In 1646 John Wallis received from Foster a theorem on spherical triangles which he afterwards published in his " Mechanica ".
22.
The relationship between area and rotations is explained by Girard's theorem relating the area of a spherical triangle to its angular excess.
23.
He also stated the law of sines for spherical triangles, discovered the law of tangents for spherical triangles, and provided proofs for these laws.
24.
He also stated the law of sines for spherical triangles, discovered the law of tangents for spherical triangles, and provided proofs for these laws.
25.
:With 2 or 3 great circles ( not all passing through the same 2 poles ), I believe nothing is possible except spherical triangles.
26.
They therefore enclose a spherical triangle on the surface of any sphere centered on that point and repeated reflections produce a multitude of copies of the triangle.
27.
Given the calculated ( angular ) distance from A to B you can construct a spherical triangle A-B-pole, which has all sides known.
28.
In his " On the Sector Figure ", he stated the law of sines for plane and spherical triangles, and provided proofs for this law.
29.
My question is whether, given any arbitrary number of great circles, configurations in which all partitions are spherical triangles are abundant or rare ( or very rare ).
30.
When one of the angles, say " C ", of a spherical triangle is equal to & pi; / 2 the various identities given above are considerably simplified.
