Books Books
The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Mensuration of lines, surfaces, and volumes - Page 98
by David Munn - 1873

## Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 4

John Mason Good - 1819 - 824 pages
...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,...

## A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1845 - 222 pages
...Euclid, Book iv., prop. 10; compare the areas of the two circles. 175. The area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and a circumscribed regular polygon of half the number of sides. 176. In a regular polygon...

## A Treatise on Plane and Spherical Trigonometry ...

Thomas Grainger Hall - Trigonometry - 1848 - 192 pages
...circle inscribed in the triangle ABO, OA* + ОБ2 + ОС1 = ab + ас + be - 12 Er. (13.) The area of a regular hexagon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribed equilateral triangle. (14.) The square of the side of a pentagon inscribed...

## The Elements of Plane Trigonometry

James Hann - Plane trigonometry - 1854 - 140 pages
...12Бг = ab + ас + bc — 12Rr ; .: АO2 + OB' + OС2 = ab + ас + bc — 12.ßr. (10) The area of a regular hexagon inscribed in a circle is a mean proportional...inscribed and circumscribed equilateral triangles. Area of hexagon = — sin — ' 2 я 6r' . 360" = — sin — ^~ Area of inscribed triangle = — sin...

## The Elements of Plane and Spherical Trigonometry

John Hind - Trigonometry - 1855 - 546 pages
...the equality, a' = jAa, we conclude that the area of a regular polygon of an even number of sides, inscribed in a circle, is a mean proportional between the areas of an inscribed and of a circumscribed regular polygon of half the number of sides : , с , ,v A, 2^N...

## Collection of Examples and Problems in Pure and Mixed Mathematics: With ...

Alfred Wrigley - Mathematics - 1862 - 330 pages
...radii of the circumscribed and inscribed circles is a cot - — n 33. The area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and a circumscribed regular polygon of half the number of sides. 34. A, B, C, are 3 regular...

## Plane trigonometry and logarithms

John Walmsley - Logarithms - 1865 - 232 pages
...the side of a pentagon inscribed in a circle be 1, the v/(5t--/5) radius = 1() • 3. The area of a regular hexagon inscribed in a circle is a mean proportional between the areas of an inscribed and a circumscribed equilateral triangle. 4. The number of sides of one regular polygon...

## A collection of elementary test questions in pure and mixed mathematics ...

James Robert Christie - Mathematics - 1866 - 426 pages
...described upon one side of each of the other two figures. 861. Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of two polygons of half the number of sides inscribed within and circumscribed about the same circle....