See a translation for the manuscript
Overview of Mathesis Generalis (1699 – 1700)
The manuscript “Mathesis generalis” belongs to the group of texts that Leibniz produced in 1699-1700 to provide rigorous demonstrations for the “foundations of calculus” (see the presentation of Prima calculi magnitudinum elementa). One point of difference with Prima calculi is that here Leibniz gives a prominent role to the notion of natural number and to the famous proof, which he would take up again in New Essays on Human Understanding, of “2 + 2 = 4” (see the text Numerus integer, which seems to be a first version of the beginning of our text). Another point of divergence is the fact that Leibniz first gives interpretations of computations with negative numbers before formulating purely formal definitions by means of the properties of the inverse (an approach that the manuscript Elémens du calcul would put to completion). Finally, this text is also more complete in that it presents proofs concerning multiplication, which Prima calculi did not deal with.
A first transcription of this text was made by Emily Grosholz and can be found in [Grosholz and Yakira, 1998], p. 89 under the title Mathesis generalis est scientia magnitudinum. However an entire folio (LH XXXV, 1, 9 fol. 14v) dealing with the axiomatization of multiplication is missing from this edition. A complete transcription and commentary, as well as a list of variants, can be found in [Leibniz 2018, pp. 157-180].