PART I. 

 MATHESIS OF THE WHOLE. 



NOTHING. 



31. The highest mathematical idea, or the funda- 

 mental principle of all mathematics is the zero = 0. 



The whole science of mathematics depends upon zero. 

 Zero alone determines the value in mathematics. 



32. Zero is in itself nothing. Mathematics is based 

 upon nothing, and, consequently, arises out of nothing. 



33. Out of nothing, therefore, it is possible for some- 

 thing to arise, for mathematics, consisting of propositions, 

 is a something in relation to 0. Mathematics itself were 

 nothing if it had none other than its highest principle 

 zero. In order, therefore, that mathematics may become 

 a real science, it must, in addition to its highest principle, 

 subdivide into a number of details, namely, first of all 

 into numbers, and, finally, into propositions. What is 

 tenable in regard to mathematics must be equally so of all 

 the sciences ; they must all resemble mathematics. 



34. The first act towards realization or the becoming 

 something, is an origination of Many. All reality can, 

 accordingly, manifest itself only in multiplicity. 



That which belongs to the Many is a Definite ; this 

 again is a Limited ; the Limited is a Finite. The Finite 

 only is real. 



The question now arises, how it happens that mathematics becomes a mul- 

 tiplicity, or, what is the same thing, a reality, a something. 



35. The reality of mathematics consists in the univer- 

 sality of its magnitudes ; viz. numbers or figures. Every 

 number, and every thing which belongs to mathematics, 

 can be derived from no other source than zero. 



