E366 -- Institutionum calculi integralis volumen secundum

(Foundations of Integral Calculus, volume 2)

Originally published with the full title: Institutionum calculi integralis volumen secundum in quo methodus inveniendi functiones unius variabilis ex data ralatione differentialium secundi altiorisve gradus pertractatur. Auctore Leonhardo Euler acad. scient. Borussiae directore vicennali et socio acad. Petrop. Parisin. et Londin. Petropli impensis academiae imperialis scientiarum 1769.

Summary:
This was the second of a comprehensive three-volume book on integral calculus. Parts one and three were given the numbers E342 and E385, respectively, by Eneström.

Publication:

Originally published as a book in 1769.
Opera Omnia: Series 1, Volume 12

Documents Available:

The book is presented here by chapters:
- Front Material and Table of Contents
  
  First Section, De resolutione aequationum differentialium secundi gradus, duas tantum variabiles involventium”
- Chapter 1, De integratione formularum differentialium secundi gradus simplicium.
- Chapter 2, De aequationibus differentio-differentialibus, in quibus altera variabilium ipsa deest.
- Chapter 3, De aequationibus differentio-differentialibus homogeneis, et quae ad eam formam reduci possunt.
- Chapter 4, De aequationibus differentio-differentialibus, in quibus altera variabilis unicam habet dimensionum.
- Chapter 5, De integratione aequationum differentialium secundi gradus, in quibus altera variabilis unam dimensionum non superat, per factores.
- Chapter 6, De integratione aliarum aequationum differentio-differentialium per idoneos multiplicatores instituenda.
- Chapter 7, De resolutione aequationis ddy + axⁿydx² = 0 per series infinitas.
- Chapter 8, De aliarum aequationum differentio-differentialium resolutione per series infinitas.
- Chapter 9, De transformatione aequationum differentio-differentialium hujus formae Nydx² + Mdxdy + Lddy = 0.
- Chapter 10, De constructione aequationum differentiodifferentialium per quadraturas curvarum.
- Chapter 11, De constructione aequationum differentiodifferentialium ex earum resolutione per series infinitas petita.
- Chapter 12, De aequationum differentiodifferentialium integratione per approximationes.
  
  Second Section, De resolutione aequationum differentialium tertii altiorumque graduum, quae duas tantum variabiles involvunt
- Chapter 1, De integratione formularum differentialium tertii altiorisve gradus simplicium.
- Chapter 2, De resolutione aequationum hujus formae: (X) sumto elemento dx constante.
- Chapter 3, De integratione aequationum differentialium hujus formae: (Y)
- Chapter 4, Applicatio methodi integrandi in capite praecedenti traditae ad exempla.
- Chapter 5, De integratione aequationum differentialium hujus formae: (Z)
Ian Bruce has translated this work into English; the translation is available here.
E366 is discussed in Ed Sandifer's How Euler Did It March 2005 column 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 E366 include:
- Dutka J., “On the early history of bessel-functions.” Arhcive for History of Exact Sciences, 49 (2), pp. 105-134 (1995).

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