John Dee’s mathematical interests have principally been studied through his Mathematicall praeface to Henry Billingsley’s 1570 translation of Euclid’s Elements. The focus here is broadened to include the notes he added to Books X–XIII of the Elements. I argue that this additional material drew on a manuscript text, the Tyrocinium mathematicum, that Dee wrote a decade earlier, probably as tutor to the youthful Thomas Digges. Using new evidence for this now-lost work, as well as his notes on Euclid, makes it (...) possible to clarify Dee’s approach to geometry. The contrasting positions adopted by his Parisian acquaintance Petrus Ramus also illuminate Dee’s geometrical choices and values. Unlike Ramus, Dee was not a pugnacious advocate of radical reform, yet he did look beyond the limits of Euclid’s geometry towards deeper disciplinary visions of knowledge. The first published work of his pupil Thomas Digges not only suggests how Dee shaped the younger man’s work but also reflects fresh light back on Dee’s own programme for a ‘more general art Mathematical.’. (shrink)