E102 -- Introductio in analysin infinitorum, volume 2

(Introduction to the Analysis of the Infinite, volume 2)

Summary:

This is the second volume of Euler's textbook in mathematical analysis. The first volume, which contains a brief summary of what Euler did in the Introductio in analysin infinitorum, is E101. This volume contains 22 chapters:

De lineis curvis in genere.
De coordinatarum permutatione.
De linearum curvarum algebraicarum in ordines divisione.
De linearum cujusque ordinis praecipuis proprietatibus.
De lineis secundi ordinis.
De linearum secundi ordinis subdivisione in genera.
De ramorum in infinitum excurrentium investigatione.
De lineis asymptotis.
De linearum tertii ordinis subdivisione in species.
De praecipuis linearum tertii ordinis proprietatibus.
De lineis quarti ordinis.
De investigatione figurae linearum curvarum.
De affectionibus linearum curvarum.
De curvatura linearum curvarum.
De curvis una pluribusve diametris praeditis.
De inventione curvarum ex datis applicatarum proprietatibus.
De inventione curvarum ex aliis proprietatibus.
De similitudine et affinitate linearum curvarum.
De intersectione curvarum.
De constructione aequationum.
De lineis curvis transcendentibus.
Solutio nonnullorum problematum ad circulum pertinentium.

Pages 321-398 contain an "Appendix de superficiebus" that consists of the following 6 chapters:

De superficiebus corporum in genere.
De sectionibus superficierum a planis quibuscunque factis.
De sectionibus cylindri, coni et globi.
De immutatione coordinatum.
De superficiebus secundi ordinis.
De superficierum intersectione mutua.

Publication:

Originally published as a book in 1748.
Opera Omnia: Series 1, Volume 9.

Documents Available:

Original Publication: E102 (Latin), available via the Bibliothèque Nationale de France's Gallica digital library.
French Translation: E102 (French), available via the Bibliothèque Nationale de France's Gallica digital library.
The Euler Archive attempts to monitor recent scholarship for articles and books that may be of interest to Euler scholars. Selected references we have found that discuss or cite E102 include:
- Chang CH, Ha CW., “Eulerian polynomials and related explicit formulas.” Fibonacci Quarterly, 40 (5), pp. 399-404 (Nov 2002).
- Daston LJ., “The physicalist tradition in early 19th-century French Geometry.” Studies in History and Philosophy of Science, 17 (3), pp. 269-295 (Sep 1986).
- Knoebel RA., “Exponentials reiterated.” American Mathematical Monthly, 88 (4), pp. 235-252 (1981).
- Maor E., e: The Story of a Number. Princeton Science Library, 2015.
- Volk O., “Miscellanea from history of celestial mechanics.” Celestial Mechanics, 14 (3), pp. 365-382 (1976).
- Wimmer HK., “On the history of the Bezoutian and the resultant matrix.” Linear Algebra and its Applications, 128, pp. 27-34 (Jan 1990).
- Gudkov DA., “Plane real projective quartic curves.” Lecture Notes in Mathematics, 1346, pp. 341-347 (1988).

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