80 A SHORT HISTORY OF SCIENCE 



tant in modern mathematical and physical science he defines 

 by saying : 



A thing is continuous when of any two successive parts, the limits, 

 at which they touch, are one and the same, and are, as the word im- 

 plies, held together. 



ARISTOTLE'S MECHANICS. In mechanics Aristotle seems 

 almost to recognize the principle of virtual velocities. He dis- 

 cusses the composition of motions at an angle with each other. 

 He enunciates the correct relation between the length of the 

 arms of a lever and the loads which will balance each other 

 upon it. He even deals with the central and tangential com- 

 ponents of circular motion. 



He asks such questions as : " Why are carriages with large 

 wheels easier to move than those with small ? ' " Why do objects 

 in a whirlpool move toward the center?" etc. 



He is convinced that the speed of falling bodies is proportional 

 to their weight - - a belief credulously accepted until Galileo's 

 experiment nineteen centuries later. He illustrates his discussions 

 by geometrical figures, and states correctly : 



If a be a force, /3 the mass to which it is applied, y the distance 

 through which it is moved, and 5 the time of the motion, then a will 

 move \ /3 through 2 y in the time 5, or through y in the time \ d. 



He adds erroneously, however : 



It does not follow that \ a will move /3 through \ y in the time 5, be- 

 cause | a may not be able to move /3 at all ; for 100 men may drag 

 a ship 100 yards, but it does not follow that one man can drag it 

 one yard. 



Of the bearing of Aristotle's physical theories Duhem says : 



Incapable of any alteration, inaccessible to any violence, the celestial 

 essence could manifest no other than its own natural motion, and 

 that was uniform rotation about the centre of the universe. 



Aristotle is the author of eight books on Physics, four on the 

 Heavens, and four on Meteorology. In physics he explains the 

 rainbow, attributes sound to atmospheric motion, and discusses 



