Writing of Principia Mathematica

Isaac Newton composed Principia Mathematica during 1685 and 1686, and it was published in a first edition on 5 July 1687. Widely regarded as one of the most important works in both the science of physics and in applied mathematics during the Scientific Revolution, the work underlies much of the technological and scientific advances from the Industrial Revolution (usually dated from 1750) which it helped to create.

Between 1685 and 1686, Newton had a very extensive correspondence with John Flamsteed, who was then the astronomer-royal.

Many of the letters are lost, but it is clear that Flamsteed was helpful, especially regarding Kepler's definition of Saturn. The publication of Newton's discoveries led to controversies involving English natural philosopher Robert Hooke, Anthony Lucas, mathematical professor at Liege; Francis Line, a physician in Liége, and many others. English astronomer and mathematician Edmond Halley attempted to mediate and get Newton to agree that Hooke deserved some credit for the invention of "the rule for the decrease of gravity being reciprocally as the squares of the distances from the centre". Halley acknowledged that although Hooke should be credited for the theory, "the demonstration of the curves generated thereby belonged wholly to Newton". In a letter, Newton responded to Halley as follows:

"Sir, In order to let you know the case between Mr Hooke and me, I give you an account of what passed between us in our letters, so far as I could remember; for 'tis long since they were writ, and I do not know that I have seen them since. I am almost confident by circumstances, that Sir Chr. Wren knew the duplicate proportion when I gave him a visit; and then Mr Hooke (by his book Cometa written afterwards) will prove the last of us three that knew it. I intended in this letter to let you understand the case fully; but it being a frivolous business, I shall content myself to give you, the heads of it in short, viz, that I never extended the duplicate proportion lower than to the superficies of the earth, and before a certain demonstration I found the last year, have suspected it did not reach accurately enough down so low; and therefore in the doctrine of projectiles never used it nor considered the motions of the heavens; and consequently Mr Hooke could not from my letters, which were about projectiles and the regions descending hence to the centre, conclude me ignorant of the theory of the heavens. That what he told me of the duplicate proportion was erroneous, namely, that it reached down from hence to the centre of the earth.

...
Wikipedia