# Physicopoeia

###### φυσικοποιΐα

# Newton's Laws of Motion as They Originally Appeared

I sometimes like to take a historical approach to Physics teaching, especially when introducing new topics. For Newton's Laws of Motion, you might like to show your pupils what Newton actually published in 1687 in Principia, so here are the laws as they appear in the original. You may be interested or surprised to see that they don't bear much resemblance to what modern textbooks usually say, even if you ignore the Latin and read the translations.

These are photos I took of an original copy, which explains why the First Law photo in particular is a bit wonky - 17th century books aren't easy to hold open flat.

Since 17th-century typesetting isn't always easy to read, I've also given transcriptions of the originals, together with the (fairly literal) translations given in Bernard-Cohen and Whitman (1999):

*AXIOMATA, SIVE LEGES MOTUS. LEX I. Corpus omne persevare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus illud a viribus impressis cogitur statum suum mutare.*

TRANSLATION:

*AXIOMS, OR LAWS OF MOTION. LAW I. Every body continues in its state of rest, or of moving uniformly straight forward, unless it is compelled to change its state by the forces impressed upon it.*

*LEX II. Mutationem motus proportionalem esse vi motrici impressae et fieri secundum lineam rectam qua vis illa imprimatur.*

TRANSLATION:

*LAW II. A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.*

*LEX III. Actioni contrarium semper et aequalem esse reactionem: sive corporum duorum actiones in se mutuo semper esse aequales et in partes contrarias dirigi.*

TRANSLATION:

*To any action there is always an equal and opposite reaction; or, the actions of two bodies upon each other are always equal and always opposite in direction.*

CENTRIPETAL FORCE

Later in the Principia, Newton derives the expression for the centripetal acceleration of a body in circular motion (a = v² / r). The conclusion is actually at the bottom of the page, under Corol. 1. Notice how Newton uses explanatory text to derive the conclusion, with far less algebra than we would use today:

REFERENCE:

Bernard-Cohen I and Whitman A (1999): *The Principia: mathematical principles of natural philosophy / Isaac Newton; a new translation*. Berkeley: University of California Press.