Adrianus Romanus and the Trigonometric Tables of Georg Joachim Rheticus

In the course of the sixteenth century, several mathematicians assiduously embarked on the calculation of trigonometric tables. Some, like Georg Joachim Rheticus,1 were ultimately successful; others, like Adrianus Romanus 2 and Christoph Grienberger,3 left their work unfinished for one reason or another. At the beginning of 1593, Romanus’s Ideae Mathematicae pars prima, sive Methodus Polygonorum 4 was published in Leuven, a work in which he calculated the sides of the regular 3-, 4-, 5-, and 15-sided polygon and of polygons generated from them by the doubling of the number of sides, for a radius of 1032 parts or units. It was the start of a chord table, from which a sine table can be derived. Romanus dedicated his book to Christoph Clavius.5 In his “Introductory Letter to the Reader„, he mentioned a number of living mathematicians, including Valentinus Otho,6 who, as Romanus learned from friends, had promised the publication of Rheticus’s Canon Triangulorum in that same year. At his death in 1574, Rheticus had entrusted his papers to his student Otho, who took it upon himself to complete the work of his master. The citation of Rheticus gave Romanus the occasion to elaborate on his work. He had a very special reason to do so: “Because, among all mathematicians, I have found none who was as close to my own plans in the building of mathematics as Rheticus, which I experienced only last year when I read the letter he wrote to Petrus Ramus in 1568 in which he wrote as follows about his work.„ Romanus then gave the entire letter.7