<p style='text-align: justify;'>A copy of the second edition of the <i>Philosophiae Naturalis Principia Mathematica</i> (Cambridge, 1713), which Newton annotated in the margins and also on interleaved sheets bound into the book. These annotations were useful for the production of the third edition, whose editor was Henry Pemberton. The third edition appeared in 1726, less than a year before Newton’s death.</p><p style='text-align: justify;'>We do not know when the project for a third edition began. The earliest letter from Pemberton concerning the revisions to the second edition is dated 11 February 1723/24. Pemberton was a careful editor, but as a mathematician he cannot be compared with Edmond Halley (the editor of the first edition, 1687) or Roger Cotes (the editor of the second edition, 1713). Moreover, by the period of preparation of the third edition, Newton was in his eighties and no longer able to engage in active mathematical research. Thus, it is no surprise that the third edition does not contain as many innovations and changes as the second. Nevertheless, Adv.b.39.2 is an invaluable source of information for our understanding of Newton’s natural philosophy. For example, on <a href='' onclick='store.loadPage(74);return false;'>p. 2</a> Newton annotates in the margin the differences between his concept of inertia and Kepler’s.</p><p style='text-align: justify;'> A notable feature of the third edition is that Newton added a fourth ‘Rule of Philosophising’ to the three of the second edition, no doubt in an attempt to answer the criticism levelled at his method by Continental philosophers, most notably Leibniz [<a href='' onclick='store.loadPage(803);return false;'>sheet facing pag. 358</a>]. Another anti-Leibnizian feature of the third edition occurs in the Scholium following Lemma II, Book 2. Here Newton completely modified the text. Rather than stating that the Leibnizian calculus, as communicated to him in 1677, differed from his ‘only in language and symbols’, he made a long statement claiming that he had systematized his ‘method of tangents’ in a ‘treatise composed on that subject in the year 1671’ (namely <a href='/view/'>Add. 3960.14</a>, the so called <i>De methodis serierum et fluxionum</i>), well before Leibniz’s invention. Newton’s tortured draft rewritings for the new version of Lemma 2 can be found on <a href='' onclick='store.loadPage(526);return false;'>pages 226-7</a>.</p><p style='text-align: justify;'>Niccolò Guicciardini, Università degli Studi di Milano, and Scott Mandelbrote, Peterhouse, Cambridge.</p>
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