Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics

TitleFrom the second unknown to the symbolic equation
Publication TypeBook Chapter (with title)
Year of Publication2010
AuthorsHeeffer, A
Secondary AuthorsHeeffer, A, Van Dyck, M
Book TitlePhilosophical Aspects of Symbolic Reasoning in Early Modern Mathematics
PublisherCollege Publications
ISBN Number978-1-84890-017-2

The symbolic equation slowly emerged during the course of the sixteenth century as a new mathematical concept as well as a mathematical object on which new operations were made possible. Where historians have of- ten pointed at Francois Viète as the father of symbolic algebra, we would like to emphasize the foundations on which Viète could base his logistica speciosa. The period between Cardano’s Practica Arithmeticae of 1539 and Gosselin’s De arte magna of 1577 has been crucial in providing the necessary build- ing blocks for the transformation of algebra from rules for problem solving to the study of equations. In this paper we argue that the so-called “second unknown” or the Regula quantitates steered the development of an adequate symbolism to deal with multiple unknowns and aggregates of equations. Dur- ing this process the very concept of a symbolic equation emerged separate from previous notions of what we call “co-equal polynomials”.

Citation Key1043033
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