## Newton’s Laws in Translation

I’m about to do some lectures about Newton’s Laws of Motion to my first-year Mathematical Physics class so I thought I’d put up a quick post about how these laws have been expressed through the years. The original versions in the Principia (frontispiece above, first published in 1687) are of course in Latin. I did five years of Latin at school, but found most of the Principia impenetrable when I tried to read it in the original

The laws of motion are however fairly clear, perhaps because they are familiar in English:

Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus illud a viribus impressis cogitur statum suum mutare.

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

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

As I am teaching in a room in the old college here in Maynooth (which was founded in 1795), I looked for a contemporary English translation. This is from 1792:

Law I: Every body perseveres in a state of being at rest or of moving uniformly straight forward except insofar as it is compelled to change its state by forces impressed.

Law II: The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

Law III: To every action there is always opposed an equal reaction: or the mutual action of two bodies upon each other are always equal, and directed to contrary parts.

And finally here’s the modern version I was taught at School:

First Law: Every body continues in a state of rest or uniform motion in a straight line unless it is acted upon by an external (unbalanced) force.

Second Law: The rate of change of momentum of a body is proportional to the impressed force, and is in the direction in which this force acts.

Third Law: To every action there is always an equal and opposite reaction,

an alternative form of the Third Law being:

Third Law: If Body A exerts a force on Body B then Body B exerts a force on Body A which is equal in magnitude and opposite in direction.

Going back to the 1792 English translation, the exposition of the second law continues:

If a force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.

If only Newton had known vector notation!