 | John Mason Good - 1819 - 822 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,... | |
 | 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... | |
 | Euclides - 1845 - 546 pages
...the square on the diameter of the circle circumscribing it is to the square on one of its sides. 172. A regular hexagon inscribed in a circle is a mean proportional between an inscribed and circumscribed equilateral triangle. 173. If two regular polygons P and Q of the same... | |
 | Thomas Grainger Hall - Trigonometry - 1848 - 192 pages
...centre of the 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... | |
 | James Hann - Plane trigonometry - 1854 - 140 pages
...10*" + 4«* + ab + ac + bc - 12ßr = ai + ac+ bc-l2Rr; .: АО' + OB' +OC' = ab + ac + bc- IZRr. (] 0) The area of a regular hexagon inscribed in a circle...inscribed and circumscribed equilateral triangles. л г г. пт* . Sir Area of hexagon = — sm — 6r" . 360° =Tsm-6= 3r* sin 60" , „ . ., i •... | |
 | John Hind - Trigonometry - 1855 - 540 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... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...equilateral and equiangular hexagon another be inscribed, to determine its ratio to the given one. 114. A regular hexagon inscribed in a circle is a mean proportional between an inscribed and circumscribed equilateral triangle. 115. The area of the inscribed pentagon, is to... | |
 | 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... | |
 | Euclides - 1864 - 448 pages
...equilateral and equiangular hexagon another be inscribed, to determine its ratio to the given one. 1 14. A regular hexagon inscribed in a circle is a mean proportional between an inscribed and circumscribed equilateral triangle. 115. The area of the inscribed pentagon, is to... | |
 | John Walmsley - Logarithms - 1865 - 232 pages
...cot—. 2n 2. If 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... | |
| |
The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. 
