How Newton Squared the Circle

I recently came across a good example of the Inventor’s Paradox, where the more general problem is easier to solve than a specific case. In the mid-seventeenth century, Isaac Newton published his integration of a circle segment – but rather than attempting to integrate $\sqrt{1-x^2}$ directly, he found a pattern in the more general integrals of the form $(1-x^2)^n$, and then plugged in $n=1/2$.

My full commentary on the related manuscripts is available here (done as part of Viktor Blasjo’s History of Mathematics Seminar)