ABSTRACT
The twentieth-century mathematician André Weil wrote that engaging with the history of mathematics is like trying to reconstruct the ocean floor from the occasional islands that protrude above the surface.2 That is a good description. More often, though, I think it is like trying to fit together a very large jigsaw in which most of the pieces are missing and one is not allowed to look at the picture on the box. One always hopes, of course, that some new and vital piece will turn up, but one knows all too well that it may not. This chapter is about putting together one small part of the jigsaw of Harriot’s mathematics, a self-contained treatise of about 140 pages, which I have called the ‘Treatise on equations’. I will explain how I reassembled it from pages scattered throughout the manuscripts and I will discuss how Harriot came to write it, what is in it and what happened to it afterwards. In doing so, I will venture a little way into some technical mathematics and make no apology for this, for there is no other way to get to the heart of Harriot’s work. But I will do my best to make it as painless as possible.
