The Book Ahead
Of Its Time -
Newton's 'Principia Mathematica'

In his memoirs, British numismatist, antiquary, mathematician and astronomer, Martin Folkes, recounted having overheard a Cambridge student’s remark as Isaac Newton passed by, “there goes the man that writt a book that neither he nor anybody else understands”. This dismissive attitude was directed towards what today is considered a seminal book of science, and of physics in particular – a book that gave the world the theory of gravity and was the first to explain all types of motion, from an apple falling from the tree to the movement of stars in the sky, using three simple rules.

And yet, there was some degree of truth in what the student had said – the scientific world of the late 17th century found it difficult to digest the great mathematician and physicist’s groundbreaking work -  “Philosophiæ Naturalis Principia Mathematica” (Latin for Mathematical Principles of Natural Philosophy), or in short, “The Principia” (the principles). These were three volumes written in Latin, the language of education at that time, which were filled with mathematical equations and new ideas. It is likely that only few scholars at the time possessed the mathematical and scientific knowledge required to understand the book in depth. It took many more years for the book, and for the ideas in it, to gain a foothold in the world of science.

Newton. A giant who stood on the shoulders of giants | Source: David Parker / Science Photo Library

The Laws That Make The World Go Round

The dominant scientific approach in the second half of the 17th century was Aristotelian physics, which was based mostly on intuition and held, among other things, that an object can move only as long as a force acts upon it. Even though Nicolaus Copernicus, Johannes Kepler, Galileo Galilei and others had already debunked Aristotle’s basic principles, a complete and coherent theory to explain the motion of bodies using systematic mathematical tools was still missing.  “The Principia”, first published on July 5, 1687, summed up more than twenty years of research and thought. During this time period, Newton formulated the laws of classical mechanics, coined basic physical concepts, such as mass, weight and momentum and applied them to calculate the motion of celestial bodies and many astronomical phenomena. 

At the highlight of his work were the three laws of motion and the law of universal gravitation. Newton’s first law, also termed the “law of inertia”, states – in complete contradiction of the Aristotelian approach – that a body remains at rest or continues to move in a straight line at a constant speed as long as no force is being applied to it; Newton’s second law states that the net force exerted on an object equals the product of its mass times its acceleration; and Newton’s third law states that when one object exerts a force on another object, that object exerts back a force equal in magnitude but opposite in direction on the first object, or in other words, when a horse pulls a cart forward, the cart will also pull the horse backwards. 

Newton’s law of universal gravitation | Source: BrainCityArts, Shutterstock

Based on the three laws of motion, Newton attempted to explain the motion of celestial bodies, and in order to do so, he developed his law of universal gravitation. Here, for the first time in “The Principia”, he combines the force that pulls objects down toward the ground with the force that governs the motion of the stars. He states that a force of gravity exists between every two objects, and that this force is inversely proportional to the square of the distance between them, such that it decreases as they are further apart, but increases with the mass of the objects. 

Beyond the physical insights, the three volumes of the book became a standard for methodical scientific writing, describing nature in a structured and harmonious fashion, with the formulation of hypotheses that are based on previous experimental results and on examination.

The driving force behind the publishing of The Principia. Edmond Halley | Source: Painting from the early 18th century, Wikipedia commons

Bumps in The Road To Publishing

Despite Newton’s high standing in Cambridge and in the British scientific community, getting his book out to print did not turn out to be a simple task. At first, he himself was not interested in its publication, claiming that the time was not ripe for it. Only vigorous solicitation by his friend, astronomer Edmond Halley, known among other things for the famous comet named after him, convinced Newton that his theory was ripe for publication. 

In 1684, Halley visited Cambridge to discuss with Newton the orbits of the planets in the solar system. Realizing that his friend had in fact no written material, Halley encouraged him to publish his findings in an article, and Newton had eventually done this in November of that year. Halley however, was not content with this, and continued pressing until Newton conceded and began writing The Principia. 

In late April 1686 Halley presented the members of the British Royal Society with the manuscript of the first volume of The Principia and requested the Society’s help with publishing it. The Royal Society promised to consider the request and appointed Halley as the person responsible for updating the Society on any developments. A month later, Halley reported to Newton that due to the absence of the president of the Royal Society and his deputy, the council could not be convened, but took advantage of an informal meeting in order to obtain an approval in-principle to fund the book's publication.

However, on June 2nd this decision was overturned, mostly due to the major financial difficulties faced by the Society due to the publication of what turned to be an unpopular and a poorly selling book, “Of the History of Fish” (“De Historia piscium”) by Francis Willughby. Thus, although the Royal Society continued to express unconditional support for the book, Halley was forced to fund the book’s publication himself. 

