...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,...

...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...

...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...

...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 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...

...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...

...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...

...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....

...+ be — I2Er = ab + ас + be — l2Rr; .-.AO2+ O1P+ OC2 = ab + no + be—l2Hr. (10) The area of a regular hexagon inscribed in a circle is a mean proportional between the areas of the inseribed and circumseribed equilateral triangles. , ,- 1 nr1 . 2яArca or hexngon = — sm — 2 n...

...+ cos (7). (6) Д + r = R (cos .Л + cos Б + cos (7). 25. Shew that 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. 26. The distances between...