The Gradual Refinement of Kepler’s Triangulation Method: Early Developments in His First Encounter with Tycho

Johannes Kepler’s early work with Tycho Brahe’s Mars observations in Benátky in 1600 marked a pivotal moment in his methodological development. This paper traces Kepler’s evolving approach to triangulation, emphasizing how he progressively refined the method to determine planetary distances with greater accuracy. Through a systematic analysis of Kepler’s calculations, this study reconstructs the steps by which Kepler transitioned from simple triangulation methods to a more sophisticated approach involving multiple observations with one celestial body at a fixed position. By following Kepler’s early reasoning, errors, and refinements, this paper sheds light on the intellectual processes that ultimately led to the breakthroughs presented in Astronomia Nova .