180 THE GREEK ASTRONOMY. 



place ; and so on ; and the greatest effect of the inequality is in the 

 octants, or points half-way between the four quarters. In an Almagest 

 of Aboul Wefa, a part of which exists in the Royal Library at Paris. 

 after describing the two inequalities of the moon, he has a Section he, 

 " Of the Third Anomaly of the moon called Muhazal or Prosneusis. r 

 He there says, that taking cases when the moon was in apogee or 

 perigee, and when, consequently, the effect of the two first inequalities 

 vanishes, he found, by observation of the moon, when she was nearly in 

 trine and in sextile with the sun, that she was a degree and a quarter 

 from her calculated place. " And hence," he adds, " I perceived that 

 this anomaly exists independently of the two first : and this can only 

 take place by a declination of the diameter of the epicycle with respect 

 to the centre of the zodiac." 



We may remark that we have here this inequality of the moon 

 made out in a really philosophical manner ; a residual quantity in the 

 moon's longitude being detected by observation, and the cases in 

 which it occurs selected and grouped by an inductive effort of the 

 mind. The advance is not great ; for Aboul Wefa appears only to 

 have detected the existence, and not to have fixed the law or the 

 exact quantity of the inequality ; but still it places the scientific 

 capacity of the Arabs in a more favorable point of view than any cir- 

 cumstance with which we were previously acquainted. 



But this discovery of Aboul Wefa appears to have excited no notice 

 among his contemporaries and followers : at least it had been long 

 quite forgotten when Tycho Brahe rediscovered the same lunar 

 inequality. We can hardly help looking upon this circumstance as 

 an evidence of a servility of intellect belonging to the Arabian period. 

 The learned Arabians were so little in the habit of considering science 

 as progressive, and looking with pride and confidence at examples of 

 its progress, that they had not the courage to believe in a discovery 

 which they themselves had made, and were dragged back by the chain 

 of authority, even when they had advanced beyond their Greek 

 masters. 



As the Arabians took the whole of their theory (with such slight 

 exceptions as we have been noticing) from the Greeks, they took from 

 them also the mathematical processes by which the consequences of 

 the theory were obtained. Arithmetic and Trigonometry, two main 

 branches of these processes, received considerable improvements at 

 their hands. In the former, especially, they rendered a service to the 

 world which it is difficult to estimate too highly, in abolishing the 



