CHAPTER III. 



SEQUEL TO THE EPOCH OF GALILEO. PERIOD OF 

 VERIFICATION AND DEDUCTION. 



THE evidence on which Galileo rested the truth 

 of the Laws of Motion which he asserted, was, 

 as we have seen, the simplicity of the laws them- 

 selves, and the agreement of their consequences 

 with facts; proper allowances being made for dis- 

 turbing causes. His successors took up and con- 

 tinued the task of making repeated comparisons of 

 the theory with practice, till no doubt remained of 

 the exactness of the fundamental doctrines : they 

 also employed themselves in simplifying, as much 

 as possible, the mode of stating these doctrines, and 

 in tracing their consequences in various problems 

 by the aid of mathematical reasoning. These em- 

 ployments led to the publication of various Treatises 

 on Falling Bodies, Inclined Planes, Pendulums, Pro- 

 jectiles, Spouting Fluids, which occupied a great 

 part of the seventeenth century. 



The authors of these treatises may be considered 

 as the School of Galileo. Several of them were, 

 indeed, his pupils or personal friends. Castelli was 

 his disciple and astronomical assistant at Florence, 

 and afterwards his correspondent. Torricelli was at 

 first a pupil of Castelli, but became the inmate and 

 amanuensis of Galileo in 1641, and succeeded him 



