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" If the radius of a circle be divided in extreme and mean ratio, the greater segment is equal to one side of a regular inscribed decagon. "
An Examination Manual in Plane Geometry - Page 122
by George Albert Wentworth, George Anthony Hill - 1896 - 138 pages
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Annual Report of the Commissioners ..., Volume 20, Part 2

1854 - 834 pages
...product by '01745. Explain what the decimal '01745 represents, and of what ratio it is the value. 5. If the radius of a circle be divided in extreme and mean ratio, prove that the greater segment is equal to the side of an inscribed decagon. C. If the arc of a segment...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...alt equal, and the angles also all ccjual. it is a regular decagon, ami may be inscribed in a circle. If the radius of a circle be divided in extreme and mean ratio, that is, 60 that the greater segment shall be a mean proportional between the whole radius and the...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...inscribed equilateral triangle is to the radius, as the square root of 3 is to 1. PROPOSITION VI. THEOBEM. If the radius of a circle be divided in extreme and mean ratio, the greater segment will be equal to one side of a regular inscribed decagon. Let ACG be a circle, OA its radius, and AB,...
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Parliamentary Papers, Volume 30, Part 2

Great Britain. Parliament. House of Commons - Bills, Legislative - 1854 - 826 pages
...product by '01745. Explain what the decimal "01745 represents, and of what ratio it is the value. 5. If the radius of a circle be divided in extreme and mean ratio, prove that the greater segment is equal to the side of an inscribed decagon. 6. If the arc of a segment...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...tnscribed equilateral triangle is to the radius, as the square root of 3 is to 1. PROPOSITION VI. THEOREM. If the radius of a circle be divided in extreme and mean ratio, the greater segment will be equal to one side of a regular inscribed decagon. Let ACG be a circle, OA its radius, and AB,...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...inscribed equilateral triangle is to the radius, as the square root of 3 is to 1. PROPOSITION VI. THEOKEM. If the radius of a circle be divided in extreme and mean ratio, the greater segment will be equal to one side of a regular inscribed decagon. Let ACG be a circle, OA its radius, and AS,...
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Elements of Geometry

Simon Newcomb - Geometry - 1881 - 418 pages
...the radius OA is divided in extreme and mean ratio at the point P (§ 440). Hence we conclude: 465. If the radius of a circle be divided in extreme and mean ratio, the greater segment will be the chord of one tenth of the circle. Construction. Divide the radius OA of the circle in extreme...
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Metrical Geometry: An Elementary Treatise on Mensuration

George Bruce Halsted - Measurement - 1881 - 266 pages
...line cuts the non-parallel sides. 9. A = 10. ^= 37. Find the side of a regular decagon. If a radius is divided in extreme and mean ratio, the greater segment is equal to a side of the inscribed regular decagon. Ww 3Q4; (Eu IV 1Q. Cv v 17) • fir lr \ — 7- 2 . . r(r...
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Elements of Plane and Spherical Trigonometry with Logarithmic and ..., Volume 1

Simon Newcomb - Logarithms - 1882 - 188 pages
...-o~. tan 30° = —^ Vs sec 30° = cos 30° = 4/3' 1/3 Functions of 18°. It is shown in geometry that if the radius of a circle be divided in extreme and mean ratio, the greater segment will be the chord of 36° ; that is, twice the sine of 18°. Putting 1 for the radius and r for the...
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A Treatise on Trigonometry

James Edward Oliver - Trigonometry - 1890 - 186 pages
...Find the primary values for a, ß that satisfy the equations sin (За- 2/3) = 1, sin (4/3- a) = ¿. If the radius of a circle be divided in extreme and mean ratio the greater segment is the side of a regular inscribed decagon : hence find the functions of 18° and of 36°. 19 §2. RELATIONS...
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