 | John Martin Frederick Wright - Mathematics - 1825 - 798 pages
...equation of this form by construction, viz. x3 - 3r*x — ч =s 0. (j. Compute the numerical value of the side of a regular decagon inscribed in a circle, whose radius is ten inches. 8. The complement of the hypothenuse of a right-angled spherical triangle cannot exceed... | |
 | John Martin Frederick Wright - Astronomy - 1831 - 282 pages
...equation of this form by construction, viz. x3 — 3r*x — </ = 0. 6. Compute the numerical value of the side of a regular decagon inscribed in a circle, whose radius is' ten inches. 7. The three angles of a plane triangle being given, and the distances of the three angular... | |
 | John Radford Young - Geometry, Modern - 1833 - 238 pages
...finding the perimeter of an inscribed polygon of 21870 sides, and for this purpose we will take c as the side of a regular decagon inscribed in a circle whose radius is 1 ; then we have c=-61803398S75 (p. 114 note) and x3— ~&x = — -61803398875. From this equation... | |
 | John Radford Young - Geometry, Analytic - 1848 - 300 pages
...equiangular. Let BC=r, AE=y Hence BD;BC: :BC;BA ». e r-\-y'.r:;r:y .\yl-\-ry=r» Andy—ir\ -J (5) — \\ as required. PROBLEM XVIII. Having given the side...radius is known, to find the side of a regular pentagon inscr,bed in the same circle. Let AB (see figure to Prob. XVI.) be the side of a regular pentagon,... | |
 | John Radford Young - Geometry, Analytic - 1850 - 294 pages
...AB— y. Hence BD : BC : : BC : BA *. e. r ~f" 2/-r» '»r*y .'.2/2-f-^=^ Ar\.dy=±r$ ^ (5) — \^\ as required. PROBLEM XVIII. Having given the side...regular decagon inscribed in the circle AFB. Suppose AF=a, AE— r, AE=y. Now GE= ^/(r2— {?/) by the last problem; ) .-. 2r ^/(r2 — ±y2)=2r* — a?,... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...the side of the regular inscribed pentagon. Cm-oUnry. If a = the side of a regular pentagon and a' = the side of a regular decagon, inscribed in a circle whose radius is R, then, a2— a'2 = R*. 274. In two circles of different radii, angles at the centres subtended by... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...the side of the regular inscribed pentagon. Corollary. If a = the side of a regular pentagon and a' = the side of a regular decagon, inscribed in a circle whose radius is R, then, a2— a'a = R2. 274. In two circles of different radii, angles at the centres subtended by... | |
 | David Munn - 1873 - 160 pages
...and r, is D ; find the lengths of their common tangents. What do these lengths become when 16. Find the side of a regular decagon inscribed in a circle whose radius is R. 17. If (/= the diagonal of a regular pentagon inscribed in a circle whose radius is R, prove that... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...inscribed square and of the regular inscribed hexagon are the sides, (v. IV., Proposition X.) 18. If a is the side of a regular decagon inscribed in a circle whose radius is R, a = (1/5-1). 19. If a = the side of a regular polygon inscribed in a circle whose radius is J?,... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...corresponding side of a similar polygon, the perimeters being, respectively, 20 feefand 30 feet ? 20. Find the side of a regular decagon inscribed in a circle whose radius is 12 inches. NUMERICAL EXERCISES. 42O. i. Find medians of a triangle, in terms of sides. m — i- V 2... | |
| |
Having given the side of a regular decagon inscribed in a circle whose radius is known, to find the side of a regular pentagon inscribed in the same circle. 