On July 5th 1687 Halley informed Newton “‘I have at length brought your Book to an end, and hope it will please you”. Twenty copies were attached to the letter “to bestow on your friends”, and forty more copies, which he entreated Newton to deliver to the ablest booksellers in Cambridge. The price per customer was set at nine shillings for a leather-bound copy of the book and six for a standard one. 

Somewhat surprisingly, it is not at all clear how many copies of this first edition were in fact printed. In a census of copies carried out in 1953 a researcher by the name of Henry Macomber was able to locate only 189 copies worldwide, in agreement with the estimates that the number of scholars who could handle such complex mathematical and scientific literature in Europe of the late 17th century was only in the order of a few hundreds. Based on this, Macomber concluded that this edition included about 250 copies. 

However, in a new copy census, the results of which were published in late 2020, no less than 387 copies were located across 27 countries, in public libraries or in documented private collections. The traces of 13 other copies, documented in the previous census, were lost after having changed ownership multiple times. Based on this, the researchers, Mordechai (Moti) Feingold of the California Institute of Technology (Caltech) and Andrej Svorenčík of the University of Mannheim in Germany, hypothesized that Halley printed 600-650 copies of The Principia, with about 60 percent of them having survived to this day.

A page from The Principia, dealing with the subject of wave theory. Select issues were distributed to key people | Source: Royal Institution of Great Britain / Photo Science Library

Selective Distribution

While attempting to distribute the book, which he justifiably regarded as a masterpiece of scientific thought, Halley found himself facing a hostile market. Newton’s colleague, John Collins, had warned him as early as 1672, that Latin language book publishers in London had no interest in books on mathematics, as they had no international market. Collins explained that not only are they unwilling to fund the publication of such books, but that they would even expect payment from the author himself. 

Feingold and Svorenčík’s follow-up work shows that even before the book was published, Halley invested a great deal of effort in building expectations for it in the scientific community. To this end, he used the Royal Society’s publications and even distributed issues of The Principia to a select group of friends, in order to spread the word. Copies sent to leading European newspapers have yielded reviews of the book and of Newton’s principles of the theory of gravity and laws of motion, which were published in a few of these newspapers. 

Many of the copies were given by Halley or by Newton himself, to leading intellectuals of the time, such as the philosopher John Locke, the astronomer John Flamsteed and even Newton’s great rival – the philosopher and mathematician Gottfried Leibniz, who developed differential calculus in parallel with Newton. Free copies were also given to people in key positions in the United Kingdom’s political system, such as the first Duke of Devonshire William Cavendish, who was one of the leaders of the Whig Party, and naturally, King James II of England. 

Word-of-mouth advertising did not yield satisfactory sales, and therefore, a few months later, Halley handed over the exclusive rights to distribute the book to distributor Samuel Smith, who had many commercial connections throughout Europe. Smith was successful in finding the proper channels to distribute the book and sold a few hundred copies by 1690, in Amsterdam, Paris, and in other centers of culture, science and commerce of the time.

Over the years the value of copies of the first edition of The Principia rocketed from six shillings to hundreds of thousands of pounds | Photo: Andrew Dunn, Wikipedia

A Collector’s Item

At the beginning of the 18th century, all copies of the first edition had been sold out and could only be purchased second hand. In 1713, at which time Newton already served as president of the Royal Society and had already been recognized as one of the great scientists of his generation, he finally agreed to publish a second edition of the book. 

This time, the market was more agreeable, and over 700 copies of the edition were sold out in just two years. An official third edition was published in 1726, a few months prior to Newton’s death, and at least two pirated editions had been published earlier in Amsterdam – one of these copies can be found at the National Library of Israel, in Jerusalem. The “Philosophiæ Naturalis Principia Mathematica” had earned its well-deserving status as one of the formative works of science. 

"By the 18th century, Newtonian ideas transcended science itself. People in other fields were hoping to find a similar single law to unify their own respective fields. The influence of Newton, just like that of Charles Darwin and Albert Einstein, exerted considerable influence on many other aspects of life, and that is what made him such a canonical figure", Feingold said in an interview to the Caltech website.

The stature and significance of the book were also manifested in the price. Copies of the first edition of The Principia, originally sold for 6-9 shillings, are sold today in public auctions for up to three million dollars, depending on the book’s condition and the genealogy of its owners over the years. For example, on July 9th 2019, a copy of the first edition of The Principia was sold at the Christie's auction house for nearly 500 thousand pounds. A similar copy, originally purchased by an Italian scholar, was sold at Sotheby’s for 375 thousand pounds. 

However, far beyond the material value of the book and its iconic status are its ideas. The Principia has shaped scientific thought and research for nearly 350 years, to the present day. The principles of mechanics and gravity discovered by Newton are still largely valid, despite some important adjustments added during the 20th century by Albert Einstein’s theory of relativity and quantum mechanics, regarding motion at velocities that approach the speed of light, as well as regarding extremely small scales. “The book no one can understand” remains to this day shining beacon of unique insights into nature.