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A triangle formed by three arcs of great circles on a sphere.
‘This work is really the first in history on trigonometry as an independent branch of pure mathematics and the first in which all six cases for a right-angled spherical triangle are set forth.’
‘It also gives the mathematics behind the construction of the tables, and it details how to solve both plane and spherical triangles.’
‘The work contains formulas for right-handed triangles, the general law of sines, and the solution of a spherical triangle by means of the polar triangle.’
‘In Book I of Sphaerica he set up the basis for treating spherical triangles as Euclid treated plane triangles.’
‘He also gave formulas for the area of a spherical triangle.’
‘His tables for solving the problems of spherical astronomy can be seen to be tables which solve spherical triangles using a method similar to the modern cosine rule.’
‘Morin realised that instruments had to be improved, improved methods of solving spherical triangles had to be found and better lunar tables were needed.’