 | William Somerville Orr - Science - 1854 - 534 pages
...л/3 And so on in other caso?. (3.) Tu determine the Area, of a Circle. If n is the number of sides of a regular polygon inscribed in a circle whose radius is r, then, as we have already eeen (Trig : Art : 45), , , «)a . Zr Area polygon = — sin. . 2т Now if... | |
 | Dublin city, univ - 1858 - 264 pages
...distances of the angles from the middle points of the opposite sides. MR. SALMON. 4. a. Assuming that if the side of a regular polygon, inscribed in a circle whose radius is unity, be a, that of the corresponding circumscribed v(4 - av of decimals. is — r-, find the side... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...radius is R, and A = the side of the similar circumscribed polygon, then, 2aR 2AR "-VUR» —a2) 272. If a = the side of a regular polygon inscribed in...circle whose radius is R, and a' = the side of the regular inscribed polygon of double the number of sides, then, R* 273. If AB and CD are two perpendicular... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...is equal to the sum of those which fall on the opposite side. • 277. If n is the number of sides of a regular polygon inscribed in a circle whose radius is R, and a point P is taken such that the sum of the squares of its distances from the vertices of the polygon... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...the side of the similar circumscribed polygon, then, 2aR 2AR 1/(4.R 2 — a 2 ) 1/(4.K 2 + A 2 ) 212. If a = the side of a regular polygon inscribed in...circle whose radius is R, and a' = the side of the regular inscribed polygon of double the number of sides, then, 213. If AB and CD are two perpendicular... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...diameter is equal to the sum of those which fall on the opposite side. 277. If n is the number of sides of a regular polygon inscribed in a circle whose radius is R, and a point P is taken such that the sum of the squares of its distances from the vertices of the polygon... | |
 | David Munn - 1873 - 160 pages
...generated by a triangle turning round any line in its plane. 30. The radii of two circles are r^ and r,,, the distance of their centres is a • find the length...the side of the similar circumscribed polygon, prove / \ * (i.) A= , . ( 2 .) a = 34. Three equal circles touch each other; find the area of the part between... | |
 | William Chauvenet - Geometry - 1875 - 466 pages
...and A = the side of the similar circumscribed polygon, then, 2aR 2AR -a-) V(4R 3 +A 3 ) 272. If o = the side of a regular polygon inscribed in a circle whose radius is R,, and a' = the side of the regular inscribed polygon of double the number of sides, then, = R(2R — 1/4 R' 2 — a-), 273. If... | |
 | William Chauvenet - Geometry - 1875 - 390 pages
...270. If d = the diagonal of a regular pentagon inscribed in a circle whose radius is R, then, d= 271. If a = the side of a regular polygon inscribed in a circle whose radiua is R, and A = the side of the similar circumscribed polygon, then, 2aR 2AR — a") I/ (4.R2... | |
 | William Chauvenet - Geometry - 1887 - 336 pages
...regular decagon inscribed in a circle whose radius is _R, a = (1/5 - 1). Suggestion. By (31), = a 19. If a = the side of a regular polygon inscribed in a circle whose radius is H, and a' = the side of the regular inscribed polygon of double the c number of sides, then Suggestion.... | |
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A = the side of the similar circumscribed polygon, then, 2aR 2AR -a-) V(4R 3 +A 3 ) 272. If o = the side of a regular polygon inscribed in a circle whose radius is R,, and a... 
