132 A SHORT HISTORY OF SCIENCE 



When we study the great conflict in the time of Copernicus be- 

 tween the ancient and modern ideas, our sympathies naturally go out 

 towards those who supported the latter, which are now known to be 

 more accurate, and we are apt to forget that those who then spoke 

 in the name of the ancient astronomy and quoted Ptolemy were indeed 

 believers in the doctrines which they had derived from the Greeks, 

 but that their methods of thought, their frequent refusal to face facts, 

 and their appeals to authority, were all entirely foreign to the spirit of 

 the great men whose disciples they believed themselves to be. 



OTHER WORKS OF PTOLEMY. In spite of his scientific attain- 

 ments Ptolemy did not disdain to write an elaborate treatise on 

 astrology. In a lost work on geometry, Ptolemy made the first 

 known of the interminable series of attempts to give a formal 

 proof of Euclid's parallel postulate, an attempt naturally fore- 

 doomed to failure. 



In a great treatise on geography, hardly less important than the 

 Almagest, Ptolemy gave a description of the known earth, locating 

 not less than 5000 places by latitude and longitude. He even gave 

 in addition to position the maximum length of day for 39 points 

 in India, a land probably better known at this period than in the 

 time of Mercator, near the end of the sixteenth century. Ptolemy 

 reckoned longitude from the "Fortunate Isles," the western 

 boundary of the known world. Various methods of projection 

 were discussed in connection with directions for map drawing. 



Ptolemy also wrote on sound and on optics, dealing particularly 

 in the latter with refraction, with what has been called " the oldest 

 extant example of a collection of experimental measures in any 

 other subject than astronomy." He discovered by careful exper- 

 iment and induction the law that light-rays passing from a rarer 

 to a denser medium are bent towards the perpendicular, and in- 

 vented a simple apparatus for measuring angles of incidence 

 and reflection. 



PAPPUS. The last two of the great Greek mathematicians were 

 Pappus and Diophantus, who lived in Alexandria about 300 A.D. 



The most important work of Pappus is his Collections, in eight 

 books, of which all but the first and a part of the second are pre- 



