 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.  Plane Trigonometry - Página 200por Daniel Alexander Murray - 1906Vista completa - Acerca de este libro
 | Daniel Cresswell - 1817 - 454 páginas
...(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 - 1819 - 446 páginas
...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... | |
 | Euclid - 1826 - 234 páginas
...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.... | |
 | Euclides - 1826 - 226 páginas
...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.... | |
 | Miles Bland - 1830 - 394 páginas
...also the areas of regular polygons of a given number of sides, both inscribed and circumscribed. 73. The area of a regular polygon inscribed in a circle is a geometric mean between the areas of an " inscribed and circumscribed regular polygon of half the number... | |
 | 1836 - 366 páginas
...opposite, having given B, a and the area of the triangle, find the remaining sides and angles. 25. Prove that the area of a regular polygon inscribed in a circle, is a geometric mean between the areas of an inscribed and of a circumscribed regular polygon of half the... | |
 | Alfred Wrigley - 1845 - 222 páginas
...hypothenuse. 174. In 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...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,... | |
 | Harvey Goodwin (bp. of Carlisle.) - 1847 - 136 páginas
...the inscribed square is an harmonica) mean between the sides containing the right angle. 19. Prove that the area of a regular polygon inscribed in a circle is a geometrical mean between the areas of an inscribed and of a circumscribed polygon of half the number... | |
 | Thomas Grainger Hall - 1848 - 192 páginas
...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 in a circle... | |
 | James Hann - 1854 - 140 páginas
...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 = —... | |
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