Leibniz as Reader and Second Inventor: The Cases of Barrow and Mengoli

Abstract

Early in his mathematical career (1672–1676) Leibniz discovered some important methods and results but had to recognize that his findings had been anticipated by other mathematicians such as Pierre de Fermat, James Gregory, Isaac Newton, François Regnauld, John Wallis, etc. This paper investigates the cases of Isaac Barrow (Part I) and Pietro Mengoli (Part II) who, earlier than Leibniz, had been familiar with the characteristic triangle, transmutations methods, the inverse connection between determining tangents and areas of curves or the sums of the reciprocal figurate numbers, and the harmonic triangle. To what extent was Leibniz aware of the results and publications of his predecessors? How did he assess their methods and results? Why did Leibniz never acknowledge any influence of these two mathematicians on his own studies? After publication of Leibniz’s manuscripts concerning the prehistory and early history of the calculus in the Academy Edition (A VII 3–6) these questions can be investigated on the solid foundation of original texts.