Knobloch, Eberhard (Author)
Archives Internationales d'Histoire des Sciences
Volume: 72
Issue: 189
Pages: 152-170
In 1672 Leibniz made the acquaintance of Christiaan Huygens in Paris. There he found his arithmetical quadrature of the circle, that is, the infinite, alternating, convergent series for π4 in 1673. In October 1674 he sent a short treatise about this subject to Huygens who reacted very positively. In 1676 Leibniz elaborated a long treatise De quadratura arithmetica circuli, ellipseos et hyperbolae and hoped to become a member of the French Académie des Sciences especially by means of this treatise. Leibniz corresponded with Huygens about this plan who encouraged him in this respect. Yet, the treatise was never published during Leibniz’s lifetime. Only in 1993, the first complete edition of the Latin text appeared in Göttingen. This article will consist of three parts. The first part mainly deals with the correspondence between Leibniz and Huygens regarding this treatise. It did not end with Leibniz’s departure from Paris in 1676 but continued up to 1690 when Huygens asked him again to publish this work. The second part explains the fundamental theorem 6. It is the core of Leibniz’s integration theory using well defined notions of infinitely small and infinite, establishing Riemann’s integral for continuous functions, and giving an absolutely rigorous demonstration. The last part explains Leibniz’s crucial distinction between infinite and unbounded.
...MoreArticle Thomas Widemann; Eberhard Knobloch (2022) Introduction. Archives Internationales d'Histoire des Sciences (pp. 6-23).
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