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(1) Special Cases. (a) Parallels to the axes. A shperic line parallel to 
the OY-axis passes through the pole of the axis OX. Hence for a parallel 
to the OY-axis B = 90° and the equation of the line becomes 
(3) tans) — tana 
and for a parallel to the O X-axis, a = 90°, and 
(4) tan — = tan 6 
(b) A line through one point. If a line (2) is to pass through (£1, m). 
we have 
tan € — tan & tan 7 — tan 7m 
(5) a0) 
tan a tan 6 
(c) A line through two points (£1, 7), (4, 2»), is given by 
tan € — tan & tan 7 — tan 7 
tan & — tan & tan yn. — tan m 
I 0G fe 4q 
Conditions of perpendicularity, parallelism, angles of intersection of spheric 
straight lines may also be expressed, but will not be included here. 
(2) Correspondence to plane geometry. The intercept form of the spheric 
straight line is similar to the corresponding equation in plane geometry, 
and may be reduced to that form by letting the radius of the sphere increase 
without limit. 
