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The area of a regular polygon inscribed in a circle is a geometric mean between the areas of an inscribed and a circumscribed regular polygon of half the number of sides.
A collection of examples in pure and mixed mathematics, with hints and ... - Pągina 116
per Alfred Wrigley - 1852
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## An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - 1817 - 436 pągines
...(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...
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## A Supplement to the Elements of Euclid

Daniel Cresswell - 1819 - 410 pągines
...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...
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## Euclid's Elements of geometry, transl. To which are added ..., Llibres 1-6

Euclides - 1826
...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....
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## Elements of Geometry, Containing the First Six Books of Euclid

Euclid, Phillips - 1826 - 180 pągines
...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....
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## Problems in the Different Branches of Philosophy: Adapted to the Course of ...

Miles Bland - 1830 - 374 pągines
...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...
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## Mathematical Problems and Examples, Arranged According to Subjects, from the ...

1836 - 335 pągines
...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...
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## A collection of problems and examples adapted to the 'Elementary course of ...

Harvey Goodwin (bp. of Carlisle.) - 1847 - 80 pągines
...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...
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## A Treatise on Plane and Spherical Trigonometry ...

Thomas Grainger Hall - 1848 - 168 pągines
...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...
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## The elements of plane trigonometry

James Hann - 1854 - 119 pągines
...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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## The elements of plane and spherical trigonometry

John Hind - 1855
...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,...
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