"Claudius Ptolemaeus, a celebrated astronomer, was a native of Egypt. ...The chief of his works are the Syntaxis Mathematica (or the ', as the Arabs call it) and the Geographica, both of which are extant. ...Ptolemy did considerable for mathematics. He created, for astronomical use, a trigonometry remarkably perfect in form. ...The fact that trigonometry was cultivated not for its own sake, but to aid astronomical inquiry, explains the rather startling fact that came to exist in a developed state earlier than plane trigonometry. ...Ptolemy has written other works which have little or no bearing on mathematics, except one on geometry. Extracts from this book made by Proclus indicate that Ptolemy did not regard the parallel-axiom of Euclid as self-evident, and that Ptolemy was the first of the long line of geometers from ancient time down to our own who toiled in the vain attempt to prove it."