A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Bob Goethe
Date: 2016 Jan 22, 15:13 -0800
No, that is the magic of spherical geometry. A line takes off from a point at a 90° angle to a meridian, and it does not remain parallel to a latitude line. (Probably, that means it was never PRECISELY parallel to a latitude line, but it appears so for short distances; this is analogous to how it is that rhumb lines are the same as great circle lines for short distances.)
If we were talking plane geometry (or, for instance, if we were doing all our calculations on a Mercator projection), then the line would start parallel to a latitude line, and it would end that way. But not on the surface of a sphere. That is part and parcel of the reason that spherical geometry solutions are hard to come up with...and people keep mulling over different solutions for centuries at a time.