De Motu Corporum in Gyrum - Contents

Contents

One of the surviving copies of De Motu was made by being entered in the Royal Society's register book, and its (Latin) text is available online.

For ease of cross-reference to the contents of De Motu that appeared again in the Principia, there are online sources for the 'Principia' in English translation, as well as in Latin.

De motu corporum in gyrum is short enough to set out here the contents of its different sections. It contains 11 propositions, labeled as 'theorems' and 'problems', some with corollaries. Before reaching this core subject-matter, Newton begins with some preliminaries:

• 3 Definitions:

1: 'Centripetal force' (Newton originated this term, and its first occurrence is in this document) impels or attracts a body to some point regarded as a center. (This reappears in Definition 5 of the Principia.)

2: 'Inherent force' of a body is defined in a way that prepares for the idea of inertia and of Newton's first law; (in the absence of external force, a body continues in its state of motion either at rest or in uniform motion along a straight line). (Definition 3 of the Principia is to similar effect.)

3: 'Resistance': the property of a medium that regularly impedes motion.

• 4 Hypotheses:

1: Newton indicates that in the first 9 propositions below, resistance is assumed nil, then for the remaining (2) propositions, resistance is assumed proportional both to the speed of the body and to the density of the medium.

2: By its intrinsic force (alone) every body would progress uniformly in a straight line to infinity unless something external hinders that.

(Newton's later first law of motion is to similar effect, Law 1 in the Principia.)

3: Forces combine by a parallelogram rule. Newton treats them in effect as we now treat vectors. This point reappears in Corollaries 1 and 2 to the third law of motion, Law 3 in the Principia.

4: In the initial moments of effect of a centripetal force, the distance is proportional to the square of the time. (The context indicates that Newton was dealing here with infinitesimals or their limiting ratios.) This reappears in Book 1, Lemma 10 in the 'Principia'.

Then follow two more preliminary points:

• 2 Lemmas:

1: Newton briefly sets out continued products of proportions involving differences:

if A/(A-B) = B/(B-C) = C/(C-D) etc, then A/B = B/C = C/D etc.

2: All parallelograms touching a given ellipse (to be understood: at the end-points of conjugate diameters) are equal in area.

Then follows Newton's main subject-matter, labeled as theorems, problems, corollaries and scholia: