Spherical geometry other geometric concepts are defined as in plane geometry, but with straight lines replaced by great circles. Thus, in spherical geometry, angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects; for example, the sum of the interior angles of a triangle exceeds 180 degrees. Spherical geometry is "not" elliptic geometry, but is rather a "subset" of elliptic geometry. For example, it shares with that geometry the property that a line has no parallels through a given point. Contrast this with Euclidean geometry, in which a line has one parallel through
Equipollence (geometry) used a special notation for the equipollence of segments "AB" and "CD": The following passages, translated by Michael J. Crowe, show the anticipation that Bellavitis had of vector concepts: Thus oppositely directed segments are negatives of each other: formula_2 On a great circle of a sphere, two directed circular arcs are equipollent when they agree in direction and arc length. An equivalence class of such arcs is associated with a quaternion versor Equipollence (geometry) In Euclidean geometry, equipollence is a binary relation between directed line segments. A line segment "AB" from point "A" to point "B" has the opposite direction