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Isaac Barrow was one of the professors who taught Isaac Newton at Cambridge. According to this page, he is said to have made contributions to the Fundamental Theorem of Calculus that was devised by Newton.

What specific contributions did Barrow make to this theorem? What formulae, conjectures, or hypotheses did Barrow develop that assisted in the formulation of the theorem?

If there are any articles or citations that document Barrow's contributions, please post an answer with the appropriate links below. Thank you in advance!

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    $\begingroup$ I am afraid you got a wrong idea. Newton did not "devise" FTC, he developed calculus concepts in which it is now formulated, and Barrow did not contribute "formulae, conjectures, or hypotheses" to it, he had a geometric theorem, which if translated into calculus language, becomes FTC. You can see it in Barrow's Fundamental Theorem by Wagner. $\endgroup$ – Conifold Jul 25 at 2:34
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Isaac Barrow had given a series of lectures in 1664-65. These lectures dealt with the general concepts of space, time and motion.

With Newton assisting in their preparation, these lectures were compiled and published in 1670 as Lectiones Geometricae. It is in the Lecture X, Proposition 11 of Lectiones Geometricae, that a geometrical theorem is mentioned, which in modern-day terminology is called the Fundamental Theorem of Calculus.

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