In this answer to a question of mine on the stackexchange physics site, I learned about the tautochrone problem. Apparently it was solved by Huygens in 1659, which is before Newton's work on mechanics.
- What did he base his assumptions on? Were there phenomenological laws, analogous to Kepler's laws for planetary motion?
- What were his assumptions and how did he solve the problem?
Answers just addressing one of these points are very welcome.