PROGRESS OF SCIENCE TO 1450 A.D. 185 



There can be no doubt that at all times medieval schools taught 

 all that their respective generations knew of arithmetic; that the 

 teachers of arithmetic in the schools were often the famous mathe- 

 maticians of their day ; that this teaching, since it kept pace with the 

 increase in the knowledge of the subject, was progressive in character, 

 and that at no time, not even in the barren generations at the close of 

 the Middle Ages, when the scholastic education had outlived its use- 

 fulness, did arithmetic cease to be a subject of study in the arts facul- 

 ties of the medieval universities. Abelson. 



THE RENAISSANCE. With the fourteenth century we enter 

 upon one of the most interesting and noteworthy periods of human 

 history; viz. the Renaissance. Neither the term nor the period 

 is, however, sharply defined, the former signifying an awakening 

 or "new birth," the latter covering loosely the fourteenth to the 

 sixteenth centuries. It is only necessary to recapitulate briefly 

 some of the phenomena touched upon in the present chapter, to 

 realize that the civilization of the later Middle Ages has been under- 

 going great changes. The Crusades marked the first and perhaps 

 most important of these, while the rediscovery or recovery of the 

 classics from Arabian and other sources in the eleventh to the thir- 

 teenth centuries, followed by the revival of (classical) learning in 

 the fourteenth must have been powerful ferments of the medieval 

 scholastic mind, expanded and uplifted as it was by the poetical 

 philosophy of Dante and challenged by the naturalism and ration- 

 alism of Roger Bacon. 



The great events of the fourteenth century were in part new, 

 and in part the natural extension and development of those of 

 the thirteenth. A strange and appalling natural phenomenon was 

 the famous epidemic known as the " black death," a quickly fatal 

 disease which carried off from one quarter to one half of all the 

 inhabitants of Europe, producing social changes such as the 

 rise of wages which are still felt. 



HUMANISM. The development of better education begun in 

 the thirteenth century was marked in the fourteenth by the found- 

 ing of many now famous universities and colleges and by that 

 revival of ancient learning which is associated especially with the 



