NOTHINt,. 7 



same, yet under the form of quantity, and, as will be 

 shown, of multiplicity. An infinity resides in both ; in 

 the Real an endlessness of individual forms ; in the Ideal 

 but one endless form ; in the latter case an eternity, in 

 the former an infinity. The quantity and multiplicity of 

 the whole of mathematics is contained in the same manner 

 in the 0, that the quantity and multiplicity of the triangles 

 are in the ideal or primaiy triangle. Mathematics is a 

 system of nullities or nothings, and this admits of being 

 easily proved. 



37. Zero is indeed the universality of mathematics, 

 this, however, is not real, but only ideal. Every number 

 issues out of zero, like the multiplicity of the real tri- 

 angles out of the primary triangle. This progression of 

 numbers out of zero takes place through a process of 

 becoming determinate and limited ; just as the real tri- 

 angles are only definitions of the absolute triangle. The 

 process of becoming determined is identical with becoming 

 a Finite ; becoming real is called becoming finite. Mathe- 

 matical singulars or numbers can, therefore, be nothing 

 else than zero disintegrated, or rendered real by deter- 

 mination. 



What zero is in infinite intensity, that are numbers in 

 endless extensity. Zero is of two forms : under the ideal 

 it is mere intensity ; under the real mere extensity, or a 

 series of numbers. The latter is only expanded intensity; 

 the former, extensity concentrated on the point ; both are, 

 consequently, one and the same in toto. Numbers are 

 identical with zero ; they are zero in a state of exten- 

 sion, w r hile zero is equivalent to numbers in a state of 

 intensity. The sense in which numbers are said to come 

 out of zero is, therefore, very clear ; they have not issued 

 forth from zeno as if they had previously resided indivi- 

 dually therein, but the zero has emerged out of itself, 

 has itself become apparent, and then was it a finite zero, 

 a number. So, also, does the idea of a circle become a 

 real circle, not from the latter emerging from the former, 

 but from this itself becoming manifest. The individual 

 circle is a manifestation or phenomena of the spiritual circle. 



