Since the angles of incidence and refraction are connected by the relation sin i=µ sin r (Snell's Law), µ being the index of refraction of the medium, then the problem may be stated as follows: to determine the value of the angle i which makes D = 2 (i - r) +n (7r - 2r) a maximum or minimum, in which i and r are connected by the relation sin i =µ sin r, µ being a constant.
He was sent in 1737 to the university of Glasgow, where he attended the lectures of Dr Hutcheson; and in 1740 he went to Balliol College, Oxford, as exhibitioner on Snell's foundation.
Grienberger, using Snell's method, calculated the ratio correct to 39 fractional places. ?
The general theorems which enabled him to do this, after a start had been made, are A2n = 11A8222;A ' n (Snell's Cyclom.), P 2A8222;A' n - 2A' 8222;AZ, Gre o A 2 8221; - A n +A2n or A' n +A28222; (g r1') where A 8222;, A'8222; are the areas of the inscribed and the circumscribed regular n-gons respectively.