9 6 



MATHEMATICAL SCIENCES. 



always accompanied by his physician, Grunpek, whose prescriptions were 

 dictated by the stars, and who paid more heed to the politics than to the 

 health of his august master. 



The exact sciences still found a home, however, in Italy at Florence, 

 where Buonencontro and the Alberti had formed a numerous school, arid 

 the application of mathematics to arts and industry was the result of a 



Fig. "0. Instruments of Mathematical Precision for executing Portraits. Fac-siinile of a Wood 

 Engraving by Albert Diirer, " Institutionum Geometricarum Libri Quatuor" (Parisiis, ex offi- 

 cina Christian! Wecheli, 1535, in folio). In the Library of M. Ambroise Firmin-Didot, Paris. 



serious and solid course of teaching. At the end of the fifteenth century 

 the astronomer Pozzo Toscanelli traced for Christopher Columbus, who 

 derived material assistance from his teaching, the route which he must take 

 across the ocean in order to reach the -western coasts of the Indies ; the 

 mathematician Paccioli was animated by Christian faith when he wrote his 

 great cosrnographical and philosophical work entitled, "De Divina Propor- 



