Abstract
It is reasonable to assume that a subject of presumably universal appeal must rely on just one style. In spite of its universality, mathematics employs many styles. In particular, there are many styles of proof. In this paper we present and analyse a number of proofs of a property of the area under an hyperbola due to Gregory of Saint-Vincent, a mathematician of the first half of the seventeenth century. There is a baroque and prolific quality to the architecture of his proofs, and this quality points to a connection between a culture and the discovery of a mathematical theory. An historical perspective shows that, in addition to many styles, the universality of mathematics implies a variety of procedures.
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This work was carried out during a period as guest professor at the Institut de physique théorique, Université de Louvain.
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Dhombres, J. Is one proof enough? Travels with a mathematician of the baroque period. Educ Stud Math 24, 401–419 (1993). https://doi.org/10.1007/BF01273373
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DOI: https://doi.org/10.1007/BF01273373