On Machines in General, § 



branch of mechanics ; and in the second place, because I do 

 not mean to treat of any machine in particular, but solely 

 of the properties which are common to all. 



This theory is founded upon three principal definitions : 

 the first regards certain movements which I call geometrical, 

 because they may be determined by the principle of geome- 

 try alone, and are absolutely independent of the rules of 

 dynamics. I have not thought that we could easily pass 

 over them without leaving some obscurity in the elucidation, 

 of the principal propositions, as I have particularly shown 

 with respect to the principle of Descartes. 



By the second of my definitions, I endeavour to fix the 

 signification of the ie,vm6 force soliciting and force resisting : 

 we cannot, in my opinion, perspicuously compare causes 

 with effects in machinery without a marked distinction be- 

 tween these difierent forces ; and this is the distinction 

 upon which I think something vague and indeterminate has 

 been always left. 



Lastly, my third definition is that by which I give the 

 iiame of moment of activity of a power, to a quantity in 

 which a power is mentioned which is really in activity or in 

 movement, and where we also take account of each of the 

 instants employed by this force, i. e. of the time during 

 which it acts. Whatever it be, we cannot refuse to allow- 

 that this quantity, under whatever denomination we de- 

 signate it, is not to be continually met with in the analysis 

 of machines in movement. 



With the assistance of these definitions, T arrive at pro- 

 positions which are very simple : I deduce all of them from 

 one same fundamental equation, which, containing a cer- 

 tain indeterminate quantity, to which we niay attribute dif- 

 ferent arbitrary values, will give successively m each par- 

 ticular case, all the determinate equations required for the- 

 solution of the problem. 



This equation, which possesses the greatest simplicity, 

 generally extends to all imaginable cases of equilibrium and 

 movement, whether the movement changes hab^tiiv, or va- 

 j;\es by insensible degrees : it is even applied to atl bodies, 

 whether hard, «r endowed with a cerbin degrc^ti of elaslicilv ; 



at>d 



