| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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,... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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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