An analytic proof in elementary geometry is a proof that represents geometric objects in a coordinate
system and establishes the desired result by algebraic reasoning. It is also
called a coordinate proof. This method belongs to analytic
geometry and contrasts with a synthetic proof
(Baldwin and Mueller 2024, p. 4).
In proof theory, the term analytic proof has a different meaning referring to restrictions on the formulas occurring
in a proof, rather than to the use of geometric coordinates
(Baaz et al. 2008, p. 160).
Baaz, M.; Hetzl, S.; Leitsch, A.; Richter, C.; and Spohr, H. "CERES: An Analysis of Fürstenberg's Proof of the Infinity of Primes."
Theoret. Comput. Sci.403, 160-175, 2008. https://doi.org/10.1016/j.tcs.2008.02.043.Baldwin,
J. T. and Mueller, A. "Supplement: Focusing a GeT Course on Axiomatic Systems
for Geometry." Jan. 2, 2024. https://www.math.uic.edu/~jbaldwin/pub/supp2Dec3.pdf.
