<p style='text-align: justify;'>Add. 3990 is a bound notebook entitled <i>De Motu Corporum Liber Secundus</i>. It is mostly written in the hand of Humphrey Newton (Isaac Newton’s amanuensis in this period). A fair copy of the first part, again in Humphrey’s hand, was deposited in the University Library to represent a set of lectures by the Lucasian Professor [Ms. Dd.4.18]. The five lectures contained in this manuscript, under the title ‘De motu Corporum Liber [secundus]’, were supposedly delivered by Newton during Michaelmas Term 1687, beginning on 29 September. </p><p style='text-align: justify;'>The manuscripts (Dd.4.18 and the first part of Add. 3990) are not, however, to be regarded as the texts of lectures actually delivered by Newton. Instead they represent a copy of part of a draft for the last book of the <i>Principia</i> that Newton later rejected. Add. 3990 is thus interesting as an example of the manner in which Newton fulfilled the requirement that, as Lucasian Professor, he should deliver suitable lectures and deposit copies of them in the University Library. It also provides an illustration of the collaboration between Newton and his amanuensis, Humphrey Newton. </p><p style='text-align: justify;'>Newton had arranged for Humphrey, who was not related to him, to come up to Cambridge from the grammar school in Grantham either in 1683 or 1684. Humphrey Newton then served as Isaac Newton’s amanuensis for five years, during which he may also have been his sizar, although Humphrey appears not to have been admitted as a member of Trinity College. Many of Newton’s compositions during this period survive in drafts written by Humphrey Newton, including both versions of ‘De motu corporum liber secundus’ Dd.4.18 and Add. 3990. The most notable manuscript in Humphrey’s hand is the one from which the text of the <i>Principia</i> was printed [<a href='/view/MS-ROYALSOCIETY-00069/1'>MS/69</a>]. </p><p style='text-align: justify;'>Humphrey Newton later returned to Grantham, where he practised as ‘a physician and manmidwife’ according to William Stukeley, and was still alive in 1728. The reminiscences of his master that he related to Stukeley and John Conduitt are the source for many of the stories of Newton’s absent-mindedness as well as providing evidence for the pattern of Newton’s life in College and his intellectual activity during the late 1680s.</p><p style='text-align: justify;'>In Add. 3990 one can find frequent corrections and additions, often as marginal postils, in the hand of Isaac Newton. Further, compositor’s marks corresponding to the intended beginnings of each printed page are clearly discernible. It is highly probable therefore that this is the copy that was used to produce after Newton’s death a book under the title <i>De Mundi Systemate Liber Isaaci Newtoni</i> (London, 1728). On the basis of Stukeley’s memoirs and annotations in his copy of the printed book, it is believed that John Conduitt, the husband of Newton’s half-niece, Catherine Barton, was responsible for this publication [MS/142, Royal Society Library, f. 19v available at Newton Project]. It may well be that Conduitt also took the decision to alter the title. The book appeared first in English, slightly earlier in the same year, with some variants.</p><p style='text-align: justify;'>Add. 3990 owes its original title to the fact that Newton initially conceived the <i>Principia</i>, which was eventually printed in 1687, as being divided into two books. A ‘Liber Primus’ (First Book), mostly devoted to a mathematical theory concerning the motion of bodies, was to be followed by a second book, dealing with the ‘System of the World’, that is, with the mathematization of the planetary system, the tides, the shape of the Earth, the motion of the Moon, and the orbits of comets. </p><p style='text-align: justify;'>It seems that Newton dictated Add. 3990 to Humphrey some time before autumn 1685. He then rethought the structure of the <i>Principia</i>, dividing his masterpiece into three books, the third of which was a much expanded and reworked version of <i>De Motu Corporum Liber Secundus</i>. Fourteen paragraphs of Add. 3990 indeed survived in Book 3 of the printed <i>Principia</i>. This manuscript is therefore invaluable for shedding light on the phases of composition of the <i>Principia</i>. </p><p style='text-align: justify;'>Niccolò Guicciardini, Università degli Studi di Milano, and Scott Mandelbrote, Peterhouse, Cambridge.</p>