214 On Machines in General, 



compressible rod, it cannot recede from it any more ; 

 for, if it receded, it is clear that in virtue of the equal and 

 directly opposite movement, which is also possible by hy- 

 pothesis, it would approach it ; which could not be on ac- 

 count of the inconipressibility of the rod : for the same, 

 reason finally it is obvious, that if it he a wire which sepa- 

 rates m from the adjacent corpuscle, it will not approach, 

 because then it would be possible to remove it by an equal 

 and directly opposite movement : now this cannot be, on 

 account of the inextensibility of the wire : therefore, what- 

 ever may be the geometrical movement impressed upon the 



possible to make the weight attached to the cylinder descend from a height 

 equal to its circumference, while the weight attached to the wheel would 

 mount from an equal height to its circumference^ but if while we cause th? 

 weight attached to the wheel to descend from a height equal to its circumfe- 

 rence, wp should cause the weight attached to the cylinder to ascend from a 

 height greater than its circumference, the movement would not be ^cnmctricalf 

 because the equal and contrary movement would be visibly impossible. 



If sevjral bodies be attached to the extremities of different wires united by 

 the other extremities to one and the same knot, and if we make the system 

 assume such a movement as that each of the bodies remains constantly re- 

 moved from the knot of one and the same quantity at t'le length of the wire 

 to which it is attached, this movement will be geometrical, even when the 

 different bodies approach to each other; but if some of them approach the 

 knot, the movement would not be geometrical, because, the wires being sup-r 

 posed to be inextensible, the equal and contrary movement would be visibly 

 impossible. 



If two bodies are attached to the extremities of a wire into which is intro- 

 duced a moveable particle, it will be sufficient, in order that the movement 

 be geometrical, that the sura of the distances from the moveable particle to 

 each of the two other bodies is constantly equal to the length of the wire ; so 

 that if these two bodies are fixed, the moveable particle will not depart from 

 an elliptical curve. 



If a body be moved by a curved surface, for instance, in the concavity of 

 a spherical shell, the movement will be geometrical, while the body will move 

 in a tangent form to the surface •, but if it be separated the movement will 

 cease to be geometrical, because the equal and contrary piovempnt is visibly 

 impossible. 



Vrom all this it is evident, that although on giving to a system a. geometrical 

 movement, the different bodies of this system may be brought near to each 

 other, yet we may say that the adjacent corpuscles, considered two by two, 

 do not tend at the first instant cither to approach or recede, as I shall prove 

 at length in the text. Bodies therefore exercise no action upon each olher in 

 virtue of a similar movement : these movements are therefore absolutely in- 

 dependent of the rules of dynamics, and it is for this reason that I have called 

 them geometrical. " 



system. 



