About the Gnomonic Projection
The Gnomonic projection is another azimuthal projection that is considered to be ancient. It has applications in the design of sun dials, and it was first used in this manner by Thales of Miletus (ca. 624-547 BC). The projection's historical names of Horologium and Horoscope refer to this sun dial application, as does the modern name of Gnomonic (a sun dial has a gnomon)). The modern name of Gnomonic was first used by Deorgan in 1836, although the similar Gnomic was in use by 1749.
The Gnomonic projection projects the Earth's surface from a point at the Earth's center to a tangent plane. This results in a projection which can only project one hemisphere, is not conformal, and cannot preserve area. For a tangent point at either of the poles, the the equator projects to infinity, and the antipodal hemisphere is un-projectable. Shape distortion is considered to be "moderate" within 30°degrees of the center.
These disadvantages are balanced by the useful property that all great circles are projected as straight lines, regardless of aspect. Ie. even oblique great circles will appear as straight lines on the Gnomonic projection. This property is useful for aerial navigation, and can be usefully applied to non-polar aspects.