Nicolas Fatio de Duillier FRS (also spelled Faccio or Facio; 16 February 1664 – 10 May 1753) was a mathematician, natural philosopher, astronomer, inventor, and religious campaigner.

Born in Basel, Switzerland, Fatio mostly grew up in the then-independent Republic of Geneva, of which he was a citizen, before spending much of his adult life in England and Holland.

Fatio is known for his collaboration with Giovanni Domenico Cassini on the correct explanation of the astronomical phenomenon of zodiacal light, for inventing the "push" or "shadow" theory of gravitation, for his close association with both Christiaan Huygens and Isaac Newton,[3] and for his role in the Leibniz–Newton calculus controversy.

His extreme religious views harmed his intellectual reputation, but Fatio continued to pursue technological, scientific, and theological researches until his death at the age of 89.

[4] Jean-Baptiste had inherited a significant fortune, derived from his father in law's interests in iron and silver mining, and in 1672 he moved the family to an estate that he had purchased in Duillier, some twenty kilometres from the town of Geneva.

[4] Jean-Baptiste, a devout Calvinist, wished Nicolas to become a pastor, whereas Cathérine, a Lutheran, wanted him to find a place in the court of a Protestant German prince.

[3] Before he was eighteen, Fatio wrote to the director of the Paris Observatory, the astronomer Giovanni Domenico Cassini, suggesting a new method of determining the distances to the Sun and Moon from the Earth, as well as an explanation of the form of the rings of Saturn.

Fenil confided to Fatio his plan to stage a raid on the beach at Scheveningen to kidnap the Dutch Prince William of Orange.

[5] Fenil showed Fatio a letter from the Marquis de Louvois, the French Secretary of State, approving of the kidnapping, offering the king's pardon as recompense for the successful completion of the operation, and enclosing an order for money.

Encouraged by Huygens, Fatio compiled a list of corrections to the published works on differentiation by Ehrenfried Walther von Tschirnhaus.

Fatio arrived in England in June 1687, carrying with him the conviction that the two greatest living natural philosophers were Robert Boyle, "for the details of his experiments concerning earthly bodies", and Christiaan Huygens "for physics in general, above all in those areas in which it is involved with mathematics.

In the winter of 1687 Fatio went to the University of Oxford, where he collaborated with Edward Bernard, the Savilian Professor of Astronomy, in an investigation into the units of measurement used in the ancient world.

[3] He vied unsuccessfully for the Savilian Professorship of Astronomy at Oxford, a post that had been left vacant by the death of his friend Edward Bernard.

In 1699, Fatio published Lineæ brevissimæ descensus investigatio geometrica duplex, cui addita est investigatio geometrica solidi rotundi in quo minima fiat resistentia ("A two-fold geometrical investigation of the line of briefest descent, to which is added a geometric investigation of the solid of revolution that produces the minimum resistance"), a pamphlet containing his own solutions to the brachistochrone and to another problem, treated by Newton in book II of the Principia (see Newton's minimal resistance problem), in what is now called the "calculus of variations".

In his book, Fatio drew attention to his own original work on the calculus from 1687, while stressing Newton's absolute priority and questioning the claims of Leibniz and his followers.

[15] Back in London, Fatio partnered with the Huguenot brothers Peter and Jacob Debaufre (or "de Beaufré"), who kept a successful watchmaking shop in Church Street, Soho.

Both men were primarily interested in chrysopoeia and the deciphering of recipes for the preparation of the philosopher's stone that circulated privately within circles of alchemical adepts.

[5] In the spring of that same year he moved to Worcester, where he formed some congenial friendships and busied himself with scientific pursuits, alchemy, and study of the cabbala.

[23] At that time, Fatio also sought Conduitt's help in his effort (which was ultimately unsuccessful) to obtain a belated reward for having saved the Prince of Orange from Count Fenil's kidnapping plot.

To optimise the capture of solar energy and thereby increase agricultural yields, Fatio suggested building sloping fruit walls, precisely angled to maximize the collection of heat from sunlight.

Having supervised the building of such walls in Belvoir Castle, in 1699 he published an illustrated treatise that described his invention and included theoretical considerations about solar radiation.

He also contrived a ship's observatory and measured the height of the mountains surrounding Geneva, planning, but never completing, a detailed map of Lac Léman.

Fatio considered that his greatest work was his explanation of Newtonian gravity in terms of collisions between ordinary matter and aetherial corpuscles moving rapidly in all directions.

[32] Fatio's account of his gravitational theory finally published in 1929, in an edition prepared by the German historian of mathematics Karl Bopp,[28] and then again independently in 1949 by Bernard Gagnebin, the conservator of manuscripts at the Geneva Library.

[7][9] Even though the modern scientific consensus is that the Fatio-Le Sage theory is inviable as an account of gravity, the process that he described does give rise to an attractive inverse-square force between particles immersed in a rare medium at a higher temperature.

[34] The Genevan naturalist Jean Senebier, writing thirty years after Fatio's death, declared that This man who was the friend of Newton, of Huygens, of Jacob Bernoulli; who learned from Newton the infinitesimal calculus and who taught it to De Moivre; who, after having been linked to Leibniz and Johann Bernoulli, crossed them by taking sides against Leibniz in his dispute over the invention of the higher calculus.

Manuel and Westfall both suggested that there might have been a sentimental or sexual element to the attachment between both men,[35][36] and that Newton's nervous breakdown in 1693 might have been connected with a rupture in that relationship.

[20] According to Newman, Any attempt to link Newton’s "derangement" to a precipitous break with Fatio around the time of the letters to Pepys and Locke can no longer be countenanced.

He appears as a supporting character in Michael White's novel Equinox (2006), in Neal Stephenson's trilogy The Baroque Cycle (2003–04), and in Gregory Keyes's novel series The Age of Unreason (1998–2001).

Among them is a Latin poem entitled N. Facii Duellerii Auriacus Throno-servatus ("N. Fatio de Duillier's Orange Throne Preserved", Addit.