Page:Spherical Trigonometry (1914).djvu/28

20. Notation. The letters $A$, $B$, $C$ are generally used to denote the angles of a spherical triangle, and the letters $a$, $b$, $c$ are used to denote the sides. As in the case of plane triangles, $A$, $B$, and $C$ may be used to denote the numerical values of the angles expressed in terms of any unit, provided we understand distinctly what the unit is. Thus, if the angle $C$ be a right angle, we may say that $C=90^{\circ }$, or that $C={\dfrac {1}{2}}\pi$, according as we adopt for the unit a degree or the angle subtended at the centre by an arc equal to the radius. So also, as the sides of a spherical triangle are proportional to the angles subtended at the centre of the sphere, we may use $a$, $b$, $c$ to denote the numerical values of those angles in terms of any unit. We shall usually suppose both the angles and sides of a spherical triangle expressed in circular measure. (Plane Trigonometry, Art. 20.)

21. In future, unless the contrary be distinctly stated, any arc drawn on the surface of a sphere will be supposed to be an arc of a great circle.

22. Conventional restriction of lengths of sides.^[1] In

spherical triangles each side is restricted to be less than a

1. See Chapter XIX.