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Historia Mathemati ca 35 (2008) 285–301 www.elsevier.com/locate/yhmat Symbolic language in early modern mathematics: The  Algebra of Pierre Hérigone (1580–1643) M a Rosa Massa Esteve  Departament de Matemàtica Aplicada I, Centre de Recerca per a la Història de la Tècnic a, Universitat P olitècnica de Cat alunya, Spain Abstract The creation of a formal mathematical language was fundamental to making mathematics algebraic. A landmark in this process was the publication of  In artem analyticem isagoge by François Viète (1540–1603) in 1591. This work was diffused through many other algebra texts, as in the section entitled  Algebra in the  Cursus mathematicus (Paris, 1634, 1637, 1642; second edition 1644) by Pierre Hérigone (1580–1643). The aim of this paper is to analyze several features of Hérigone’s  Algebra. Hérigone was one of the first mathematicians to consider that symbolic language might be used as a universal language for dealing with pure and mixed mathematics. We show that, although Hérigone generally used Viète’s statements, his notation, presentation style, and procedures in his algebraic proofs were quite different from Viète’s. In addition, we emphasize how Hérigone handled algebraic operations and geometrical procedures by making use of propositions from Euclid’s  Elements formulated in symbolic language. © 2008 Elsevier Inc. All rights reserved. Resum La creació del llenguatge formal matemàtic va ser foname ntal pel procés d’algeb ritza ció de les matemàtiq ues. Un dels punts crucials va ser la publicació el 1591 de l’obra In Artem Analyticem Isagoge de François Viète (1540–1603). Aquest text va ser difós a través de molts altres textos com ara l’Algebra del Cursus Mathematicus (Paris, 1634, 1637, 1642; segona edició 1644) de Pierre Hérigone (1580–1643). L’objectiu d’aquest article és analitzar alguns trets característics de l’Algebra d’Hérigone. Hérigone va ser un dels primers matemàtics que va considerar que el llenguatge simbòlic podia ser emprat com un llenguatge universal per tractar la matemàtica pura i la matemàtica mixta. Mostrem que, encara que Hérigone generalment utilitza els mateixos enunciats que Viète, no va fer servir ni la seva notació, ni la mateixa presentació, ni els mateixos procediments en les demostracions algebraiques. A més volem emfasitzar com emprava els Elements d’Euclides per introduir el llenguatge algebraic en els procediments geomètrics. © 2008 Elsevier Inc. All rights reserved.  MSC: 01A45; 15-03; 15A06 Keywords: François Viète; Pierre Hérigone; Algebra;  Cursus mathematicus; Symbolic language; Seventeent h century 0. Intr oducti on The process of making mathematics algebraic rather than geometric took place from the beginning of the 17th century to the beginning of the 18th century. 1 It was mainly the result of the introduction by Viète, Fermat, and Descartes of algebraic procedures for solving geometrical problems. In this process of algebraicization, the creation  E-mail address: m.rosa.massa@upc .edu. 1 There are many useful studies on this subject, including  Bos [1998, 291–317], Mahoney [1980, 141–156], Mancosu [1996, 84–86], and Pycior [1997, 135–166] . 0315-0860/$ – see front matter  © 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.hm.2008.05.003

Historia Mathematica Volume 35 issue 4 2008 [doi 10.1016%2Fj.hm.2008.05.003] Ma Rosa Massa Esteve -- Symbolic language in early modern mathematics- The Algebra of Pierre Hérigone

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