L. Euler’s unpublished manuscript Calculus Differentialis

Abstract

L. Euler’s Latin manuscript Calculus Differentialis is preserved at the Leningrad branch of the Archive of the USSR Academy of Sciences (f. 136, op.1, No. 183, 15 leaves). This is a fair copy quite carefully written on both sides of each of the 15 leaves¹. It is subdivided into four chapters: chapter 1, De Calculo Differentiarum Finitarum (§§ 1–16); chapter 2, De Calculo Differentiali in Genere (§§ 1–12); chapter 3, De Differentiatione Functionum Algebraicarum (§§ 1–20) and chapter 4, De Differentiatione Quantitatum Logarithmicalium et Exponentialium (§§ 1–20). Describing Euler’s scientific manuscripts, preserved at the said Archive, G. K. Mikhailov supposes that the manuscript “evidently” (offenbar) dates back to the 1730s ([1], p.264). Nevertheless, bearing in mind its contents, as well as the terminology and notation used, I believe that the manuscript was most likely written somewhat earlier, ca. 1727. Presumably, it was intended for the purpose of instruction, e.g. for the students of the University at the Petersburg Academy of Sciences.