François Viète's method for calculating the eccentricity in a bisected model and its possible application to Kepler's Vicarious Hypothesis (2022)
According to Kepler's own words in Astronomia Nova, he invested five years trying to find the values for the eccentricities for his “vicarious” hypothesis. At some point, he asked Herwart von Hohenburg, to ask François Viète's help to solve his problem, but there is no evidence that Viète received this request. At that time, Viète was working on his unpublished Ad harmonicon coeleste. In it, he proposes a new method for bisected models, which can easily be extended to non-bisected models. In this paper, I describe Viète's method, analyze its accuracy, and show how to extend it to non-bisected models, making it suitable for solving Kepler's problem. Resumen Según cuenta en Astronomia Nova, Kepler invirtió cinco años en tratar de encontrar los valores de las excentricidades de su hipótesis “vicaria”. En algún momento, le pidió a Herwart von Hohenburg que, a su vez, le pidiera ayuda de François Viète para resolver el problema. Sin embargo, no hay evidencia de que Viète haya recibido este pedido. En ese momento, Viète estaba trabajando en su Ad harmonicon coeleste. En esta obra inédita, Viète propone un nuevo método para obtener las excentricidades en modelos bisectados. El método, sin embargo, puede extenderse fácilmente a modelos no bisecados. En este artículo, describo el método de Viète, analizo su precisión y muestro cómo extenderlo a modelos no bisecados, volviéndolo apropiado para resolver el problema de Kepler.
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