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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 /3 = 90° and the equation of the line becomes 



(3) tan £ = tan a. 

 and for a parallel to the OX-axis, a = 90°, and 



(4) tan £ = tan (3 



(b) A line through one point. If a line (2) is to pass through (£i, 771), 

 we have 



tan £ — tan £1 tan 77 — tan 171 



(5) - + - - = O. 



tan a tan j8 



(c) A line through two points (£1, 771), (£ 2 , 772), is given b>' 



tan £ — tan £1 tan 77 — tan 771 



tan £ 2 — tan £1 tan 772 



tan 771 



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. 



