THE PREDECESSORS OF COPERNICUS. 325 



The Arabian school of astronomers added nothing to the theory 

 of Ptolemy. They transmitted the text of the Almagest to the west 

 accompanied by intelligent comment and almost without criticism 

 except in the cases of Alpetragins and Geber. The Arab observations 

 were very numerous, and resulted in fixing new and much more 

 accurate values of the constant of precession, the length of the year, 

 the obliquity of the ecliptic, the eccentricity of the sun's orbit and 

 the motion of its apogee. Their arithmetic was the clumsy sexagesimal 

 arithmetic of the Greeks, until in the eleventh century the Hindu 

 decimal system began to make its way in Egypt, Spain and Europe. 

 Geometry is not indebted to the Arabs for any marked advances. On 

 the other hand, trigonometry was greatly improved. 



As observers the astronomers of the Arab school had great merit. 

 They grasped the need for continuous observations, whereas the 

 Greeks in general had contented themselves with making observations 

 at certain critical times only — at the solstices and equinoxes, for in- 

 stance. The Arabs were the first to assign the exact time at which 

 any phenomenon occurred — a fundamental datum. They measured 

 the altitude of the sun at the beginning and ending of solar eclipses, 

 for example, in order that the time might be known. The calcula- 

 tion of a spherical triangle enabled the instants of beginning and 

 ending to be accurately assigned. The Greeks never employed this 

 device and the times of phenomena recorded by them are seldom known 

 with any accuracy. Indeed Ptolemy has no formula by which to 

 calculate the time when the sun's altitude is given, and it is note- 

 worthy that the Arab device was not known in Europe until 1457, 

 when Purbach used it for the first time. Yet it was employed at 

 Bagdad at the solar eclipse of A. D. 829, six hundred 3^ears earlier. 

 Even the times of phenomena recorded by Tycho Brahe in 1600 are 

 seldom known so close as a quarter of an hour. Short intervals of 

 time were measured by the Arabs by counting the beats of pendulums. 



A few of the greatest Arabians are named in what follows. 

 Albategnius was an Arab prince of Syria who flourished at the end of 

 the ninth century of our era. His observations were made at Aracte 

 (Eachah) in Mesopotamia and at Antioch, between the years 878 and 

 918. After studying the Syntaxis of Ptolemy he set himself to cor- 

 rect the errors of its catalogue of stars by observations of his own, 

 made with apparatus fashioned after Ptolemy's descriptions. It ap- 

 pears that some of his instruments could be read to single minutes (1') 

 and were divided possibly to 2' (or it may be to 6'). He detected the 

 change of position of the sun's apogee, determined the obliquity of 

 the ecliptic, the length of the year, the precession-constant (54"), 

 observed and calculated solar and lunar eclipses and computed new 

 tables of the planetary motions, although he did not seek to improve 

 Ptolemy's planetary theory. He was original and inventive as an 



