 The area of any regular polygon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed polygons of half the number of sides.  Elements of Geometry - Page 476by Andrew Wheeler Phillips, Irving Fisher - 1896 - 540 pagesFull view - About this book
 | Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...(LXII.) To describe a polygon, similar to a given polygon, and having a given ratio to it. (LXIII.) Any regular polygon, inscribed in a circle, is a mean proportional between the inscribed and circumscribed regular polygons of half the number of sides. (LXIV.) If from two points... | |
 | Daniel Cresswell - Geometry - 1819 - 446 pages
...from E. 20. 6., that it will have to the given polygon the given ratio. PROP. LXVI. 75. THEOREM. > Any regular polygon, inscribed in a circle, is a mean proportional between the inscribed and circumscribed regular polygons of half the number of sides. Let BGFA be a polygon inscribed... | |
 | 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,... | |
 | Euclides - 1826 - 226 pages
...rectilineal figures are to one another in the duplicate ratio of their homologous sides. QEF Deduction. Any regular polygon inscribed in a circle, is a mean proportional between the inscribed and circumscribed regular polygon of half the number of sides. PROPOSITION XXI. » THEOREM.... | |
 | Euclid - 1826 - 234 pages
...upon the first to the similar and similarly described rectilineal figure upon the second. Deduction. Any regular polygon inscribed in a circle, is a mean proportional between the inscribed and circumscribed regular polygon of half the number of sides. PROPOSITION XXI. THEOREM.... | |
 | Alfred Wrigley - 1845 - 222 pages
...the figure of 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... | |
 | Thomas Grainger Hall - Trigonometry - 1848 - 192 pages
...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
...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 = — sm — 6r" . 360° =Tsm-6= 3r* sin... | |
 | 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... | |
 | Alfred Wrigley - Mathematics - 1862 - 330 pages
...the sum of the 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... | |
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