 | 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 of n sides,... | |
 | 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... | |
 | 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 is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles. л г г. пт* . Sir Area of hexagon = —... | |
 | 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 and from the equality,... | |
 | 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 octagons; a... | |
 | 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...proportional between the areas of an inscribed and a circumscribed equilateral triangle. 4. The number of sides of one regular polygon exceeds that of... | |
 | Robert Potts - 1865 - 528 pages
...equilateral and equiangular hexagon another be inscribed, to determine its ratio to the given one. 264. A regular hexagon inscribed in a circle is a mean proportional between an inscribed and circumscribed equilateral triangle. 265. The diameter of a circle ia a mean proportional... | |
 | James Robert Christie - Mathematics - 1866 - 428 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.... | |
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Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribing polygon of half the number of sides. 
