On hyperbolic analogues of some classical theorems in spherical geometry

TL;DR

This paper develops hyperbolic versions of classical spherical geometry theorems, extending their applicability and providing more precise results within hyperbolic geometry.

Contribution

It introduces hyperbolic analogues of several well-known spherical geometry theorems, enhancing understanding of geometric relationships in hyperbolic space.

Findings

Hyperbolic analogues of Menelaus, Euler, Lexell, Ceva, and Lambert theorems.

More precise formulations of some spherical geometry results.

Extension of classical theorems to hyperbolic geometry context.

Abstract

We provide hyperbolic analogues of some classical theorems in spherical geometry due to Menelaus, Euler, Lexell, Ceva and Lambert. Some of the spherical results are also made more precise.