1.4 Napier and motion
So where did the idea of motion which is found in Napier's work come from? It was again a concept used by Archimedes, in his study of spirals, so there was a classical precedent for propositions about points moving along lines (see, for example, Proposition 1 of On spirals, linked below). Further, although much of the Western mathematical tradition had been rather nervous of the concept of motion hitherto, there had been exceptions to this three centuries or so earlier: both the Merton School in fourteenth-century Oxford and Nicole Oresme at the University of Paris had made prolonged study of issues involving this concept. The details of Napier's education are obscure – we know he spent a year at the University of St Andrews in his early teens, but not what he did or learned thereafter – but it is not implausible that he became aware of mediaeval studies of motion at some stage.
Click the link below to open Proposition 1 of On spirals.