Isaac Newton & the Principia

1687 CE · Deep-Dive Event Pages · critical-turning-points

The mathematical codification of the physical universe.

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Isaac Newton publishes the "Philosophiæ Naturalis Principia Mathematica", establishing the laws of motion and universal gravitation. It is arguably the most important scientific book ever written.

Key Numbers

Published: July 1687, London
Newton's age: 44
First-edition copies traced: 387 (of ~500-650 printed)
Editions in Newton's lifetime: 3 (1687, 1713, 1726)
Books / volumes: 3

Verified Facts

The full title, Philosophiae Naturalis Principia Mathematica ('Mathematical Principles of Natural Philosophy'), was published in Latin in July 1687, when Newton was 44 and Lucasian Professor of Mathematics at Cambridge.
The book was sparked by a famous August 1684 visit from Edmond Halley, who asked Newton what curve a planet would trace under an inverse-square attraction; Newton immediately answered an ellipse, said he had proved it, but could not find the proof and promised to reconstruct it.
Newton's reconstructed answer became the short tract De motu corporum in gyrum, sent to Halley in November 1684 and registered at the Royal Society; over roughly the next 18 months it grew into the three-book Principia.
Halley not only midwifed the work but personally financed its printing: the Royal Society had exhausted its book budget on the poorly-selling De Historia Piscium (a history of fishes), so Halley, then the Society's clerk, paid for the Principia out of his own pocket and contributed a Latin ode to Newton in the first edition.
The Principia laid out the three laws of motion (inertia, F-proportional-to-acceleration, and equal-and-opposite reaction) and the law of universal gravitation, in which every mass attracts every other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
It is organized in three books: Book I treats motion in a void, Book II treats motion through resisting fluids (pioneering fluid mechanics and demolishing Descartes's vortex theory of planetary motion), and Book III, 'The System of the World,' applies the results to planets, moons, comets, and the tides.
Book III predicted that the Earth is an oblate spheroid (flattened at the poles), explained the ocean tides as the combined gravitational pull of the Moon and Sun, and treated comets as bodies on conic-section orbits governed by the same gravitation as planets.
Newton proved that a spherically symmetric body attracts external objects as though all its mass were concentrated at its center, the result that justified treating the Sun and planets as point masses across the entire solar system.
Publication was nearly derailed by a priority dispute: Robert Hooke claimed he had given Newton the inverse-square idea, and an enraged Newton struck nearly all references to Hooke from the manuscript before Halley smoothed things over to keep the project alive.
The famous methodological slogan 'Hypotheses non fingo' ('I feign no hypotheses') is not in the 1687 first edition; Newton added it in the General Scholium appended to the second edition of 1713, responding to critics who said gravity was an unexplained occult force.
A 2020 census in the journal Annals of Science traced 387 surviving copies of the 1687 first edition, revising older estimates of about 250 copies upward and suggesting an original print run on the order of 500-650; the book was printed by Joseph Streater for bookseller Samuel Smith.
Newton continued revising the work for decades, issuing corrected and expanded second (1713) and third (1726) editions; the first English translation, by Andrew Motte, appeared in 1729, two years after Newton's death.

The World at This Moment

When the Principia issued from Joseph Streater's press in London in July 1687, the wider world was dominated by consolidating gunpowder empires rather than mathematical physics. In the Deccan, Aurangzeb annexed Golconda in 1687, pushing the Mughal Empire to its greatest territorial extent. The Kangxi Emperor's Qing dynasty was stabilizing China; in 1687 French Jesuits reached Beijing and entered the imperial Bureau of Astronomy, carrying European mathematics eastward. The Ottoman Empire reeled after its 1683 failure at Vienna, the 1687 Battle of Mohács, and the deposition of Mehmed IV. In England, the Catholic James II's policies were nearing the crisis that produced the 1688 Glorious Revolution; Newton himself would soon resist royal interference at Cambridge. Across the Channel, Louis XIV's France had revoked the Edict of Nantes (1685), scattering Huguenots. The Principia thus appeared amid imperial expansion and confessional conflict, a Latin treatise printed in a vernacularizing age, intelligible to perhaps a few dozen mathematicians across Europe yet destined to outlast every dynasty contemporary to it.

