Introductio in analysin infinitorum
Introductio in analysin infinitorum (Introduction to the Analysis of the Infinite) is a two-volume work by Leonhard Euler which lays the foundations of mathematical analysis. Written in Latin and published in 1748, the Introductio contains 18 chapters in the first part and 22 chapters in the second.
Carl Boyer's lectures at the 1950 International Congress of Mathematicians compared the influence of Euler's Introductio to that of Euclid's Elements, calling the Elements the foremost textbook of ancient times, and the Introductio "the foremost textbook of modern times". Boyer also wrote:
- The analysis of Euler comes close to the modern orthodox discipline, the study of functions by means of infinite processes, especially through infinite series.
- It is doubtful that any other essentially didactic work includes as large a portion of original material that survives in the college courses today...Can be read with comparative ease by the modern student...The prototype of modern textbooks.
The first translation into English was that by John D. Blanton, published in 1988. The second, by Ian Bruce, is available online. A list of the editions of Introductio has been assembled by V. Frederick Rickey.
Reviews of Blanton translation 1988
- Doru Stefanescu MR1025504
- Marco Panza (2007) MR2384380
- Ricardo Quintero Zazueta (1999) MR1823258
- E. Hairer & G. Wanner (1996) Analysis by its History, chapter 1, pp 1 to 79, Undergraduate Texts in Mathematics #70, ISBN 978-0-387-77036-9 MR1410751
- Carl Boyer (April 1951). "The Foremost Textbook of Modern Times". American Mathematical Monthly. Mathematical Association of America. 58 (4): 223–226. doi:10.2307/2306956. JSTOR 2306956.
- Leonhard Euler; J. D. Blanton (transl.) (1988). Introduction to analysis of the infinite, Book 1. Springer. ISBN 978-0-387-96824-7.
- Introductio in analysin infinitorum.
- V. Frederick Rickey A Reader’s Guide to Euler’s Introductio