Interesting links: 1600s Mathematics Edition
Descartes’s “The Geometry,” the book which invented algebra as we know it today. Before this, people literally did multiplication geometrically with a compass and straightedge.
How does one visualize a function with a discontinuous second derivative?
Selected correspondences of Descartes Descartes was absolutely savage.
How did Descartes know what sort of curve an equation traces?
That last one answered the question I had originally set out to investigate. I wanted to know how Descartes defined the folium of Descartes at the time, since math was communicated very differently back then.
It’s an interesting way of going about things. It seems like BC=x, CD=y, so I guess D is the origin? I still want to dig in further and figure out exactly what he was doing with this construction.
You can find the complete letter which defines the folium in this book. The full definition starts at the very bottom of page 129.
Credit also to this paper which tipped me off to the particular letter before I found the StackExchange post that identified the definition.