The Validity of Newton's Lemma 28

AbstractIsaac Newton's Lemma 28 (Principia, Book I) argues that the areas of oval figures are not expressible in finite algebraic equations. Although D. T. Whiteside criticized this lemma, his counterexample is not infinitely smooth and thus would not have been admitted by Newton. Copyright 2001 Academic Press.Le lemme 28 d'Isaac Newton (Principia, livre I) propose que les aires defigures ovales ne sont pas exprimables par des équations algébriques finies. Bien que D. T. Whiteside ait critiqué ce lemme, son contre-exemple n'est pas infiniment dérivable, et Newton ne l'aurait donc pas admis. Copyright 2001 Academic Press.MSC 2000 classification numbers: 01A45, 14M81, 26A27