TITLE: Before Abel's proof, what did they used for trying to find the general solution for quintics?
QUESTION [14 upvotes]: Whenever I read about the history of algebra, I end up with the same conclusion: They solved the general cubic, then the general quartic and then spent lots of years trying to solve the general quintic, which later was proved impossible by Abel and Galois (I guess Ruffini also made contributions to the topic).
There's a gap in time, from the first atempts at finding the general solution of the quintic to Abel's proof - what have people tried before Abel's proof? I am curious about what kind of techniques they tried to use for finding the general quintic.

REPLY [7 votes]: You may enjoy reading these books:

Abel's Proof by Peter Pesic.
Galois Theory for Beginners: A Historical Perspective by Jörg Bewersdorff (MAA review)