From Cardano's great art to Lagrange's reflections. Filling a gap in the history of algebra
type: Item
instance of: scholarly article
title: From Cardano's great art to Lagrange's reflections. Filling a gap in the history of algebra
zbMATH Open document ID: 1231.01006
DOI: 10.4171/092
published in: Heritage of European Mathematics
publication date: 2011-03-31T00:00:00Z
review text: Jacqueline Stedall opens her book with Lagrange's observation from 1771 that since Cardano there had been little progress in solving equations. Her objective is to investigate to which extent this was true and to which extent it was wrong. The pivots of the argument are four figures who, each in his own moment of history, rounded off and completed what had been done until then and at the same time opened the field for new development: Cardano himself, Viète, Newton, and Lagrange. Between these, the contributions of a large numbers of other contributors to the understanding of algebra and equation theory are discussed, some major (including Harriot, Descartes, Leibniz, Euler and Bézout) and many minor but still significant in one way or the other. Stedall challenges (p. ix) ``the view that mathematics somehow progresses only by means of `great and significant works' and `substantial changes' '' -- a view that she takes to explain that not only general histories of mathematics but also works explicitly dealing with the history of algebra tend to jump directly from Descartes to Lagrange. Part I of the book (chapters 1-3), ``From Cardano to Newton: 1545-1707'' is organized chronologically, and follows the emergence of various ideas and insights, first from Cardano's Ars magna over Bombelli, Stevin, Viète, Harriot and Girard until Descartes' Geometrie, and next (as the latter work had become the standard reference) in the works of Jan Hudde, Delaurens, John Collins, Gregory, Tschirnhaus, Leibniz (and several others), with culmination in Newton's Arithmetica universalis. Among these insights and ideas may be mentioned the various ways to solve cubics and quartics; the (merely partial) replacement of paradigmatic examples by literal general equations; results concerning the number and nature of roots as dependent on coefficients; Viète's introduction of proportion theory as a tool for understanding and formulating algebraic problems (which the reviewer but not always the a…
reviewed by: Jens Høyrup
Mathematics Subject Classification ID: 01A50
Mathematics Subject Classification ID: 01A40
Mathematics Subject Classification ID: 01A45
Mathematics Subject Classification ID: 12-03
Mathematics Subject Classification ID: 12E12
zbMATH DE Number: 5872771
zbMATH Keywords: Cardano
zbMATH Keywords: Viète
zbMATH Keywords: Harriot
zbMATH Keywords: Descartes
zbMATH Keywords: Gregory
zbMATH Keywords: Tschirnhaus
zbMATH Keywords: Leibniz
zbMATH Keywords: Newton
zbMATH Keywords: Maclaurin
zbMATH Keywords: Euler
zbMATH Keywords: Bézout
zbMATH Keywords: Lagrange
zbMATH Keywords: Ruffini
zbMATH Keywords: Cauchy
zbMATH Keywords: equation theory
author: Jacqueline Stedall
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/092
OpenAlex ID: W4301874626
description: scientific article; zbMATH DE number 5872771