APPENDIX H 329 



little to be broken, and this is so, according to my 

 system 31 , in which there is conservation of force and 

 direction, and none of the natural laws of bodies are 

 broken, notwithstanding the changes which take place 

 in body in consequence of changes in the soul. 



APPENDIX H. 



ON THE ELEMENTS OF EXTENSION. 



ONE of Foucher's objections to the New System was based on 

 the contention that extension has no ultimate real elements 

 (E. 1 29 a ; Gr. iv. 487). In some Remarques sur les Objections de 

 M. Foucher (G. iv. 490) Leibniz replies : ' The author of the 

 objection does not seem to have rightly understood my view. 

 Extension or space, and the surfaces, lines and points that can 

 be conceived in it, are nothing but relations of order or orders 

 of co-existence, both as regards that which actually exists 

 and as regards the possible thing that might be put in place 

 of that which exists. Thus they have no ultimate component 

 elements [principes], any more than number has. And as 

 a broken number, for instance , can be further broken into 

 two-fourths or four-eighths and so on ad infinitum, without our 

 being able to reach the absolutely smallest fractions or to 

 conceive the number as a whole formed by the combination of 

 ultimate elements, so it is with a line which can be divided, 

 just like this number. Again, strictly speaking, the number ^ 

 in the abstract is a perfectly simple ratio [rapport], not at all 

 formed by the compounding of other fractions, although in 

 numbered things there is equality between two -fourths and 

 one -half. And we may say as much regarding an abstract line, 

 since compounding takes place only in concrete things, or the 

 masses of which these abstract lines indicate the relations. 

 And it is also in this way that mathematical points are to be 

 regarded : they are merely modalities, that is to say extremi- 

 ties. And as in the abstract line all is indefinite, it has 

 reference to everything which is possible, as in the case of 



31 E. reads ' and this ' [i. e. the breach of the law] ' is avoided by 

 my system.' 



