330 APPENDIX H 



fractions of a number, without our troubling about divisions 

 actually made, which indicate points in the line in various 

 ways. But in actual substantial things the whole is a sum or 

 aggregate of simple substances or rather of a multitude of real 

 units [unites]. And it is the confounding of the ideal and the 

 actual that has brought the whole matter into confusion and 

 has produced the labyrinth de compositione continui. Those 

 who have supposed the line to be made up of points have 

 sought for the primary elements in ideal things or relations, 

 which was quite a mistake ; and those who have found that 

 relations like number or space (which includes the order or 

 relation of possible co-existent things) cannot be formed by 

 the aggregation of points, have usually made the mistake of 

 denying the primary elements of substantial realities, as if 

 they had no primary unities, or as if ^there were no simple 

 substances. Nevertheless number and the line are not chimeri- 

 cal things, although they are not thus compounded, for they 

 are relations which involve eternal truths, in accordance with 

 which the phenomena of nature are ordered. Hence it may 

 be said that, considered in the abstract, \ and \ are indepen- 

 dent of one another, or rather the total ratio [rapport] \ is 

 anterior in the order of reason [dans le signe de la raison], as 

 the Scholastics say to the partial ratio ^, since it is by the 

 subdivision of the half that we come to the fourth, following 

 the order of what is ideal ; and the same is the case with the 

 line, in which the whole is anterior to the part because the 

 part is only possible and ideal. But in realities, in which 

 there are only divisions actually made, the whole is merely 

 a sum or aggregate, as in the case of a flock of sheep. It is 

 true that the number of simple substances which enter into 

 a mass, however small it be, is infinite, since in addition 

 to the soul which constitutes the real unity of the animal, the 

 body of the sheep (for instance) is actually subdivided, that 

 is to say it is also an aggregate of invisible animals or plants 

 (which are likewise compound) besides that which constitutes 

 also their real unity ; and although this proceeds ad infinitum, 

 it is manifest that ultimately all is reducible to these unities, 

 the remainder or the aggregates being merely well-founded 

 phenomena.' 