The Paradigm Shift

The Principia welded terrestrial and celestial mechanics into a single mathematical system. From three laws of motion and the inverse-square law of universal gravitation, Newton deduced Kepler's planetary laws, the tides, the precession of the equinoxes, and the orbits of comets, demonstrating that the same force governing a falling apple binds the Moon to the Earth. This unification dissolved the ancient Aristotelian divide between sublunary and supralunary realms and supplied a working program for "rational mechanics." Methodologically, Newton fused rigorous geometry with physical argument, treating force quantitatively and insisting (in the later General Scholium) that explanation proceed by deduction from phenomena rather than speculative hypotheses. As I. Bernard Cohen argued in The Newtonian Revolution (1980), Newton's "style" of moving between idealized mathematical constructs and physical nature became the template for mathematical physics through Laplace, Lagrange, and beyond. The Principia made prediction and quantitative testing the criterion of natural philosophy, reframing the cosmos as a law-governed mechanism and furnishing the Enlightenment with its emblem of human reason's reach.

In Their Own Words

"Hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses [hypotheses non fingo]; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy." — Isaac Newton, General Scholium, added to the second edition of Philosophiae Naturalis Principia Mathematica (1713), Andrew Motte's 1729 English translation.

If I have seen further it is by standing on the shoulders of Giants.
Isaac Newton, in a letter to Robert Hooke, dated 5 February 1675 (Old Style; 1676 New Style). Newton's own words; widely reproduced in modernized spelling. The autograph manuscript reads with period orthography (e.g. 'ye sholders of Giants'). — source

I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses.
Isaac Newton, General Scholium, appended to the second edition (1713) of Philosophiae Naturalis Principia Mathematica (Latin: 'hypotheses non fingo'). English from the I. Bernard Cohen & Anne Whitman translation, 1999 (often older-rendered 'I frame no hypotheses' in Andrew Motte's 1729 translation). — source

Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago.
John Maynard Keynes, 'Newton, the Man' — a lecture written for the Royal Society's Newton Tercentenary; Keynes died in April 1946, so it was read posthumously by his brother Geoffrey Keynes at the celebration in July 1946. This is a 20th-century scholar's interpretation reflecting on Newton's alchemy and theology, not Newton's own words. — source

In Depth

The Universe Becomes a Single Equation

When Isaac Newton's Philosophiæ Naturalis Principia Mathematica appeared on July 5, 1687 — financed and shepherded into print by the astronomer Edmond Halley — it did something no book had done before. It collapsed the heavens and the earth into one mathematical law. The fall of an apple and the orbit of the Moon were shown to be the same phenomenon, governed by a single inverse-square force acting between every particle of matter in the cosmos. For the first time, the same equations that described a thrown stone described the path of a comet. The split between the sublunar and the celestial — inherited from Aristotle (sv-aristotle) and ratified for nearly two thousand years — simply dissolved.

Deep Preconditions

Newton did not invent from nothing; he famously wrote of seeing further by "standing on the shoulders of giants." Those giants were specific. Johannes Kepler had distilled Tycho Brahe's observations into three empirical laws of planetary motion, which the Principia derived from first principles rather than merely describing. Galileo (sv-galileo), peering through his telescope and rolling balls down inclines, had shown that nature speaks the language of mathematics and that motion obeys quantifiable rules. René Descartes (sv-descartes) supplied both the principle of inertia that became Newton's first law and the analytic geometry Newton would transcend — though the Principia is pointedly anti-Cartesian, adding Mathematica to its borrowed title to signal proof over speculation. Behind all of them stood the deductive scaffolding of Euclid (sv-euclid), whose geometric method Newton wielded as his proof engine, and the deep atomist intuition reaching back to Democritus (sv-democritus) that the world is made of particles obeying law. The Gutenberg press (sv-printing-press) and the institutional ferment of the Renaissance (sv-renaissance) made such cumulative scholarship possible at all.

