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" The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. "
Elements of Plane and Solid Geometry - Page 221
by George Albert Wentworth - 1877 - 398 pages
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 4

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,...
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The Elements of Plane Trigonometry

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 •...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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...
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Mensuration of lines, surfaces, and volumes

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...
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Catalogue - Harvard University

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', . . . ....
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Exercises on mensuration

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...
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Elements of Geometry with Exercises for Students: An an Introduction to ...

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...
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Exercises Contained in Wentworth's Geometry: With Key, Followed by a ...

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...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

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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