Early developments in trigonometry began with the ancient Egyptians and Babylonians who studied ratios of sides in similar triangles. Trigonometry advanced significantly through the works of Hipparchus, Euclid, Archimedes, and later Islamic mathematicians such as Al-Khwarizmi, who produced the first table of tangents. Nasir al-Din al-Tusi established spherical trigonometry as an independent field and listed the six cases of right triangles. Modern analytic trigonometry was established by Euler, while Brook Taylor derived general Taylor series for all six trigonometric functions.