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John Napier

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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, in Reading 2 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.

Reading 2: Proposition 1 of On Spirals

(b) Proposition 1

If a point move at a uniform rate along any line, and two lengths be taken on it, they will be proportional to the times of describing them.

Two unequal lengths are taken on a straight line, an two lengths on another straight line representing the times; and they are proved to be proportional by taking equimultiples of each length and the corresponding time after the manner of Euclid’s Elements, V, Def.5.