"Ptolemy’s great treatise, the '... was founded on the observations and writings of Hipparchus, and from the notes there given we infer that the chief discoveries of Hipparchus, and from the notes there... we infer that the chief discoveries of Hipparchus... [H]is observations and calculations... placed the subject for the first time on a scientific basis. ...[His] theory accounted for all the facts which could be determined with the instruments then in use, and... enabled him to calculate... eclipses with considerable accuracy. ...No further advance in the theory of astronomy was made until the time of Copernicus, though the principles laid down by Hipparchus were extended and worked out in detail by Ptolemy. Investigations such as these naturally led to trigonometry, and Hipparchus must be credited with the invention of that subject. ...[I]n plane trigonometry he constructed a table of chords of arcs... practically the same as... natural sines; and... in spherical trigonometry he had some method of solving triangles: but his works are lost, and we can give no details."