Philosophiæ Naturalis Principia Mathematica

Philosophiæ Naturalis Principia Mathematica (English: The Mathematical Principles of Natural Philosophy), often called simply the Principia (/prɪnˈsɪpiə, -ˈkɪp-/), is a book by Sir Isaac Newton that explains Newton's laws of motion and his law of universal gravitation. Written in Latin, the Principia has three volumes and was first published in 1687. It was approved by Samuel Pepys, the President of the Royal Society, before it was released to the public.

This important book helped create the foundation for classical mechanics and is considered one of the greatest works in the history of science. In it, Newton used special math methods that are now part of calculus, showing his ideas through geometric shapes. He also explained why planets move the way they do, supporting Johannes Kepler's laws of planetary motion.

Newton’s work showed that he did not just guess about how nature worked, but used real observations. The Principia remains a key piece of science history, showing how one person’s ideas can help us understand the universe.

Contents

The Principia explains how objects move and the forces that affect their motion. Newton wrote it in Latin, and it has three main parts.

Book 1 looks at how objects move without any resistance, like in space. It talks about forces pulling objects toward each other and how this creates paths such as ellipses. This book also begins to explore the tricky problem of how three objects, like the Sun, Earth, and Moon, affect each other's motion.

Book 2 examines how objects move through materials that offer resistance, like air or water. Newton tested ideas about how resistance changes with speed and used experiments with pendulums to learn more about air resistance.

Book 3 applies the ideas from the earlier books to the Solar System. It explains the orbits of planets and moons, the pull of gravity between them, and phenomena like tides and the slow shift in the stars called the precession of the equinoxes. Newton also used this book to support the idea that the Sun, not the Earth, is at the center of our solar system.

Rules of Reason

In his book Philosophiæ Naturalis Principia Mathematica, Sir Isaac Newton included a section called "Rules of Reasoning in Philosophy" starting from the second edition in 1713. These rules help scientists understand nature by using careful observations and logical thinking.

Newton's four rules guide scientists to use only true and needed explanations, to use the same causes for similar effects, to recognize qualities that all bodies share, and to trust conclusions drawn from many observations until new information appears. These ideas became important for modern science.

The General Scholium is an essay Newton added in later editions. He used it to defend his ideas about gravity, stating that while gravity exists, its cause was still unknown and should not be guessed at without evidence. He also discussed the design of the universe as evidence of a creator.

Main article: General Scholium

Publishing the book

Edmond Halley played a key role in helping Isaac Newton write and publish his important book, Philosophiae Naturalis Principia Mathematica. In 1684, Halley talked with Newton about planetary motion, which inspired Newton to start working on the book. Newton sent Halley a manuscript called De motu corporum in gyrum in 1684, which showed early ideas that would become part of the Principia.

The first edition of the Principia was published in 1687, with Halley paying for the printing himself. Newton later made changes and corrections for new editions in 1713 and 1726. Halley’s support was crucial in getting Newton’s work shared with the world.

Historical context

Further information: History of gravitational theory

Nicolaus Copernicus changed our view of the universe by moving the Earth away from the center with his theory in 1543. Johannes Kepler later discovered that planets move in elliptical orbits around the Sun and that their speeds change in a special way. These ideas helped lay the groundwork for understanding how objects move in space.

Isaac Newton built on these earlier works. During his time at Cambridge, he developed new mathematical ideas and studied light and color. He also began exploring how objects move, especially when they collide or orbit each other. Newton’s interest in these topics grew even more when he corresponded with other scientists, which eventually led to his famous book.

Location of early edition copies

Many copies of the first edition of Newton's Principia still exist today. Important libraries that hold these copies include the Cambridge University Library, which has Newton's own copy with notes, and the Folger Shakespeare Library in Washington, D.C., which has both a first and second edition. Other notable holders include the Huntington Library in San Marino, California and the Uppsala University Library in Sweden.

In 2016, a first edition sold for $3.7 million, showing its great value. The second edition had 750 copies printed, and the third edition had 1,250 copies.

Later editions

Two later editions of the Principia were published by Newton. The second edition came out in 1713, after Newton was encouraged to update his work because the first edition had become rare and expensive. Richard Bentley and Roger Cotes helped prepare this edition, making many important changes.

The third edition was published in 1726, when Newton was 80 years old. It was prepared by Henry Pemberton. Later, French scholars created detailed versions of this edition, and Émilie du Châtelet translated the Principia into French, making it easier for readers to understand.

Translations

The Principia has been translated into English four times. The first translation, done by Andrew Motte in 1729, remains valuable for showing Newton's original ideas clearly. Later, in 1999, I. Bernard Cohen, Anne Whitman, and Julia Budenz worked together to create a modern English version. Another translation by Ian Bruce is available on his website. The most recent translation was completed by Charles Leedham-Green in 2021. He spent twenty years on this project to make Newton's ideas easier for today’s scientists to understand.

Additionally, Dana Densmore and William H. Donahue translated the main arguments of the work in 1996, adding explanations and comments to help students learn from it.

Legacy

The Principia had a huge impact on science. Many great thinkers praised it highly. Alexis Clairaut said it started a big change in physics. Joseph-Louis Lagrange called it the greatest work of the human mind. Pierre-Simon Laplace said it was the best ever made by humans.

A study in 2020 found many more copies of the first edition than people thought. This shows that the Principia influenced science much more than we used to believe.

Varia

In 1977, the spacecraft Voyager 1 and Voyager 2 left Earth carrying a picture of a page from Newton's Principia Mathematica as part of the Golden Record, a special collection of messages for space travelers.

In 2014, British astronaut Tim Peake named his mission to the International Space Station Principia to honor Britain's greatest scientist. The mission launched on December 15, 2015, aboard Soyuz TMA-19M.