“Bürgi not only used this method, but... improved it. He found the second formula, for Brahe and Wittich only knew the first. In addition, he improved the computation of the {{w|spherical law of cosines}}...{{center/s}}\cos c = \cos a \cos b + \sin a \sin b \cos C{{center/e}}Using the method of prosthaphæresis... cos a cos b and sin a sin b... could be computed but two new multiplications were... left... Bürgi realized that... prosthaphæresis could be used a second time, and... all multiplications could be replaced by additions or subtractions.”