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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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Text-book of Elementary Plane Geometry

Julius Petersen - Geometry, Modern - 1880 - 86 pages
...paper with the side a? 208. Prove that the area of a regular 2n sided figure inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed n sided figure. 210. How great is the radius of a circle, in which a sector of 7 12' has an area...
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Text-book of Elementary Plane Geometry

Julius Petersen - Geometry, Plane - 1880 - 73 pages
...paper with the side a? 2o8. Prove that the area of a regular 2n sided figure inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed n sided figure. 2o9. How great is the radius of a circle, the area of which is 1D'? 210. How great...
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Elements of Geometry

Simon Newcomb - Geometry - 1881 - 418 pages
...any circumscribed polygon as its circumference to the perimeter of the polygon. 3. The area of the regular inscribed hexagon is a mean proportional between...inscribed and circumscribed equilateral triangles. BOOK VII. OF LOCI AND CONIC SECTIONS. CHAPTER I. LINES AND CIRCLES AS LOCI. 497. To fix the position...
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Elements of Geometry

George Albert Wentworth - Geometry, Plane - 1879 - 250 pages
...side of a circumscribed equilateral triangle is double the side of an inscribed equilateral triangle. 5. Show that the area of a regular inscribed hexagon...that the area of a regular inscribed hexagon is a | I mean proportional between the areas of the inscribed and cir- ,; Icumscribed equilateral triangles....
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...of a regular inscribed hexagon equals threefourths the area of a regular circumscribed hexagon. 5. The area of a regular inscribed hexagon is a mean...inscribed and circumscribed equilateral triangles. 6. If the vertices of a square are taken as centres and half the diagonal as a radius and circles be...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1884 - 368 pages
...inscribed hexagon is three-fourths of that of the regular circumscribed hexagon. 200. The area of the regular inscribed hexagon is a mean proportional between the areas of the inscribed and circtmiscribed equilateral triangles. 261. A plane surface may be entirely covered (as in the construction...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...vertex. 7. The figure bounded by the five diagonals of a regular pentagon is a regular pentagon. 8. The area of a regular inscribed hexagon is a mean proportional between the areas of an inscribed, and of a circumscribed equilateral triangle. 9. In the figure of Prop. VIII., prove that...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 331 pages
...regular inscribed triangle is one-half the area of the regular inscribed hexagon. 6. The area of the regular inscribed hexagon is three-fourths of that of the regular circumscribed hexagon. 7. The area of the regular inscribed hexagon is a mean proportional between the areas of the inscribed...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 274 pages
...to threefourths of that of the circumscribed regular hexagon. 392. The area of an inscribed regular hexagon is a mean proportional between the areas of the inscribed and the circumscribed equilateral triangles. 393. The area of an inscribed regular octagon is equal to...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 418 pages
...inscribed hexagon is threefourths of that of the regular circumscribed hexagon. 5. The area of the regular inscribed hexagon is a mean proportional between...inscribed and circumscribed equilateral triangles. G. If the perpendicular from A to the side BC of the equilateral triangle ABC meet BC in D, and the...
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