Newton's laws of motion

By Abhijit Menon-Sen <ams@toroid.org>

2011-12-22

Ammu is studying Newton's laws of motion this year in Physics, but she can never remember what the three laws are (partly because they don't seem to be stated clearly in her textbook).

I learned the three laws from a very old-fashioned British textbook that belonged to my great-grandfather—long before I had internet access—so it was a treat to be able to look up Newton's original formulation in the "Philosophiæ naturalis Principia Mathematica" on Gutenberg. After the preface and a series of definitions followed by explanatory notes, the laws of motion are presented in a section entitiled “Axiomata sive Leges Motus” (“Axioms; or, The Laws of Motion”).

Lex. I.

Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.

In other words, “Every body perseveres in its state of rest or uniform motion in a straight line, unless a force upon it compels it to change that state.”

Lex. II.

Mutationem motus proportionalem esse vi motrici impressæ, & fieri secundum lineam rectam qua vis illa imprimitur.

“The change in motion is proportional to the force impressed and takes place in the direction of the straight line in which that force is impressed.”

Lex. III.

Actioni contrariam semper & æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales & in partes contrarias dirigi.

“To every action, there is always an equal and opposite reaction: or the actions of two bodies upon each other are always equal, and directed to opposite parts.”

I don't know enough Latin to follow along comfortably, but I can see what's happening just by looking at the diagrams.

For a more educated translation of the Principia Mathematica, archive.org provides a copy of Andrew Motte's 1846 translation (which includes a biography of Newton).