Overview of Numerus integer est totum ex unitatibus collectum
Numerus integer est totum ex unitatibus collectum appears as a first draft for the opening part of mathesis generalis (besides the similarity in content, it was also written on a paper which is used for the second manuscript). The manuscript was already transcribed with variants by Emily Grosholz (Grosholz & Yakira 1998). It testifies for an attempt in which the notion of natural number was presented before that of magnitude. By contrast, the final version comes back to the idea that magnitude is the central concept of algebraic calculus and that natural number should be defined, as measure of magnitudes, in terms of parts (Numerus integer est totum ex unitatibus tanquam partibus collectum). Another very interesting aspect of the text is a comment Leibniz wrote in front of the notations for the first nine digits and which he finally erased: “Where the following is produced from the preceding by adding 1. Let the preceding be p and the following S, we will have in general that p+1 is the same as S” (Ubi sequens semper fit ex praecedente adjecto seu 1. Nempe praecedens sit p et sequens sit S, eritque generaliter p +1 idem quod S) – where Leibniz seems very close to define the natural numbers by the notion of successor. This group of texts is also important since they give an immediate context for the famous proof that “2+2=4”, based on definitions and identical axioms, which was presented in the Nouveaux Essais pour l’entendement humain (IV, 7 § 10; A VI, 6, 413-414).