Fundamentum Astronomiae is a historic manuscript presented by Jost Bürgi to Emperor Rudolf II. in 1592. It describes Bürgi's algorithms called Kunstweg which can be used to calculate sines at arbitrary precision. Bürgi used these algorithms to compute a Canon Sinuum, a table of sines to 8 sexagesimal places in steps of 2 arc seconds. Such tables were extremely important for navigation at sea. Johannes Kepler called the Canon Sinuum the most precise known table of sines.(reference???) The iterative algorithms obtains good approximations of sines after few iterations, but cannot be used on large subdivisions, because it produces very large values. This was an early step towards difference calculus.
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