Barrow and Leibniz on the fundamental theorem of the calculus

TL;DR

This paper examines the historical development of the fundamental theorem of calculus, revealing that Leibniz's proof closely resembles Barrow's earlier work, challenging claims of independence.

Contribution

It uncovers the similarities between Leibniz's geometrical proof and Barrow's 1670 proof, highlighting historical connections in calculus development.

Findings

Leibniz's proof closely resembles Barrow's 1670 proof

Leibniz's dispute with Newton involved claims of originality

Historical analysis links Leibniz's work to Barrow's earlier contributions

Abstract

In 1693, Gottfried Whilhelm Leibniz published in the Acta Eruditorum a geometrical proof of the fundamental theorem of the calculus. During his notorious dispute with Isaac Newton on the development of the calculus, Leibniz denied any indebtedness to the work of Isaac Barrow. But it is shown here, that his geometrical proof of this theorem closely resembles Barrow's proof in Proposition 11, Lecture 10, of his Lectiones Geometricae, published in 1670.