
 [No title] 
  As Riemann emphasized in his 1854 habilitation lecture, his philosophical fragments, and his lectures on Abelian and hypergeometric functions, and as Gauss had spoken earlier, the common, intuitive notions concerning geometrical objects presupposes a set of assumptions concerning the fundamental nature of the "space" in which those objects arise. 
  On this basis, Riemann was able to demonstrate, using Leibniz's principle of "analysis situs", that all the essential characteristics of a complex function, are determined by the relationship of the boundary to the branching points, or the other singularities. 
  Riemann demonstrated, using a method similar to the one used by Gauss in his proof of the fundamental theorem of algebra, that those complex functions associated with these higher transcendentals generate surfaces with two sheets, but with more than the two branch points expressed by the algebraic, circular, hyperbolic or exponential functions. 
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