Adequality

Adequality is a technique developed by Pierre de Fermat in his treatise Methodus ad disquirendam maximam et minimam[1] (a Latin treatise circulated in France c. 1636 ) to calculate maxima and minima of functions, tangents to curves, area, center of mass, least action, and other problems in calculus. According to André Weil, Fermat "introduces the technical term adaequalitas, adaequare, etc., which he says he has borrowed from Diophantus. As Diophantus V.11 shows, it means an approximate equality, and this is indeed how Fermat explains the word in one of his later writings." (Weil 1973).[2] Diophantus coined the word παρισότης (parisotēs) to refer to an approximate equality.[3] Claude Gaspard Bachet de Méziriac translated Diophantus's Greek word into Latin as adaequalitas.[citation needed] Paul Tannery's French translation of Fermat’s Latin treatises on maxima and minima used the words adéquation and adégaler.[citation needed]

  1. ^ METHOD FOR THE STUDY OF MAXIMA AND MINIMA, English translation of Fermat's treatise Methodus ad disquirendam maximam et minimam. wikisource
  2. ^ See also Weil, A. (1984), Number Theory: An Approach through History from Hammurapi to Legendre, Boston: Birkhäuser, p. 28, ISBN 978-0-8176-4565-6
  3. ^ Katz, Mikhail G.; Schaps, D.; Shnider, S. (2013), "Almost Equal: The Method of Adequality from Diophantus to Fermat and Beyond", Perspectives on Science, 21 (3): 283–324, arXiv:1210.7750, Bibcode:2012arXiv1210.7750K, doi:10.1162/POSC_a_00101, S2CID 57569974