Spherical geometry

However, two great circles on a plane intersect in two antipodal points, unlike coplanar lines in Elliptic geometry.

In the intrinsic approach, a great circle is a geodesic; a shortest path between any two of its points provided they are close enough.

This is the same as Euclid's method of treating point and line as undefined primitive notions and axiomatizing their relationships.

If developed as a part of solid geometry, use is made of points, straight lines and planes (in the Euclidean sense) in the surrounding space.

The earliest mathematical work of antiquity to come down to our time is On the rotating sphere (Περὶ κινουμένης σφαίρας, Peri kinoumenes sphairas) by Autolycus of Pitane, who lived at the end of the fourth century BC.

[3][4] The Book of Unknown Arcs of a Sphere written by the Islamic mathematician Al-Jayyani is considered to be the first treatise on spherical trigonometry.

However, Gerolamo Cardano noted a century later that much of its material on spherical trigonometry was taken from the twelfth-century work of the Andalusi scholar Jabir ibn Aflah.