Despite recent work on scientific instruments by historians of science, the meeting ground between historians and curators of collections has been disappointingly narrow. This study offers, first, a characterization of sixteenth-century mathematical instruments, drawing on the work of curators, as represented by the online database Epact. An examination of the relationship between these instruments and the natural world suggests that the ‘theoric’, familiar from studies of the history of astronomy, has a wider relevance to the domain of practical mathematics. This (...) outcome from a study of collections is then used in re-examining an established question in the history of science, the position of William Gilbert on the motion of the Earth. (shrink)