930 On Machines hi General, 



ittents is ta change the state of the system, without altering 

 the reciprocal aptioii of the bodies which compose it. To 

 leave, however, some distinction between them, we may 

 Call the first ahsolute geometrical movemciitSy and the others 

 geoinetrkal movements hy supposition: but when I speak 

 simply of geometrical movements, without otherwise de- 

 signing them, I shall imply both indifferently. 



This being done, — since we have explained how we may 

 determine, without the assistance of any mechanical prin- 

 ciple, all the geometrical movements of which a given sy- 

 stem is susceptible, it follows that the general problem which 

 we proposed is entirely reduced by the general equation (F) 

 to operations purely geometrical and analytical : we must, 

 however, observe, that it is not sufficient to attribute to the 

 arhitrarles u different values, but we must also attribute to 

 them different relations or directions; for, if we are con- 

 tented to attrii)ute different values to them without changing 

 any thing in the relations or directions, we should obtain 

 different equations, quite true and correct, but which would 

 be evidently reduced to the same on multiplying them by 

 different constants. 



Second Remark, 



XIX. As we are only speaking of hard bodies here, it is 

 clear that among the different values which we may attri- 

 bute to u, the velocity V is itself comprehended ; i, e. that 

 the real movement of the system is itself one of the geome- 

 trical movements of which it is susceptible : the first equa- 

 tion (E) is therefore contained in the indeterminate equa- 

 tion (F), and consequently we may reduce to this single 

 equation (F) all the laws of equilibrium and of movement 

 in hard bodies. 



Now we have seen, that this equation is nothing else 

 than the first (E), to which we have succeeded in giving 



system be reduced to two adjacent globes, and pushing each other, i t is clear, 

 that if we force these bodies to separate or to move in a direction contrary to 

 each other, this movement will not be impossible, but that at the same tiqie 

 bodies cannot assume it without ceasing to act upon each other. This move- 

 ment, therefore, is not proper for attaining the object proposed, which is to 

 (ph^inge nothing in the reciprocal action of bodies. 



_ . n-iorc 