The Ripple Forward

The Principia did more than solve a physics problem; it furnished a template for what knowledge could be. It promised a clockwork universe legible to reason — an idea that detonated through the Enlightenment. The founders who wrote the Federalist Papers (sv-federalist-papers) and launched the American Revolution (sv-american-revolution) consciously imagined politics as a Newtonian system of balanced forces. The confidence that hidden laws govern visible phenomena drove the Industrial Revolution (sv-industrial-revolution), whose engineers needed exactly the predictive mechanics Newton had codified. The same intellectual nerve emboldened Charles Darwin (sv-charles-darwin) to seek a single law beneath the diversity of life, and it set the agenda for every physicist who followed.

That agenda eventually broke Newton open. Michael Faraday (sv-michael-faraday) and James Clerk Maxwell (sv-james-maxwell) unified electricity, magnetism, and light into fields that Newton's particle-mechanics could not contain. Then Albert Einstein (sv-einstein) overturned the absolute space and time the Principia had assumed, reconceiving gravity not as a force but as the curvature of spacetime. Yet Einstein did not erase Newton; relativity reduces to Newtonian mechanics at ordinary speeds, and engineers still use the Principia's equations to send craft to the Moon, as in Apollo 11 (sv-apollo11).

The Longer Arc

There is a through-line from the Principia to the present moment of machine intelligence. Newton's wager — that reality is compressible into law, that prediction is possible — is the same wager underlying every model that learns patterns from data, from AlexNet (sv-alexnet-convnets) to the Transformer (sv-transformer-paper). When Kurzweil frames biology becoming information technology (sv-kurzweil-genome) or intelligence as substrate-independent computation, he extends Newton's original audacity: that the universe is intelligible, and intelligibility is power. The Principia was the first proof that a finite mind could write down the rules of the world. Every later attempt to build minds that read those rules for us descends from that single, world-shifting book.

Causes & Consequences

What led to it

Johannes Kepler's three laws of planetary motion (published 1609 and 1619) gave Newton precise empirical regularities to explain, including the elliptical orbit and the area law, which the Principia later derived mathematically from an inverse-square central force.
Galileo Galilei's experiments on falling bodies and inclined planes (c. 1602-1638) established that all bodies accelerate at the same rate and articulated a restricted principle of inertia, which became the foundation of Newton's first and second laws of motion.
Robert Hooke, in correspondence with Newton in 1679-1680, proposed analyzing orbital motion by compounding a tangential velocity with a central attraction and suggested the attraction fell off as the inverse square of distance, sharpening the very problem Newton went on to solve.
Newton's own development of his 'method of fluxions' (calculus), worked out during the plague years at Woolsthorpe around 1665-1667, gave him the mathematical machinery of limits and rates of change that underlies the geometric 'first and last ratios' arguments of the Principia.
Edmond Halley's August 1684 visit to Cambridge, where he asked Newton what orbit an inverse-square attraction would produce, directly prompted Newton to compose the tract 'De motu' that grew into the Principia.
Halley then personally edited the manuscript and paid for its printing out of his own pocket after the Royal Society, depleted by funding the 'De Historia Piscium,' could not cover the cost, making publication of the 1687 first edition possible.

What it set in motion

The Principia unified terrestrial and celestial motion under a single law of universal gravitation, founding classical mechanics as the dominant framework of physics for the next two centuries.
Edmond Halley used Newton's gravitational theory to predict that the comet seen in 1531, 1607, and 1682 would return around 1758; its reappearance on Christmas Day 1758 was a dramatic public confirmation of Newtonian physics.
Newtonian celestial mechanics enabled the 1846 discovery of Neptune, which Urbain Le Verrier and John Couch Adams predicted from perturbations in Uranus's orbit before Johann Galle observed it near the calculated position.
Pierre-Simon Laplace recast Newton's geometry into calculus-based analysis in his 'Traite de mecanique celeste' (1799-1825), arguing the solar system was stable without divine intervention and inspiring the deterministic worldview later dubbed 'Laplace's demon.'
The Principia's demonstration that nature obeyed discoverable mathematical laws became a model for the European Enlightenment, encouraging thinkers to apply reason and empirical method across philosophy, politics, and the human sciences.
The mechanistic, law-governed picture of the universe established by Newton supplied the conceptual and quantitative foundations that later underpinned engineering and the broader scientific revolution leading into the Industrial Revolution.

