1. In order to understand why Newton used the term “vis inertiae” rather than simply “inertia,” we must keep in mind that Newton, as he says explicitly in Def. 3, was giving a new and better name to the then-current concept of “vis insita.” Thus he merely changed one qualifier (“insita”) to another (“inertiae”).
2. On Newton’s mathematical methods in the Principia and the history of the ways in which his successors read and revised Newton’s rational mechanics, see Niccolò Guicciardini’s masterful analysis, Reading the “Principia”: The Debate on Newton’s Mathematical Methods for Natural Philosophy from 1687 to 1736 (Cambridge: Cambridge University Press, 1999).
3. On Newton’s concept of limit and on the methods of book 1, sec. 1, of the Principia, see Bruce Pourciau, “Newton and the Notion of Limit,” Historia Mathematica 28 (2001): 18–30, and “The Preliminary Mathematical Lemmas of Newton’s Principia,” Archive for History of Exact Sciences 52 (1998): 279–295.
4. On Book 1, Lemma 28, see Bruce Pourciau, “The Integrability of Ovals,” Archive for History of Exact Sciences 55 (2001): 478–499.
5. On the solid of least resistance and Newton’s thoughts concerning the design of ships, see A. Rupert Hall, Ballistics in the Seventeenth Century (Cambridge: Cambridge University Press, 1952), pp. 141–145.