"In 1605 Bürgi went to Prague and lived there as a at the Emperor’s Chamber until 1631... [and] was... involved in astronomical observations and interpretations. ...... worked at the court. Among... temporary visitors... ... and Ursus... who had both worked with . Wittich... brought... knowledge of ... by which multiplications and divisions can be replaced by additions and subtractions of trigonometrical values... based on the identity\sin \alpha \cdot \sin \beta = \frac{1}{2}[\sin (90^\circ - \alpha + \beta) - \sin(90^\circ - \alpha -\beta)],this... achieves the same as logarithms, which were invented... decades later."