 | James Edward Oliver - Trigonometry - 1881 - 140 pages
...TRIGONOMETRIC FUNCTIONS. LEMMA. If 6 be an infinitesimal angle, then lim (sin0 : 0) = 1, and lim (tan 0 : 0) = 1. For, let c be the circumference of a circle, ^...PP', TT', parallel each to each. Draw OAX-LPP' and TT', then : -.• p<c<p', whatever the number of sides, and ••• p approaches indefinitely near... | |
 | James Edward Oliver - Trigonometry - 1881 - 120 pages
...angle, then lim (sino : в) =1, and lim (tano: 0) = 1. For, let c be the circumference of a circle, о the centre, p and p' the perimeters of two regular...circumscribed about the circle, and having their sides PP', rr', parallel each to each. Draw OAX-LPP' and тт', then : •.• p<c<p', whatever the number of... | |
 | James Edward Oliver - Trigonometry - 1889 - 178 pages
...lim (tan в : в) = 1 . For, let с be the circumference of a circle, о the centre ; let p, p' be the perimeters of two regular polygons of the same...other circumscribed about the circle, and having their pairs of sides pp', тт', ... parallel ; draw OAX perpendicular to PP', тт' ; then -.. j><c<X, whatever... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...polygon approaches the circumference of the circle as its limit. D_ H Hypothesis. Let p and P denote the perimeters of two regular polygons of the same number of sides, the former inscribed in the O ABG, and the latter circumscribed about the same O. Let C denote the circumference... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...polygons of the same number of sides have the same ratio as their radii or as their apothems. D' B' Given P and P' the perimeters of two regular polygons of the same number of sides, having the radii OA and O'A', and the apothems OD and O'D' respectively. To prove P:P'=OA:O'A'... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...polygons of the same number of sides have the same ratio as their radii or as their apothems. Given P and p' the perimeters of two regular polygons of the same number of sides, having the radii OA and O'A', and the apothems OD and O'D' respectively. To prove P: P' = OA... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...polygons of the same number of sides have the same ratio as their radii or as their apothems. AT Given P and P' the perimeters of two regular polygons of the same number of sides, having the radii OA and O'A', and the apothems OD and O'D' respectively. To prove P:P' = OA:0'A'... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...polygons of the same number of sides have the same ratio as their radii or as their apothems. B Given P and P' the perimeters of two regular polygons of the same number of sides, having the radii OA and O'A', and the apothems OD and O'D' respectively. To prove P : P' = OA... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1925 - 504 pages
...same number of sides have the same ratio as their radii, or as their apothems. o k DB A' D' B Given P and P', the perimeters of two regular polygons of the same number of sides, having the radii OA and O'A', and the apothems OD and O'D' respectively. To prove P : P' = OA... | |
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ABCDE and A'B'C'D'E' are similar. QED Ex. 1313. To construct a regular hexagon equivalent to one half of a given regular hexagon. PROPOSITION X. THEOREM 416. The perimeters of regular polygons of the same number of sides have the same ratio as their radii... 