PRELUDE TO THE EPOCH OF GALILEO. 319 



whose reasonings respecting the lever much resemble those of Leo- 

 nardo. Da Vinci also anticipated Galileo in asserting that the time of 

 descent of a body down an inclined plane is to the time of descent 

 down its vertical length in the proportion of the length of the plane to 

 the height. But this cannot, I think, have been more than a guess : 

 there is no vestige of a proof given.] 



The contemporaneous progress of the other branch of mechanics, 

 the Doctrine of Motion, interfered with this independent advance of 

 Statics ; and to that we must now turn. We may observe, however, 

 that true propositions respecting the composition of forces appear to 

 have rapidly diffused themselves. The Tractatus de Motu of Michael 

 Varro of Geneva, already noticed, printed in 1584, had asserted, that 

 the forces which balance each other, acting on the sides of a right- 

 angled triangular wedge, are in the proportion of the sides of the tri- 

 angle; and although this assertion does not appear to have been 

 derived from a distinct idea of pressure, the author had hence rightly 

 deduced the properties of the wedge and the screw. And shortly after 

 this time, Galileo also established the same results on different princi- 

 ples. In his Treatise Delle Scienze Mecaniche (1592), he refers the 

 Inclined Plane to the Lever, in a sound and nearly satisfactory man- 

 ner ; imagining a lever so placed, that the motion of a body at the 

 extremity of one of its arms should be in the same direction as it is 

 upon the plane. A slight modification makes this an unexceptionable 

 proof. 



Sect. 3. Prelude to the Science of Dynamics. Attempts at the First 

 La iv of Motion. 



WE have already seen, that Aristotle divided Motions into Natural 

 and Violent. Cardan endeavored to improve this division by making 

 three classes : Voluntary Motion, which is circular and uniform, and 

 which is intended to include the celestial motions ; Natural Motion, 

 which is stronger towards the end, as the motion of a falling body, 

 this is in a straight line, because it is motion to an end, and nature 

 seeks her ends by the shortest road ; and thirdly, Violent Motion, in- 

 cluding in this term all kinds different from the former two. Cardan 

 was aware that such Violent Motion might be produced by a very 

 small force ; thus he asserts, that a spherical body resting on a hori- 

 zontal plane may be put in motion by any force which is sufficient to 

 cleave the air ; for which, however, he erroneously assigns as a reason, 



