If I have seen further it is by standing on the shoulders of giants.

Sir Isaac Newton in a letter to Robert Hooke, 5 Feb. 1676


The Principia is arguably the single most original and powerful work ever produced by human intellect.

It was published in 1687, by the 45-year-old Sir Isaac Newton (1642-1727)

The Principia is the foundation of all modern scientific understanding of our world, and the universe beyond.

Without the Principia, there are no laws of motion; no concept of gravity, no Newtonian mechanics. Without the Principia we are no better than cavemen, idly watching leaves fall and blow randomly in the wind. Without the Principia, we can do no more than stare dumbly at the skies, with no understanding of the motions of the planets, or knowledge of earthly movement.

If for nothing else, the book should be remembered for finally ending the argument over whether the earth or the sun is at the centre of our little bit of space, and thereby ending the dominance of the Church in matters of scientific truth.

If this book is so fundamental to any kind of true understanding of the natural world, the philosophy of science and the way we know things, then why do so few people read it?

First, it was written in Latin, and there are not many people who can use that language well enough to read and understand the original text.

Second, the only English translation for 270 years was done in 1729 By Andrew Motte, and it’s quite hard to read.

Here is a sample of the Motte version. It is the first sentence of Newton’s preface to the first edition:

Since the ancients (as we are told by Pappas), made great account of the science of mechanics in the investigation of natural things; and the moderns, lying aside substantial forms and occult qualities, have endeavoured to subject the phænomena of nature to the laws of mathematics, I have in this treatise cultivated mathematics so far as it regards philosophy.

Most of the more important parts of this translation are on the web (see the list of URLs below), but it remains in the style of obscure 18th century writing, and is very hard for the modern student to follow.

The translation was updated in 1934, but the updates have since been discredited as ‘full of errors’.

The first modern translation for 270 years is titledThe Principia by Dr. I. Bernard Cohen and the late Anne Whitman, with assistance from Julia Budenz, all of Harvard University. It was published in September 1999 by the University of California Press. Cohen, Harvard’s first-ever Ph.D in the History of Science and Whitman a renowned (it sez here) Latin scholar each made their own translation, compared their notes and then went through many cycles of revision and editing in an attempt to make the work understandable and accurate. Unfortunately, Whitman died 10 years after the project began, leaving Cohen and his research assistant, Budenz to finish the translation. That took another five years. This version is based on Newton's third (1726) and final edition of the Principia. The new translation is published as ISBN 0-520-08817-4

Another interpretation is Newton's Principia: The Central Argument, by Dana Densmore with translations and diagrams by her husband, William H. Donahue. This book claims to offer more insight into the core of the original work, including highlighting some errors in the great man's work. It concentrates primarily on book 1, and the earlier chapters of book 3 (see below) ISBN 1-888009-00-4

A third interpretation, Newton's Principia for the Common Reader, by Subrahmanyan Chandrasekhar, was published by OUPin 1995. ISBN 0-19-851744-0


The Principia is divided into three parts. Each part contains a number of propositions, or Lemmae, together with analysis and explanation of Newton’s solutions. Newton chose to show his results through geometry, diagrams and simple mathematical concepts. There is almost no calculus or algebra in the book.

The list of contents below is taken from Motte's 1729 version, and retains the flavour of 18-century writing.

Book 1 covers dynamics, and introduces Newtons three laws of motion First Law, Second Law, Third Law

  1. Of the method of first and last ratios of quantities, by the help whereof we demonstrate the propositions that follow
  2. Of the invention of centripetal forces
  3. Of the motion of bodies in eccentric conic sections
  4. Of the finding of elliptic, parabolic, and hyperbolic orbits, from the focus given
  5. How the orbits are to be found when neither focus is given
  6. How the motions are to be found in given orbits
  7. Concerning the rectilinear ascent and descent of bodies
  8. Of the invention of orbits wherein bodies will revolve, being acted upon by any sort of centripetal force
  9. Of the motion of bodies in moveable orbits, and of the motion of the apsides
  10. Of the motion of bodies in given superficies, and of the reciprocal motion of funependulous bodies
  11. Of the motion of bodies to each other with centripetal forces
  12. Of the attractive forces of spherical bodies
  13. Of the attractive forces of bodies which are not of a spherical figure
  14. Of the motion of very small bodies when agitated by centripetal forces tending to the several parts of any very great body

Book 2 covers fluid mechanics and related topics

  1. Of the motion of bodies that are resisted in the ratio of velocity
  2. Of the motion of bodies that are resisted in the duplicate ratio of their velocities
  3. Of the motions of bodies which are resisted partly in the ratio of the velocities, and partly in the duplicate of the same ratio
  4. Of the circular motion of bodies in resisting mediums
  5. Of the density and compression of fluids; and of hydrostatics
  6. Of the motion and resistance of funependulous bodies
  7. Of the motion of fluids and the resistance made to projected bodies
  8. Of motion propagated through fluids
  9. Of the circular motion of fluids

Book 3 unifies the terrestrial mechanics introduced in Book 1, with celestial mechanics, extending the principle of gravity to a universal principle, which explains Kepler's laws of planetary motion as well as the fall of an apple.

Unfortunately I can't find the contents of book 3 anywhere. If anyone has a listing, or knows of one on the web, let me know and I'll post it here.

Thanks to krimson for help and guidance


Sources http://www.newton.org.uk/essays/Giants.html http://members.tripod.com/~gravitee/ http://www.encyclopedia.com/articles/09202ThePrincipia.html http://www.clas.ufl.edu/users/rhatch/HIS-SCI-STUDY-GUIDE/0090_halleysReviewNewton.html http://www.ucpress.edu/books/pages/6491.html http://www.greenlion.com/principi.html http://www.oup.co.uk/isbn/0-19-851744-0 http://www.hno.harvard.edu/gazette/1999/10.21/newton.html http://www.lib.udel.edu/ud/spec/exhibits/treasures/science/newton.html

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