Archimedes for the rest of us: Thinking commentary with Guidobaldo dal Monte

ABSTRACT For Archimedes’ work to have furnished the ‘key theoretical tools’ for the scientific revolution, the texts must have been comprehensible to early modern readers. Yet as Archimedes’ readers and commentators have observed for centuries, his work can be very difficult going indeed. In this chapter, I explore how commentaries and other explanatory texts, like Guidobaldo dal Monte’s 1588 ‘paraphrase’ commentary to Archimedes’ Planes in Equilibrium, can help unfurl the difficulties of Archimedes’ sparse proofs by means of additional explanations and examples that help the reader develop their own ability to follow Archimedes’ reasoning. I give particular attention to insights from contemporary cognitive science into how strategic repetition of information, the materiality of the text, and highlighting connections between mathematics and the material world can all aid in the learning process.