1 68 THE POPULAR SCIENCE MONTHLY 



The activity incident to these great movements made Florence and 

 Venice renowned for their wealth, while it also gave the Hanseatic 

 League command of the trade of the north. With the growth of pros- 

 perity came increased leisure for intellectual development, resulting in 

 the Italian Eenaissance and the European Eevival of Learning. The 

 crusades also influenced development still more directly by opening lines 

 of communication with the east, whereby the learning that had lain 

 dormant in the Byzantine empire became current in Europe. 



Toward the close of the fifteenth century the discovery of America, 

 closely followed by the circumnavigation of the world, gave dominance 

 once more to the influence of the sea. The effect of such a strong sug- 

 gestion of boundless and unknown possibilities, intensified by the ele- 

 ment of hazard and daring, became at once an important factor in 

 development, stimulating ambition, creating moral fiber and inspiring 

 a passion for freedom. With the opening of the sixteenth century the 

 narrow and vague ideas characteristic of scholasticism began to giv.e 

 place to clear and strong thinking. As the church had been the center 

 and source of medieval authority, the struggle for freedom naturally 

 centered around this institution. Beginning with the reform of certain 

 abuses, the spirit of the reformation ended by repudiating the entire 

 authority of the church, epitomized by the action of Luther in nailing 

 his ninety-five theses to the door of the church in Wittemberg, thus 

 undermining the whole system of tradition and inaugurating a new 

 principle of action based on individuality. 



The relation of this mental attitude to the development of culture 

 was nowhere more evident than in the trend taken by mathematics. 

 Everywhere old methods were questioned and new ones substituted. 

 The first great advance naturally occurred in Germany and Italy. In 

 the former the time-honored system of Ptolemaic astronomy gave place 

 to the Copernican theory, and notable advances were also made in other 

 branches of mathematics, especially algebra and trigonometry. The in- 

 tervention of the Thirty Years' War, followed by the Prussian war, stayed 

 German development for a time, but with the return of peace the Ger- 

 man spirit again manifested itself in the critical attitude toward science 

 and religion which found expression in mathematics in the function 

 theory, and in philosophy and religion in agnosticism. 



In France where the invigorating effects of climate and race were 

 less marked, the sixteenth century was characterized by such acts of 

 religious intolerance as the massacres of Vassy and St. Bartholomew, 

 leaving no energy for scientific pursuits. The ascension of Henry IV. 

 to the throne, however, followed by the Edict of Nantes which termi- 

 nated the religious strife, produced an immediate effect, the Age of 

 Bichelieu being remarkable for scientific and cultural progress. Great 

 literature was produced and in mathematics the period was made illus- 



