On Machines in 'General. 33 



or fixed points, as moveable bodies, as well as all the others ; 

 but of a mass infinitely large, or, what comes to the same 

 thing, as bodies of an infinite density, and which do not 

 diffet from all the other bodies of the system except in this 

 point. Hence a considerable advantage will result, as we 

 shall be able to make the system into which these bodies 

 enter, take anv given geometrical movements; for the instant 

 we suppose these obstacles moveable like all other bodies, 

 they will become susceptible of assuming any movements, 

 and the general system must be regarded as an assemblage 

 of bodies perfectly moveable : consequently, the quantities 

 of movements absorbed by the obstacles may be estimated 

 as vvilh respect to all the other parts of the system ; in such 

 a manner, that if we call R the resistance of any given fixed 

 point, this quantity R will be in the equation (F), with re- 

 spect to the point in question, what 7« U is with respect to 

 the body m : we shall therefore find by this equation, this 

 same quantity R like all the other forces m U, which could 

 not be the case by considering the obstacles as absolutely im- 

 moveable, without having recourse to some new mechanical 

 principle, which we must have made concur with the general 

 equation (F), in order to attain the complete solution of each 

 particular problem. Thus this method of considering the 

 fixed points is not only the most conformable to nature, as 

 we have said before, but also the simplest and the easiest. 



As to the wires, rods, or any other portions of the system, 

 the masses of which may be supposed to be infinitely 

 sniall, we u)ay neglect, i. e. suppose each of their mole- 

 cules m equal to zero, or, what comes to the same thincr, 

 regard their density as infinitely small, or as nothino- : our 

 equation [¥) will therefore become independent of these 

 quantities, i. e. the same as if we had abstracted these 

 masses from the bodies; and it is thus that we shall easily 

 find the mathematical theory of each n)achine, ?'. c. by mak- 

 ing the abstractions spoken of (VI 11.) 



XXIX. From this remark it results, that although there 

 is only a single kind of bodies in nature, we di=;tinguish them 

 however, for the facility of calculations, into three different 

 classes, which are, 1st, Those which we consider as what 



Vol. 31. No. 121. J/me 1608. C thev 



