Remark 1

Theorem 1 can be proved without invoking the theory of ordered fields by using properties of the topology of the field $\mathbf{C}$, which will be defined below (no. 2); see § 2, Exercise 2 and also the part of this series devoted to algebraic topology, where the theorem of d’Alembert-Gauss will appear as a consequence of results on the degree of a mapping.