no SCIENCE AND THE HUMAN MIND 



: validity. But true science, he held, began with 

 observation ; if mathematical reasoning could then 

 be applied, greater certitude might be reached, but 

 " those sciences are vain and full of errors which are 

 not born from experience, the mother of all certainty, 

 and which do not end with one clear experiment (che 

 non terminano in nota experientia) ." Science gives 

 certainty, and science gives power. Those who rely 

 on practice without science are like sailors without 



. rudder or compass. 



When we turn from Leonardo's method to his 

 actual results, we are astonished at his insight. In 

 face of all the prepossession of the centuries, of 

 the universal belief that all motion must be main- 

 tained by a cause continually acting, he enunciates 

 the principle of inertia, afterwards demonstrated by 

 Galileo. " Nothing perceptible by the senses," says 

 da Vinci, " is able to move itself ; . . . every body has 

 a weight in the direction of its movement." He knows 

 that the speed of a falling body increases with the time, 

 though he misses the right law for the space fallen 

 through. 



He clearly understands the experimental impossi- 

 bility of " perpetual motion " as a source of useful 

 power, and inveighs against those who attempt it. He 

 uses this principle to demonstrate the law of the lever 

 by the method of virtual velocities, hitherto attributed 

 to Ubaldi and Galileo. The shorter arm raises the 

 greater weight slowly, while the longer arm is pushed 

 down by the smaller weight quickly ; these motions 

 must be in the proportion of the lengths of the arms, 

 so that the weights must be inversely as the lengths 

 of the arms. Leonardo regards the lever as the 



