Methods of integration by arcs of conic sections in echelons of modules. Legendre as reader of Landen
type: Item
instance of: scholarly article
title: Methods of integration by arcs of conic sections in echelons of modules. Legendre as reader of Landen
zbMATH Open document ID: 1223.01011
author: Ivahn Smadja
published in: Archive for History of Exact Sciences
publication date: 2011-07-01T00:00:00Z
review text: In 1786, \textit{A.-M. Legendre} published two papers on integration by arcs of ellipse [``Memoire sur les int'egrations par arcs d'ellipse'', Histoire de l'Académie Royale des Sciences, 616--643 (1786); Second memoire sur les intégrations par arcs d'ellipse, et sur la comparaison de ces arcs. Histoire de l'Acad'emie Royale des Sciences, 644--683 (1786)]. In the intervening period he became acquainted with \textit{J. Landen}'s article [``An investigation of a general theorem for finding the length of any conic hyperbola, by means of two elliptic arcs'' (1775)]. The present author analyzes in detail how Landen's results influenced on Legendre's constructions.
Mathematics Subject Classification ID: 01A50
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 28-03
zbMATH DE Number: 5916732
zbMATH Keywords: integration by arcs of conic sections
zbMATH Keywords: Legendre
zbMATH Keywords: Landen
zbMATH Keywords: history of mathematics
reviewed by: V. N. Saliĭ
MaRDI profile type: Publication
full work available at URL: s00407-010-0077-7
OpenAlex ID: W1980447407
cites work: Gauss, Landen, Ramanujan, the Arithmetic-Geometric Mean, Ellipses, π, and the Ladies Diary
cites work: The arithmetic-geometric mean of Gauss
cites work: Q4333401
cites work: A commentary on Gauss's mathematical diary, 1796--1814, with an English translation
cites work: Q3998994
cites work: John Landen, F.R.S. (1719-1790)--Mathematician
cites work: Q4401917
cites work: Le départ de Lagrange de Berlin et son installation à Paris en 1787
cites work: Inventaire chronologique de l'œuvre de Lagrange
cites work: Q3312297
DOI: 10.1007/S00407-010-0077-7
description: scientific article; zbMATH DE number 5916732