Page:Spherical Trigonometry (1914).djvu/28

10 '''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. In



spherical triangles each side is restricted to be less than a