The Mathematical Principles of Natural Philosophy (Principia)

The Mathematical Principles of Natural Philosophy, known as the Principia, is Isaac Newton’s founding work of mathematical physics. The edition described here is the First American Edition, published in New York by Daniel Adee in 1846. It presents Andrew Motte’s English translation, revised and corrected, together with Newton’s System of the World, a portrait taken from the bust in the Royal Observatory at Greenwich, and a life of the author by N. W. Chittenden.

The edition opens with a dedication by Chittenden to the teachers of the Normal School of the State of New York. He calls teaching the highest and most responsible office a person can fill, and he offers the Principia to educators as the greatest work of the greatest Teacher. An introduction to the American edition follows. It remarks that the book had remained little known in the country, because Latin copies were few and English copies were very expensive. The editor says that this edition places the work within the reach of all, and that great care was taken, by collation and revision, to make it accurate.

The introduction also argues for the educational value of geometrical synthesis. Chittenden notes that Newton, though the inventor of fluxions, criticised the treatment of geometrical subjects by algebraic calculation and preferred the geometrical method in his maturer opinions. He suggests that students who have worked through Euclid or Legendre might proceed to the Principia, where geometry is used from the familiar to the sublime.

The contents show the shape of the treatise itself. After the author’s preface come the Definitions and the Axioms, or Laws of Motion, which set out the basic terms and principles. Book I, on the motion of bodies, is divided into fourteen sections. It begins with the method of first and last ratios, which Newton uses to demonstrate the propositions that follow. It then treats the invention of centripetal forces and the motion of bodies in conic sections. Later sections cover finding orbits from a given focus or without one, motion in given orbits, rectilinear ascent and descent, movable orbits and the motion of the apsides, and motion on given surfaces, including pendulums. Further sections examine bodies attracting one another, the attractive forces of spherical and non-spherical bodies, and the motion of very small bodies acted on by forces directed to the parts of a large body.

Book II, also titled on the motion of bodies, turns to resisting mediums. Its sections consider resistance proportional to velocity, to the square of velocity, and to a mixture of both. They also treat circular motion in resisting media, the density and compression of fluids and hydrostatics, the motion and resistance of pendulums, and the motion of fluids and the resistance met by projected bodies. The listed contents continue with the propagation of motion.

The original Latin work was first published in 1687. This 1846 volume is therefore a later English-language presentation of it, framed for American readers and teachers, and it adds biographical and explanatory matter around Newton’s text.