In this Unpublished manuscript, Newton integrates the hyperbola and the circle between arbitrary points on the x axis, by considering a wider class of curves whose curves are easy. This is a good example of the Inventor’s Paradox, where the more general problem is easier to solve than a specific case of it.
Click here to download my full commentary, done as part of a requirement for Seminar History of Mathematics with Viktor Blåsjö at the University of Utrecht.
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