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)

This paper investigates the emergence, in the second part of the 17th century, of a new body of experimental knowledge dealing with the chemical transformations of water taking place in plants. We call this body of experimental knowledge a “chemical history of vegetation.” We show that this chemical natural history originated, in terms of recipes and methods of investigation, in the works of Francis Bacon and that it was constructed in accordance with Bacon's precepts for putting together natural and experimental (...) histories. Our paper covers a wide array of experimental investigations, carried out by people with different backgrounds, theoretical assumptions, and metaphysical allegiances (Thomas Browne, Robert Sharrock, Robert Boyle, Nehemiah Grew, John Beale, and John Evelyn). We claim that, despite their differences, these naturalists had a lot in common. First, they treated plants as laboratories of chemical investigation. Second, they used the experiments with plants to develop tools, hypotheses, and operational concepts, which travelled from one naturalist to the other, even when their respective explanatory vocabularies were widely different. Third, we show that some of them also manifested an interest in defining and clarifying the limits and structure of this new body of experimental knowledge, displaying, thus, a certain disciplinary unity. (shrink)

Mathematical practitioners in seventeenth-century London formed a cohesive knowledge community that intersected closely with instrument-makers, printers and booksellers. Many wrote books for an increasingly numerate metropolitan market on topics covering a wide range of mathematical disciplines, ranging from algebra to arithmetic, from merchants’ accounts to the art of surveying. They were also teachers of mathematics like John Kersey or Euclid Speidell who would use their own rooms or the premises of instrument-makers for instruction. There was a high degree of interdependency (...) even beyond their immediate milieu. Authors would cite not only each other, but also practitioners of other professions, especially those artisans with whom they collaborated closely. Practical mathematical books effectively served as an advertising medium for the increasingly self-conscious members of a new emerging professional class. Contemporaries would talk explicitly of ‘the London mathematicians’ in distinction to their academic counterparts at Oxford or Cambridge. The article takes a closer look at this metropolitan knowledge culture during the second half of the century, considering its locations, its meeting places and the mathematical clubs which helped forge the identity of its practitioners. It discusses their backgrounds, teaching practices and relations to the London book trade, which supplied inexpensive practical mathematical books to a seemingly insatiable public. (shrink)