 In his Paradoxes of the Infinite (Bolzano 1851) and in the Theory of Quantity Bolzano took the first steps towards the development of set theory and anticipated many of its important ideas. In this connection mention is especially often made of Bolzano’s grasp of the “paradoxical” fact that an infinite set can and must be equipollent with one of its proper subsets, i.e., is “reflexive”. This special feature of infinite sets was later used for their definition by Dedekind. For Bolzano, equipollence and “having exactly the same kind of construction” (die ganz gleiche Entstehungsart haben) are taken together as a sufficient condition for infinite sets being equinumerous or having the same cardinal number. This view, however, contradicts the unrestricted application of the classical Euclidean principle that the whole is greater than each of its parts. Bolzano was aware of this conflict and therefore restricted the principle to finite sets. From here the step is not far to Dedekind’s view that equipollence is a sufficient condition for equinumerosity.