<p style='text-align: justify;'>The large collection of papers gathered in Add. 3965 concerns the production, publication and revision of the <i>Philosophiae Naturalis Principia Mathematica</i>, Newton’s masterpiece (the <i>Principia</i>, for short) on the laws of motion and the law of gravitation that was printed in London in 1687. Two revised editions were published during Newton’s lifetime: the second edition in Cambridge in 1713 and the third, again in London, in 1726, just one year before Newton’s death.</p><p style='text-align: justify;'>Newton was prompted to write the <i>Principia</i> when in 1684 Edmond Halley visited him in his rooms in Cambridge with the purpose of asking a question concerning planetary motions he was discussing with Christopher Wren and Robert Hooke. Newton’s first reply took the form of a small tract entitled <i>De Motu Corporum in Gyrum</i>, which he sent to Halley in November 1684 (a draft in Newton’s hand is <a href='' onclick='store.loadPage(109);return false;'>fols 55-62</a>). In this collection one can find succeeding drafts in the hand of Newton’s amanuensis, Humphrey Newton [<a href='' onclick='store.loadPage(45);return false;'>fols 23r-26r</a>; <a href='' onclick='store.loadPage(79);return false;'>fols 40r-54r</a>], as well as a transcription in Halley’s hand [<a href='' onclick='store.loadPage(127);return false;'>fols 63r-70r</a>].</p><p style='text-align: justify;'>Halley reacted enthusiastically and actually took upon himself the task of financing the publication of a much longer treatise, which took the form of a hefty book, eventually dedicated to the king, James II [<a href='' onclick='store.loadPage(1549);return false;'>fols 759-64</a>]. The <i>Principia</i> made Newton famous, even though not many on the Continent accepted the idea of a force acting at a distance among all masses in the Universe. The level of sophistication of Newton’s mathematics and the accurate agreement with most (even though not all!) astronomical data did not fail to impress the most competent readers.</p><p style='text-align: justify;'>In the early 1690 Newton soon became unsatisfied with his printed publication and began planning revisions. Some of the papers in Add. 3965 show the depth and breadth of Newton’s intended restructurings [<a href='' onclick='store.loadPage(53);return false;'>fols 27r-39r</a>]. On <a href='' onclick='store.loadPage(77);return false;'>fol 39r</a> note that Newton uses his dot notation, which he invented in the early 1690s, in order to express the equation for the vertical motion of a body acted upon by ‘gravity’. Rumours about the imminent publication of a second edition began to spread, thanks also to the reports of two of Newton’s acolytes Nicolas Fatio de Duillier and David Gregory. Only after 1709, however, and thanks to the intermediation of the great classicist Richard Bentley and the editorial work of a young Cambridge Professor of astronomy, Roger Cotes, did Newton begin work on a second edition, which eventually appeared from the University Press in Cambridge in 1713.</p><p style='text-align: justify;'>In Add. 3965 we can find several revisions and additions intended for the second edition. Among them are drafts and revisions for the famous ‘General Scholium’ that Newton added to that edition, as well as notes for the distribution of the printed edition [<a href='' onclick='store.loadPage(729);return false;'>fol. 358r</a>]. Many drafts concern the mathematization of fluid motion and a proposition of the second book that was mistaken [<a href='' onclick='store.loadPage(387);return false;'>fols 190r-220v</a>]. In this proposition, the tenth of the second book, Newton deals with the motion of a projectile, acted on by constant gravity and moving in a rare fluid, exerting a resistance proportional to the square of the speed. In the context of the priority dispute on the invention of the calculus that had erupted in 1712, Johann and Nicolaus I Bernoulli, who were on Leibniz’s side, were working hard in order to find mistakes in the <i>Principia</i>. A joint paper was soon submitted to the Academy of Sciences in Paris: in the main paper by Johann, a mistake in Newton's proposition 10 was noted and an alternative calculus solution was given; in the appendix by Nicolaus I it was stated that this mistake was due to Newton's misunderstanding of the meaning of the higher-order infinitesimals occurring in the coefficients of a Taylor series.</p><p style='text-align: justify;'>In September 1712 Nicolaus I Bernoulli, Johann's nephew, arrived in London. He met Newton and informed him that Johann had detected a mistake in Proposition 10. Newton recognized immediately that Nicolaus I was right. Since Roger Cotes had not noticed any error in Proposition 10, the pages with the unaltered 1687 version had already been printed in the second edition, which was currently at the press. Newton worked strenuously in order to reach an understanding of his mistake and produce a correct demonstration, which was pasted in as a correction to the second edition at the last moment. </p><p style='text-align: justify;'>In order to prepare the new editions of the <i>Principia</i> Newton annotated and interleaved his own copies. The University Library owns two interleaved exemplars of the first and second editions of the <i>Principia</i> with Newton’s extensive annotations [<a href='/view/PR-ADV-B-00039-00001'>Adv.b.39.1</a> and <a href='/view/PR-ADV-B-00039-00002'>Adv.b.39.2</a>]. They are precious documents that offer to scholars a unique chance to follow Newton’s mind in revising, rethinking and extending his masterpiece.</p><p style='text-align: justify;'>See I. Bernard Cohen, <i>Introduction to Newton's Principia</i> (Cambridge, 1971), pp.29-32 for general information on the collection.</p><p style='text-align: justify;'>Some of the texts are published in D.T. Whiteside, <i>The Mathematical Papers of Isaac Newton</i> (Cambridge, 1967-1981) and A.R. Hall and M.B. Hall, <i>Unpublished Scientific Papers of Isaac Newton</i> (Cambridge, 1962).</p><p style='text-align: justify;'>Niccolò Guicciardini, Università degli Studi di Milano, and Scott Mandelbrote, Peterhouse, Cambridge.</p>
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