THE RENAISSANCE 109 



geometry ; he knew Luca Pacioli the mathematician, 

 and was helped in his anatomical researches by Antonio 

 della Torre. It is clear that, a century before the days 

 of Galileo, a small circle of kindred spirits lived in 

 Italy who were more interested in things than in 

 books, in experimental enquiry than the opinions of 

 Aristotle. 



But there is a link with Greek thought behind these 

 men too, a link with Archimedes. Archimedes' books 

 had not yet been printed, and good manuscripts were 

 rare. Leonardo notes the names of his friends and 

 patrons who could procure him copies, and expresses 

 admiration at the genius of the great Syracusan. 

 Interest in Archimedes grew rapidly ; in 1543 the 

 mathematician Tartaglia published a Latin translation 

 of some of his works, and other editions followed, so 

 that they were well known by the time of Galileo, who 

 studied them carefully. In Archimedes, the man 

 of science, and not in Aristotle, the encyclopaedic 

 philosopher, is to be sought the veritable Greek proto- 

 type of modern physical science, of which Archimedes 

 alone of the ancient writers who have survived 

 possessed the true spirit. 



Leonardo da Vinci perceived intuitively and used 

 effectively the right experimental method a century 

 before Francis Bacon philosophized about it inade- 

 quately, and Galileo once more put it into practice. 

 Leonardo wrote no treatise on method, but incident- 

 ally his ideas about it clearly appear. He knew that 

 mathematics, arithmetic and geometry, gave absolute 

 certitude within their own realm ; they were concerned 

 with ideal mental concepts (e tutta mentale) of universal 



