Eléments d'algébre

“Dig Where You Stand” 7. Proceedings of the Seventh International Conference on the History of Mathematics Education. September 19-23, 2022, Mainz, Germany

“…Bourdon later gives an interpretation of negative numbers as numbers less than zero, explaining that this is the interpretation used by algebraists (1817/1828, p. 95). Bourdon demonstrates this idea by way of a pattern: 1817/1828Ross 1831, p. 78). He concludes that -1 can be regarded as a number less than 0 and that -1 is greater than -2.…”

“…Because of this view of negative numbers, Bourdon avoids them altogether in the beginning of the book and assumes without stating, in fact, that unknown quantities are positive. 5 Negative numbers are introduced formally much later in the book, in the context of solving equations and interpreting a result that happens to be negative (Bourdon 1817(Bourdon /1828. Bourdon says that negative results often arising in algebra present "des circonstances singulières qui embarrassent au primier abord" [circumstances that are embarrassing at first sight] but can be explained (1817/1828, p. 86).…”

“…5 See p. 5 where he states that x + b must be larger than x. Even in his treatment of series near the end of the book, Bourdon assumes without stating so that the common ratio must be positive(Bourdon, 1817(Bourdon, /1828.6 For a discussion of Bourdon's conflicted ideas about negative numbers and how his work fits into the broader history of the development of the concept of number, seeSchubring, 2005, pp. 568-569.…”