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

CHAPTER II.
FORMULAE CONNECTING THE SIDES AND ANGLES OF A
SPHERICAL TRIANGLE.
22. A spherical triangle has six elements, namely, the three
sides a, b, c, and the three angles A, B, C respectively opposite to them. The triangle is completely determined when any
three of the six elements are given, as there exist relations
between the given and the sought parts by means of which the
latter may be found. The object of this chapter is to establish
these relations. Our formulae will be divided into three classes
as follows:-The first class includes all formulae into which
enter four elements of the triangle. The second those which
contain five elements, and the third class the formulae into
which enter all six. The formulae which we are going to
investigate apply equally to "trihedral angles." The sides of
the spherical triangle correspond to the plane angles, forming
the trihedral, and the angles of the spherical triangle to the
dihedral angles of the trihedral.
SECTION I.-FIRST CLASS.
23. There are four Cases of the First Class:I. Three Sides and an Angle.
II. Two Sides and the Angle opposite to one of them.
III. Two Sides and two Angles, one of which is contained
by the sides.
IV. Three Angles and a Side.
Case I.-Three Sides and an Angle.
24. Let ABC be a spherical triangle, O the centre of the
C 2