Ptolemy quotes
To give here an elaborate account of Pappus would be to create a false impression. His work is only the last convulsive effort of Greek geometry which was now nearly dead and was never effectually revived. It is not so with Ptolemy or Diophantus. The trigonometry of the former is the foundation of a new study which was handed on to other nations indeed but which has thenceforth a continuous history of progress.
Ptolemy
He left in his Optics, the earliest surviving table of angles of refraction from air to water. ...This table, quoted and requoted until modern times, has been admired... A closer glance at it, however, suggests that there was less experimentation involved in it than originally was thought, for the values of the angles of refraction form an arithmetic progression of second order... As in other portions of Greek Science, confidence in mathematics was here greater than that in the evidence of the senses, although the value corresponding to 60° agrees remarkably well with experience.
Ptolemy
Claudius Ptolemy's great contribution to astronomy was his famous work the Almagest, which presented formally the astronomical theories of the day that had evolved from the great debates within the different Greek philosophical schools. Claudius Ptolemy freely admitted that he had contributed little original research to the treatise but rather had based his conclusions principally on the work of Hipparchus. ...Ptolemy did not claim that his cosmological model described the actual conditions. It simply reproduced geometrically the observed motions of the known heavenly bodies and enabled their positions to be easily predicted for any particular time. ... Ironically, even when Copernicus' heliocentric theory had replaced the Ptolemaic system, many astronomers used Ptolemy's model to predict the motion of the planets, since its intricate calculations produced more accurate values.
Ptolemy
