Isaac Newton (1642–1727)

*De motu corporum in gyrum*

Cambridge, ca 1684

This folio, illustrating a body in orbit, is taken from a large collection of papers written after Edmond Halley’s 1684 visit to Newton in Cambridge. Earlier on in this collection Newton had coined the term centripetal force to describe a force acting towards the centre of an attracting body. This was as he wrote his preliminary version of *De motu corporum*< and it remained as his Definitio V at the very beginning of the *Principia mathematica* where the centripetal is identified with the force of gravity holding a moving body in its orbit.

The collection of papers in which this folio is included has been digitised, and can be viewed by clicking ‘Open Digital Library’ below.

MS Add.3965, f. 55r

In a pivotal and celebrated moment in the history of western science Edmond Halley travelled to Cambridge to visit Isaac Newton in the summer of 1684 with a very specific purpose in mind. At a meeting of the Royal Society early that year some of England’s greatest natural philosophers, Robert Hooke, Christopher Wren and Halley himself had discussed whether or not the law of gravitational attraction holding the Solar System together would depend on the inverse of the square of the radius of a planet’s orbit. That this was how gravitational attraction fell away with distance would explain Kepler’s laws that the planets moved in ellipses and that the square of the time it takes a planet to orbit the Sun is proportional to the cube of the radius of the orbit but the gentlemen had no proof.

Halley visited Newton to discuss this problem but was told during their meeting that Newton had already achieved a mathematical proof. Not locating the paper, Newton promised to re-work the proof and send it on and in due course. However Halley’s visit and the discussion of the inverse square law proof stimulated Newton into a period of philosophical creativity comparable to the annus mirabilis twenty years before. In November 1684 Halley did indeed receive from Newton a nine-page manuscript *De motu corporum in gyrum*, the motion of a body in orbit, and it was circulated amongst the great of the Royal Society in London but this composition was simply the beginning of a much greater venture a work into which Newton distilled all his thought on corporeal motion and the laws governing the known universe.

Some of his work he used to give lectures as Lucasian Professor, to the mystification of his audience. Contemporary accounts testify to the intensity of Newton’s concentration on all the problems and proofs that arose; after two-and-a-half years’ of reflection and composition this resulted in the publication in 1687 of the Philosophiae naturalis principia mathematica, a publication that owed much to the championship and dedication of Halley himself who underwrote the costs involved – the Royal Society had experienced a failure with its previous publishing venture, Francis Willughby’s *De Historia Piscium*, and consequently had no money to fund the printing of Newton’s next work.

In common with his colleagues of the Royal Society, Halley may not have understood all the manuscript Newton was sending him for the press but he did understand how important it was to publish it for the world. This first edition of the *Principia mathematica* owned by its author bears some testimony to Halley’s frantic work to get it published but also how much on further reflection Newton decided he should amplify what he had to say. This early page in the work shows not simply that Newton inserted words into the printed text for the second edition but also drafted whole sheets of extra material as with his Definition V. After noting that gravity pulls the planets from a straight path into an orbit he marks a dagger † – opposite is his manuscript text for this insertion, a further 600 words perhaps, carried into the second and third editions, Lapis in funda circumactus… where he draws the analogy between a stone in sling, how a body would fall under gravity and as we would say today ‘go into orbit’ around the Earth. And this, it must be remembered, is at the very beginning of his analysis.