E212 -- Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum
(Foundations of Differential Calculus, with Applications to Finite Analysis and Series)
This is a volume on differential calculus. It is divided into two books, one of which has 9 chapters and other 18. The Euler Archive has provided a 1787 printing of the Latin text (Ticino: Petri Galeatii), shown below.
- Front Matter
- Part I
- Chapter 1: De differentiis
- Chapter 2: De usu
differentiarum in doctrina serierum.
- Chapter 3: De infinitis
atque infinite parvis.
- Chapter 4: De
differentialium cujusque ordinis natura.
- Chapter 5: De
differentiatione functionum algebraicarum unicam variabilem involventium.
- Chapter 6: De
differentiatione functionum transcendentium.
- Chapter 7: De
differentiatione functionum duas pluresve variabiles involventium.
- Chapter 8: De formularum
differentialium ulteriori differentiatione.
- Chapter 9: De
- Part II
- Chapter 1: De
- Chapter 2: De
investigatione serierum summabilium.
- Chapter 3: De inventione
- Chapter 4: De conversione
functionum in series.
- Chapter 5: Investigatio
summae serierum ex termino generali.
- Chapter 6: De summatione
progressionum per series infinitas.
- Chapter 7: Methodus
summandi superior ulterius promota.
- Chapter 8: De usu calculi
differentialis in formandis seriebus.
- Chapter 9: De usu calculi
differentialis in aequationibus resolvendis.
- Chapter 10: De maximis et
- Chapter 11: De maximis et
minimis functionum multiformium pluresque variabiles complectentium.
- Chapter 12: De usu
differentialium in investigandis radicibus realibus aequationum.
- Chapter 13: De criteriis
- Chapter 14: De
differentialibus functionum in certis tantum casibus.
- Chapter 15: De valoribus
functionum, qui certis casibus videntur indeterminati.
- Chapter 16: De
differentiatione functionum inexplicabilium.
- Chapter 17: De
- Chapter 18: De usu
calculi differentialis in resolutione fractionum.
- Supplementary Material
- Originally published as a book in 1755
- Opera Omnia: Series 1, Volume 10
- Book I was translated into English by John Blanton, and published by Springer in 2000. Selections are available via Google Books: E212.
- Much of Chapters 5 and 6 of Book II have been translated into English by David Pengelley, and are available, along with many other excellent resources, at his Teaching with Original Historical Sources in Mathematics web page in pdf and dvi formats.
- E212 is discussed in Ed Sandifer's How Euler Did It September 2005 column published online by the MAA.
- Alexander Aycock (aaycock at students dot uni dash mainz dot de) has made a draft translation of Book II into English. These chapters are available online at Euler-Kreis Mainz. Please send your comments or feedback to him at the email address indicated above.
- The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E212 include:
- Ferraro G., “Analytical symbols and geometrical figures in eighteenth-century calculus.” Studies in History and Philosophy of Science, 32A (3), 535-555 (Sep 2001).
- Ferraro G., “Differentials and differential coefficients in the Eulerian foundations of the calculus.” Historia Mathematica, 31 (1), pp. 34-61 (Feb 2004).
- Gould HW., “Euler formula for nth differences of powers.” American Mathematical Monthly, 85 (6), pp. 450-467 (1978).
- Grabiner JV., “The changing concept of change - the derivative from Fermat to Weierstrass.” Mathematics Magazine, 56 (4), pp. 195-206 (1983).
- Ruthing D., “Some definitions of the concept of function from Bernoulli, Joh. to Bourbaki, N..” Mathematical Intellingencer, 6 (4), pp. 72-77 (1984).
- Volkert K., “History of pathological functions - on the origins of mathematical methodology.” Archive for History of Exact Sciences, 37 (3), pp. 193-232 (1987).
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