PRELUDE TO THE EPOCH OF GALILEO. 317 



ticipating any wider proofs of the impossibility of a perpetual motion, 

 drawn from principles subsequently discovered, but would be referring 

 the question to certain fundamental convictions, which, whether put 

 into Axioms or not, inevitably accompany our mechanical conceptions. 



In the same way, Stevinus of Bruges, in 1586, when he published 

 his Beghinselen der WaagJiconst (Principles of Equilibrium), had been 

 asked why a loop of chain, hung over a triangular beam, could not, as 

 he asserted it could not, go on moving round and round perpetually, 

 by the action of its own weight, he would probably have answered, 

 that the weight of the chain, if it produced motion at all, must have a 

 tendency to bring it into some certain position, and that when the chain 

 had reached this position, it would have no tendency to go any fur- 

 ther ; and thus he would have reduced the impossibility of such a per- 

 petual motion, to the conception of gravity, as a force tending to pro- 

 duce equilibrium ; a principle perfectly sound and correct. 



Upon this principle thus applied, Stevinus did establish the funda- 

 mental property of the Inclined Plane. He supposed a loop of string, 

 loaded with fourteen equal balls at equal distances, to hang over a tri- 

 angular support which was composed of two inclined planes with a 

 horizontal base, and whose sides, being unequal in the proportion of 

 two to one, supported four and two balls respectively. He showed that 

 this loop must hang at rest, because any motion would only bring it 

 into the same condition in which it was at first; and that the festoon 

 of eight balls which hung down below the triangle might be removed 

 without disturbing the equilibrium ; so that four balls on the longer 

 plane would balance two balls on the shorter plane ; or in other words, 

 the weights would be as the lengths of the planes intercepted by the 

 horizontal line. 



Stevinus showed his firm possession of the truth contained in this 

 principle, by deducing from it the properties of forces acting in oblique 

 directions under all kinds of conditions ; in short, he showed his entire 

 ability to found upon it a complete doctrine of equilibrium ; and upon 

 his foundations, and without any additional support, the mathematical 

 doctrines of Statics might have been carried to the highest pitch of 

 perfection they have yet reached. The formation of the science was 

 finished ; the mathematical development and exposition of it were alone 

 open to extension and change. 



[2d Ed.] [" Simon Stevin of Bruges," as he usually designates him- 

 self in the title-page of his work, has lately become an object of gene- 

 ral interest in his own country, and it has been resolved to erect a 



