Read the Masters Session: Euler's Introductio

MathFest 2019, Cincinnati OH

Thursday, August 1, 3:40-5:40pm
Duke Energy Convention Center, Room 201


Leonhard Euler's Introductio in Analysin Infinitorum (1748) is a key text in the history of mathematics. In it, Euler provided the foundation for much of today's mathematical analysis, focusing in particular on functions and their development into infinite series. Later in his career, Euler built a theory of differential and integral calculus atop this foundation, with the Institutiones calculi differentialis (1755) and the Institutionum calculi integralis (1768-70) being the primary works in this area.

In this session, we will read Chapter VII from Book I of the Introductio, in which Euler uses infinite series as a tool to define and analyze exponential and logarithmic functions. Our reading is taken from John Blanton's 1988 English translation.
The Day's Reading: Chapter 7 of Euler's Introductio

For the curious, the original Latin text and some early translations (into French and German) are available below.


  • Latin original (1748), available via the Bibliothèque Nationale de France's Gallica digital library.
  • Latin reprinting (1922), from Leonhardi Euleri Opera Omnia, Series 1, Volume VIII.
  • French translation ("The Fourth Year of the French Republic," 1796), also from Gallica.
  • German translation (1885), available via the Euler Archive.

Additional information on Euler's Introductio can be found via the E101 and E102 catalog listings at the Euler Archive.