E342 -- Institutionum calculi integralis volumen primum
(Foundations of Integral Calculus, volume 1)
Originally published with the full title: Institutionum calculi integralis volumen primum in quo methodus integrandi a primis
principiis usque ad integrationem aequationum differentialium primi gradus pertractatur.
Auctore Leonhardo Eulero acad. scient. Borussiae directore vicennali et socio acad. Petrop.
Parisin, et Londin. Petropoli impensis academiae imperialis scientiarum 1768.
Summary:
This is the first volume (of three) of the Calculus Integralis.
Volumes two and three have the Eneström numbers E366
and E385, respectivley.
According to the records, the
work was presented to the St. Petersburg Academy on August 7, 1766.
Publication:
-
Originally published in as a book, in 1768
-
Opera Omnia: Series 1, Volume 11
The other two parts of the Institutiones are:
Documents Available:
- The book is presented here by chapters:
- Introduction:
"Praenotanda de calculo integrali in genere"
First Section, De integratione formularum differentialum
- Chapter 1, De integratione formularum differentialium rationalium.
- Chapter 2, De integratione formularum
differentialium irratioinalium.
- Chapter 3, De integratione formularum differentialium per series infinitas.
- Chapter 4, De integratione formularum logarithmicarum et exponentialium.
- Chapter 5, De integratione
formularum angulos sinusve angulorum implicantium.
- Chapter 6, De evolutione integralium per series
secundum sinus cosinusve angulorum multiplorum progredientes.
- Chapter 7, Methodus genaralis
integralis integralia quaecunque proxime inveniendi.
- Chapter 8, De valoribus integralium, quos certis
tantum casibus recipiunt.
- Chapter 9, De evolutione integralium per producta infinita.
Second Section, De integratione aequationum differentialum
- Chapter 1, De separatione
variabilium.
- Chapter 2, De integratione aequationum differentialium ope multipliclatorium.
- Chapter 3, De
investigatione aequationum differentialium, quae per multiplicatores datae formae integrabiles
reddantur.
- Chapter 4, De integratione particulari aequationum differentialium.
- Chapter 5, De comparatione
quantitatum transcendentium in forma (X) contentarum.
- Chapter 6, De comparatione
quantitatum transcendentium in forma (Y) contentarum.
- Chapter 7, De
integratione aequationum differentialium per approximationem.
- Third Section (not divided into chapeters)
Third Section, De
resolutione aequationum differentialium,
in quibus differentialia ad plures dimensiones assurgunt
vel adeo transcendentes implicantur.
- Ian Bruce has translated this work into English; the translation is available here.
- E342 is discussed in Ed Sandifer's How Euler Did It November and December
2004 columns published online by the MAA.
- 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 E342 include:
- Grabiner JV., “Is mathematical truth time-dependent.” American Mathematical Monthly, 81 (4), pp. 354-365 (1974).
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