# Roger Cotes and Newton

Student notes on one of Roger Cotes's lectures, from: Natural philosophy [manuscript]. [S.l.: s.n., 18th. cent.] [Wheatstone Collection QC19 COT]The first Plumian Professor of Astronomy and Experimental Philosophy at Cambridge, Roger Cotes (1682-1716) is best remembered today as the editor of the second edition of Newton’s *Principia* (1713) and for his preface to that edition, in which he strongly defended Newton’s theory of universal gravitation against its Cartesian critics.

Patient, meticulous, tactful and a talented mathematician, he was well qualified for the job. Cotes was not content merely to proof-read Newton’s copy and to check his mathematics but made suggestions and asked questions which made Newton reconsider and amend *Principia* to a much greater extent than he had originally intended.

Cotes died unexpectedly in June 1716 aged only 33, having only published one mathematical paper during his lifetime. His cousin Robert Smith collected, edited and published his unpublished mathematical work as *Harmonia mensuarum* in 1722. Cotes was highly regarded as a mathematician by his peers and in his short life made important contributions to areas such as the theory of logarithms, numerical methods and integral calculus. In his own copy of *Harmonia mensuarum* Smith wrote ‘Sir Isaac Newton, speaking of Mr. Cotes, said “if he had lived, we might have known something.”’

The item on display is a volume of what appear to be student notes on a course of lectures on hydrostatics and pneumatics first given by Cotes and William Whiston (1667-1752) in 1707. Unusually for the time, Cotes and Whiston used practical demonstrations in their teaching and required students to carry out experiments in advance of lectures. Cotes’s contributions to this lecture series were edited and published by Robert Smith as *Hydrostatical and pneumatical lectures* (1738).

## In this exhibition

- A society of virtuosi
- Boyle and Hooke
- Wilkins and Locke
- Silviculture
- Newton and his champions I
- Newton and his champions II
- Hauksbee and Newton
- Keill's lectures on natural philosophy
- Roger Cotes and Newton
- Smith's Opticks

- The wider world
- Biologists at the Royal Society
- Scrutinizing the skies
- Select bibliography