mean proportional between the areas of the** regular inscribed and circumscribed triangles. 9. The area of a regular inscribed dodecagon is equal... | |
| George Albert Wentworth - 1879 - 196 pages
...is equiangular, and hence equilateral. .'. DA = BA. In like manner we may prove EA = CA. = 2 AB. Ex. **5. Show that the area of a regular inscribed hexagon...three.fourths of that of the regular circumscribed hexagon.** Let O be the centre of the O, HK a side of the regular inscribed hexagon. Join OH, and draw OC _L to... | |
| Isaac Sharpless - Geometry - 1879 - 282 pages
...to the area of the regular inscribed hexagon as TT is to f 1/3. 10. The area of an inscribed polygon **is a mean proportional between the areas of the inscribed and circumscribed** polygons of one half the number of sides (V. 22). II. The area of a circle whose radius is 1 is f.... | |
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