190 SCIENCE IN GRECO-ROMAN ANTIQUITY 



philosophers and with them Lucretius (II, 235) : 

 " Consequently the atoms, in spite of the inequality 

 of their masses, must move with equal velocity in 

 empty space." 



Again let us take a body subject to a force which 

 remains the same and to a resistance which continuously 

 increases until it becomes equal to the force, for ex- 

 ample, when a stake is driven into the sand. Ex- 

 perience teaches us that the velocity becomes nil at 

 a given moment, but, according to the law of Aristotle, 

 that is impossible, since we have the constant : 



Aristotle saw this difficulty, but in order to remove 

 it he simply laid down the law that a small force 

 cannot move a large body. " Because a whole force 

 moves a body along a certain distance, it does not 

 result that half this force moves this body along any 

 distance during any time. A single man would in 

 that case be able to move the ship which all the 

 haulers pull, if, the force of the haulers being divided 

 by a certain number, the distance traversed were also 

 divided by the same number." x Aristotle could not 

 explain by his theory why it is easier to move with 

 a given force a carriage having large wheels than one 

 having small wheels. His mistake lay in considering 

 as simple and elementary, facts which are really very 

 complex. 



From the formula he had stated, F = R x V, Aris- 

 totle drew the conclusion that the properties of the 

 lever and the balance are related to the study of the 

 velocities with which circular arcs are described. Two 

 forces are equivalent if by moving unequal weights 

 with unequal velocities they give the same value to 

 the product of the weight by the velocity. 



1 Phys. 250 a, 10, quoted from 13 Duhem. Systeme, I, p. 194. 