The Live Academic Debate

A durable debate concerns how much Newton owed to Robert Hooke. In their 1679-80 correspondence Hooke suggested an inverse-square attraction and the decomposition of orbital motion into tangential inertia plus central attraction; he later demanded credit. Historians such as Westfall granted Hooke genuine heuristic influence, while emphasizing that Hooke could not supply the mathematical proof, which was Newton's achievement; Newton retaliated by deleting acknowledgments. Recent work (e.g., Nauenberg) reexamines Hooke's graphical methods, partially rehabilitating his contribution. A second debate, pressed by I. B. Cohen and Betty Jo Teeter Dobbs, concerns Newton's intellectual unity: was the rationalist author of the Principia continuous with the alchemist and heterodox theologian revealed in his manuscripts? Dobbs (The Janus Faces of Genius) argued his physics and alchemy were intertwined; others treat them as separable. A third, framed by Steven Shapin and Simon Schaffer's broader program, asks how far the Principia's authority was socially constructed through the Royal Society versus secured by its demonstrative success. These disputes remain unresolved.

Leibniz and the calculus priority dispute

The standard heroic image of Newton is complicated by the bitter Newton–Leibniz calculus controversy. Around 1712 the Royal Society published the Commercium Epistolicum, the report of a committee that ruled Newton the first inventor of the calculus and implied Leibniz had plagiarized it. As historians note, the committee was packed with Newton's allies, Leibniz was never asked for his account, and Newton himself secretly orchestrated and even ghost-wrote much of the report; modern scholarship holds that Gottfried Wilhelm Leibniz developed his calculus independently, with his own superior notation (the d and ∫ symbols still used today).

The Counterfactual

The Principia's appearance was genuinely contingent. Richard Westfall's Never at Rest documents that Newton wrote the work only after Edmond Halley's 1684 visit prompted him to reconstruct his proof that an inverse-square force yields elliptical orbits. The Royal Society, having drained its budget on Francis Willughby's poorly selling De Historia Piscium, could not fund publication; Halley paid from his own pocket and shepherded the proofs. Absent Halley's prompting and patronage, Newton, secretive and embroiled with Hooke's priority claims, might have left the synthesis unpublished, as he nearly did with Book III. Continental mechanics under Huygens and Leibniz would have advanced, but along a more Cartesian, vortex-based path, plausibly delaying universal gravitation by decades. Yet one should resist strong counterfactuals: the inverse-square idea was in the air, debated by Hooke, Wren, and Halley themselves. What was singular was Newton's mathematical demonstration. Without the Principia specifically, the analytic synthesis might have arrived later and in fragments, slowing the eighteenth-century program that produced Clairaut's and Laplace's celestial mechanics.

Myth vs. Reality

Myth: An apple fell on Newton's head and he instantly discovered gravity in a flash of genius.

Reality: No source — including Newton's own accounts via William Stukeley and John Conduitt — says the apple struck his head; that detail is a later embellishment. Newton recalled merely watching an apple fall around 1665-66, which prompted him to wonder whether the same force reached as far as the Moon. Far from an instant revelation, the full theory required years of additional work, and it was only from 1684 to 1687 that he developed it into the Principia. Historians such as Thony Christie note the legend mainly flatters the romantic idea of sudden, isolated genius.

Myth: Newton invented or discovered gravity.

Reality: Gravity as the tendency of objects to fall was obvious long before Newton, and the idea of an inverse-square attraction was already circulating among figures like Bullialdus, Borelli, Hooke, Wren, and Halley. Newton's achievement was different and greater: he showed gravitation is universal — that the force pulling an apple down is the same force holding the Moon and planets in orbit — and proved it mathematically, deriving Kepler's laws, the tides, and the precession of the equinoxes. It was the first great unification in physics, not the discovery of a previously unknown phenomenon.

Myth: Newton single-handedly produced all his great work during the 'plague year' (1665-66) annus mirabilis.

Reality: Modern scholarship treats the annus mirabilis as a myth largely shaped by Newton's own later, self-serving recollections. During the plague closures of 1665-67 he made important early progress in mathematics, optics, and mechanics, but nothing was finished: his 1666 work was far from the calculus he later developed, and the theory of universal gravitation was not yet worked out. The decisive labor came in the 1680s, making the 'lone flash in one miraculous year' narrative misleading.

