I'm interested in learning more about the mathematical history of birational geometry. I'm writing my thesis about certain obstructions to various types of rationality (ie. intermediate jacobians, brauer groups), however I'd like to learn more about the history of the subject (I mean pre 20th century). I think it would be interesting to learn about how mathematicians used to think about these questions, for example the existence of 'parametric equations' defining solutions to polynomials. I'm interested in what sort of problems pre 20th century mathematicians were interested in, and what methods they had at their disposal to try and solve them.
Thanks.