Slope of Tangent to Cycloid/Historical Note

Historical Note on Slope of Tangent to Cycloid
Some sources suggest that the first to solve the problem of constructing a tangent to the cycloid was, along with his pupil at the time.

Other sources cite the geometric proof of, which dates to $1638$, although yet other sources suggest it was in the same year.

It has been documented that solved the problem immediately once it had been proposed to him.