Myth: Newton stole the inverse-square law of gravity from Robert Hooke.

Reality: When the Principia appeared, Hooke claimed Newton had taken the inverse-square 'notion' from him, but Hooke himself conceded that the mathematical demonstration of the resulting orbits was wholly Newton's. The inverse-square hypothesis predated both men, and Hooke's version lacked the mathematical rigor to prove that such a force produces elliptical orbits — which is precisely what Newton accomplished. Newton, stung by the accusation, removed several references to Hooke, but historians regard the substantive achievement as Newton's, not plagiarized.

Myth: Newton was a purely rational scientist, and the Royal Society readily published the Principia.

Reality: Newton devoted enormous effort to alchemy and to unorthodox theology and biblical chronology — millions of words, by some estimates more than he wrote on physics — which he saw as part of one unified quest to understand God's creation, though historians caution he avoided astrology and ritual magic. As for publication, the Royal Society had drained its funds on the lavishly illustrated but poorly selling 'De Historia Piscium' (History of Fishes) and could not pay for the Principia; Edmond Halley financed it personally, and was later partly reimbursed in unsold copies of the fish book.

Frequently Asked Questions

When was Newton's Principia published and what is its full title?

Isaac Newton's masterwork was published on July 5, 1687, by the Royal Society of London. Its full Latin title is Philosophiae Naturalis Principia Mathematica, usually translated as 'Mathematical Principles of Natural Philosophy.' Newton wrote it in Latin, the standard scholarly language of the era, and it appeared in three books (volumes). Two later editions followed in 1713 and 1726, the last published the year before Newton's death.

What did the Principia actually contain?

The Principia laid out Newton's three laws of motion and his law of universal gravitation, the principle that every two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. Across its three books Newton used these principles to explain the elliptical orbits of planets, the paths of comets, the rise and fall of the tides, and the flattening of the Earth at its poles. The work united terrestrial and celestial mechanics under a single mathematical framework, founding what is now called classical mechanics.

Did Edmond Halley really pay to publish the Principia?

Yes. The Royal Society had agreed to publish the book but found its funds exhausted, having recently spent its publication budget on a lavishly illustrated and poorly selling work, De Historia Piscium (a history of fishes). The astronomer Edmond Halley, who had originally prompted Newton with a question about planetary orbits in 1684, paid the printing costs out of his own pocket. Halley also edited the manuscript and shepherded it through the press, a considerable sacrifice given that he was not a wealthy man.

Did Newton use calculus in the Principia?

Newton had developed his version of calculus (which he called the method of fluxions), but the Principia presents its results almost entirely through classical geometry rather than calculus notation. Scholars debate how much of the underlying reasoning was worked out with calculus, but the published proofs are geometric, partly to make the arguments accessible to readers unfamiliar with his new techniques. Newton did not publish a full account of his fluxional methods until 1704, a delay that later fueled his bitter priority dispute with Gottfried Wilhelm Leibniz over who invented calculus.

How long did it take Newton to write the Principia, and what prompted it?

Newton composed the bulk of the Principia in an intense burst of roughly two and a half years, from 1684 to 1687. The spark was a 1684 visit from Edmond Halley, who asked what curve a planet would follow under an inverse-square force; Newton replied that it would be an ellipse. That exchange led Newton to expand a short tract known as De Motu into the full three-volume work. Some of the foundational ideas, however, trace back to his earlier reflections during the plague years of 1665 to 1666.

Why is the Principia considered so important?

The Principia is widely regarded as one of the most important scientific works ever written and a defining achievement of the Scientific Revolution. It demonstrated that the same mathematical laws govern both falling objects on Earth and the motions of planets and comets, overturning earlier views of the cosmos. Its synthesis of mathematical deduction and empirical observation helped shape the modern scientific method, and Newtonian mechanics remained the dominant framework of physics until Einstein's relativity and quantum theory in the early twentieth century. Its influence even extended beyond science, informing Enlightenment political and philosophical thought.