A treatise on spherical trigonometry, and its application to geodesy and astronomy, with numerous examples. By John Casey.

Parallelopipeds and Tetrahedra. 135
in the points a, b, c, e, respectively; then we have, by Stewart's
theorem,
cos COE = (cos a. sin a Oe + cos f sin b Oe) sin y;
0. 2 = a2 b2+ c2 + 2ab cosy
2e. 0.E
+ O (cos a. sin a Oe + cos,8 sin b e);
sin y
but OE sin a Oe = b sin y, and OE. sin b Oe = a sin y.
Eence
D2 = a2+ b2 + 2 + 2bc cos a + 2ca cos, + 2ab cos y. (440)
126. To find the radius of a sphere circumscribed to a tetrahedron.
D
AF. ---
Fig. 53.
ErrST METHOD (STAIDT'S):Through the centre O of the circumsphere draw a plane perpendicular to the radius DO, cutting the sides of the trihedral
angle D in the plane triangle A'B'C'. This plane being parallel
to the tangent plane to the sphere at -D,
Â'B' is antiparallel to AB in the angle ADB,
B' C' BC,, BDC,
C'A', CA, CDOA.