Part II.   Newton’s Laws of Motion and Concepts of Universal Gravitation
N.   Newton’s Axioms for Gravity

Before Newton began to describe and explain his concepts of universal gravitation in Book Three of the Principia (entitled the System of the World) he strongly advised his readers that his Definitions, his Laws of Motion, and the first three sections of Book One must first be carefully read and understood, before any reader attempts to read Book Three.[1] The first three sections of Book One dealt with (in order): 1) the Ratios of Quantities; 2) the Determination of Centripetal Forces; and 3) the Motions of Bodies in Eccentric Conic Sections (i.e. ellipses).[2]

Newton then described four axioms which would guide him throughout Book Three. These axioms are stated as follows:

Rule 1. “No more causes of natural things should be admitted than are both true and sufficient to explain their phenomena.”[3]

Rule 2. “Therefore, the causes assigned to natural effects of the same kind must be, so far as possible, the same.”[4]

Rule 3. “Those qualities of bodies that cannot be [changed] and that belong to all bodies on which experiments can be made should be taken as qualities of all bodies universally…[Thus], if it is universally established by experiments and astronomical observations that all bodies on or near the earth gravitate toward the earth, and do so in proportion to the quantity of matter in each body, and that the moon gravitates toward the earth in proportion to the quantity of its matter, and that our sea in turn gravitates toward the moon, and that all planets gravitate toward one another, and that there is a similar gravity of comets toward the sun, it will have to be concluded by this third rule that all bodies gravitate toward one another.” [5]

Rule 4. “In experimental philosophy, propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions. This rule should be followed so that arguments based on induction may not be nullified by hypotheses.”[6]