...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,...

...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...

...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...

...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...

...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...

...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...

...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...

...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...

...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...

...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...