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On Machines in GeneraL 21 D 



xvbich will be done by supposing the wire annihilated, i. e. 

 by treating as geometrical the motions which would be so 

 effectively if the wire in question did not exist. 



From this it follows, that in order to extract in each par- 

 ticuJar case from the general equation (F) all the determi- 

 nate equations which it can give, we must first make the 

 system assume all the geometrical movements of which it is 

 susceptible; secondly, to treat also as such all those which 

 would become so by suppressing some machine or part of a 

 machine, the action of which upon the rest of the system 

 is null, or by regarding as permeable to each other, the 

 bodies among which, although adjacent, no pressure is ex- 

 ercised. 3dly. In the last place, if we are in doubt whether 

 a certain wire, rod, or any part of the machine has or has 

 rot a real action upon the other parts of the system, or that 

 there was a real pressure between two adjacent bodies, we 

 must first clear up this doubt, by supposing the thing in 

 question as we have above explained it, and by treating as 

 • geometrical the movements which these suppositions shall 

 have discovered as being capable of being taken for such. 



According to this remark, it seems proper therefore to 

 extend the name of geometrical, to all the movements, 

 which, without being so effectively, become so on suppress- 

 ing some machine or part of a machine which has no in- 

 fluence upon the state of the system, and on regarding also 

 as perfectly permeable to each other, bodies in contact, 

 without any pressure being exercised among them, i. e, 

 without there being any ihing except a simple juxtaposi- 

 .tion : thus we shall presently comprehend all these move- 

 ments, under the title of geometrical movements, since in 

 tact they are equally well determined by operations purely 

 geometrical, and are employed in the same way for extract- 

 ing from the general equation (F) determinate equations, 

 ^whilc the general and exclusive property* of these move- 

 ments 



* It Is evident that this property belpngs successively to the movements 

 -'vvhlch I here cali geometrical, and that it woyld consequeutly be a very false 

 idea of them to regard them as movements simply possible, i.e. compatible 

 with the iiDpen«trability of matter: for, suppcsi rg, lor instance, that all the 



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