Gersonides. Like most Jewish philosophers, he earned his bread by            
practicing medicine, and realized Hippocrates's ideal of the                 
physician-philosopher. Born at Bagnols (1288) in a family of scholars,       
he lived nearly all his life in Orange, Perpignan, and Avignon,              
where he worked in peace under the protection of the popes. There            
was hardly a science that he did not deal with, hardly a problem in          
philosophy that he left untouched. He was a learned Talmudist, he            
contributed to the mathematics of music, he wrote poetry.                    
    In mathematics and astronomy he was among the lights of the age.           
He anticipated (1321) the method later formulated by Maurolico               
(1575) and Pascal (1654), of finding the number of simple permutations       
of  n  objects by mathematical induction. His treatise on trigonometry       
paved the way for Regiomontanus, and was so widely esteemed that             
Pope Clement VI commissioned its translation into Latin as  De               
sinibus, chordis, et arcubus    (1342). He invented, or materially             
improved, the cross-staff for measuring the altitude of stars; this          
remained for two centuries a precious boon to navigation. He made            
his own astronomic observations, and ably critized the Ptolemaic             
system. He discussed but rejected the heliocentric hypothesis, in a          
manner suggesting that there were quite a few adherents of it in his         
time. He perfected the    camera obscura,    and used it, with the               
cross-staff, to determine more accurately the variations in the              
apparent diameter of the sun and moon.                                       
    As ben Gerson's science stemmed from the Arabic mathematicians and         
astronomers, so his philosophy was based on a critical study of the          
commentaries in which Averroes had expounded Aristotle. During the           
years 1319-21 Levi composed commentaries on these commentaries,              
covering Aristotle's treatises on logic, physics, astronomy,                 
meteorology, botany, zoology, psychology, and metaphysics; and to            
these studies he added, of course, repeated readings of Maimonides.          
His own philosophy, and most of his science, were embodied in a Hebrew             
work entitled, in the fashion of the age,  Milchamoth Adonai                 
( Battles of the Lord,    1317-29). It ranks second only to the  Moreh         
Nebuchim    in Jewish medieval philosophy, and continues Maimonides's          
attempt to reconcile Greek thought with Jewish faith, much to the            
detriment of the faith. When we consider the similar efforts of              
Averroes and Thomas Aquinas to harmonize Mohammedanism and