CHAPTER XI 



PROGRESS OF MATHEMATICS AND MECHANICS IN THE 

 SIXTEENTH CENTURY 



IT was not alone the striving for universal culture which attracted 

 the great masters of the Renaissance, such as Brunelleschi, Leonardo 

 da Vinci, Raphael, Michael Angelo and especially Albrecht Diirer, with 

 irresistible power to the mathematical sciences. They were conscious 

 that, with all the freedom of the individual phantasy, art is subject 

 to necessary laws and, conversely, with all its rigor of logical structure, 

 mathematics follows esthetic laws. Rudio. 



The miraculous powers of modern calculation are due to three 

 inventions : the Arabic Notation, Decimal Fractions and Logarithms. 

 Cajori. 



The invention of logarithms and the calculation of the earlier tables 

 form a very striking episode in the history of exact science, and, with 

 the exception of the Principia of Newton, there is no mathematical 

 work published in the country which has produced such important 

 consequences, or to which so much interest attaches as to Napier's 

 Descriptio. Glaisher. 



It is Italy, which is the fatherland of Archimedes, whose creative 

 power embraces all domains of the mechanical science, the land of 

 the Renaissance, from out of which those mighty waves of new ideas 

 and new impulses in science and art have come forth into the world 

 the fatherland of Galileo the creator of experimental physics, of 

 Leonardo da Vinci the engineer, of Lagrange who has given its form 

 to modern analytical mechanics. W. v. Dyck. 



Dynamics is really a product of modern times, and affords the 

 rare example of a development fulfilled in a single great personage 

 Galileo. Nothing is finer than how he, beginning in the 'Aristotelian 

 spirit, gradually frees himself from its bondage and, instead of empty 

 metaphysics, introduces well-directed methodical investigations of 

 nature. Timerding. 



The period from the invention of printing about 1450 to that of 

 analytic geometry in 1637 was one of very great importance for 

 mathematics and mechanics as well as for astronomy. At the 



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