Synthetic geometry is an approach to geometry that develops its results directly from geometric objects, their relations, and axioms.
Its characteristic method is the synthetic proof,
in contrast to the coordinate calculations of analytic
geometry (Baldwin and Mueller 2024, p. 4).
Synthetic methods can be used in both Euclidean geometry and projective geometry (Coxeter
1993, pp. ix-x; Hartshorne 2000). The term therefore describes a method of developing
geometry, rather than a single fixed system of geometric
axioms.
