The mathematics behind Jost Bürgi's method for calculating sine tables

Jost Bürgi (1552–1632) is not only one of the first persons who set up tables of logarithms for practical use but also invented a method to calculate highly precise tables of the sine function with small increment of the argument, and this with only a modest amount of calculations. Bürgi's manuscript on his method, however, was never published by him and got lost for almost four centuries until Menso Folkerts discovered it, cf. [2]. The article [1] on this manuscript gives a proof for the correctness of this method which, however, relies on the Theorem of Perron-Frobenius that is over three centuries younger than Bürgi's method. The present contribution discusses how Bürgi may have come to his method and what considerations may have convinced him that it should work. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)