PROGRESS OF MATHEMATICS AND MECHANICS 253 



altitude of the triangle. Arriving thus at the parallelogram of 

 forces in equilibrium, he expresses his astonishment by exclaim- 

 ing "Here is a wonder and yet no wonder." 



In studying pulleys and their combinations he arrives at the 

 far-reaching result that in a system of pulleys in equilibrium " the 

 products of the weights into the displacements they sustain are 

 respectively equal" a remark containing the principle of virtual 

 displacement. He reaches correct results in regard to basal and 

 lateral pressure by reasoning analogous to that about the chain, 

 and by assuming on occasion that a definite portion of the 

 liquid is temporarily solidified. By ingenious experiments he 

 proves the dependence of fluid pressure on area and depth, 

 and takes proper account of upward and lateral pressure. He 

 studies the conditions of equilibrium for floating bodies, show- 

 ing that the centre of gravity of the body in question must lie 

 in a perpendicular with that of the water displaced by it, and 

 that the deeper the centre of gravity of the floating body the 

 more stable is the equilibrium. 



In analyzing the lateral pressure of a fluid Stevinus anticipates 

 the calculus point of view by dividing the surface into elements on 

 each of which the pressure lies between ascertainable values. In- 

 creasing the number of divisions, he says it is manifest that one 

 could carry this process so far that the difference between the con- 

 taining values should be made less than any given quantity how- 

 ever small all quite in harmony with our present definitions of 

 a limit. 



Stevinus' work and that of Galileo seem to have been quite 

 independent of each other, the former confining his theory to 

 statics, the latter laying a solid foundation for the new science 

 of dynamics. Torricelli, a disciple of Galileo best known for his 

 invention of the mercurial barometer, extended dynamics to 

 liquids, studying the character of a jet issuing from the side 

 of a vessel. 



Throughout this period the universities lagged. In Italy 

 Galileo lectured to medical students who were supposed to need^ 

 astronomy for medical purposes i.e. astrology. At Wittenberg 



