skip to content

Newton Papers : Arithmetica Universalis

Newton Papers

<p style='text-align: justify;'>The <i>Arithmeticae universalis liber primus</i> was described in the <i>Catalogue of the Portsmouth Collection of Books and Papers written by or belonging to Sir Isaac Newton</i> (Cambridge, 1888) as ‘A MS copy of a portion of the <i>Arithmetica Universalis</i>, apparently an earlier copy’ (p. 47). In fact, Add. 3993 is most probably a later revision of the text of the Lucasian lectures on Algebra [Dd. 9. 68], which were deposited in the University Library late in 1683 or early in 1684. In 1707 William Whiston, Newton’s successor in the Lucasian chair, published [Dd. 9. 68], perhaps following the example of Add. 3993, with the title <i>Arithmetica Universalis: Sive de Compositione et Resolutione Arithmetica Liber</i>. This a book that was often reprinted and that enjoyed great success during the eighteenth century.</p><p style='text-align: justify;'> Add. 3993 is partly in Newton’s own hand and partly in the hand of his amanuensis Humphrey Newton [evident after <a href='' onclick='store.loadPage(18);return false;'>page 10</a>]. Humphrey worked as Newton’s secretary most probably from winter 1683 to the end of 1688: therefore, one can date Add. 3993 to that period. The fact that Add. 3993 was meant for a reader (a ‘lector’) might be revealed by the following phrases ‘Eandem aequationem ex alijs sex supra inventis aequationum modis tentet Lector exercitationis gratia derivare’ (Let the reader attempt to derive the same equation from the other six above-found modes of equations as an exercise) [<a href='' onclick='store.loadPage(73);return false;'>page 65</a>] and ‘Postquam Lector Problemata in aequationes derivare et aequationes illas reducere didicit’ (After the reader has learnt how to derive problems into equations and to reduce those equations) [<a href='' onclick='store.loadPage(74);return false;'>page 66</a>].</p><p style='text-align: justify;'> On the 25 September 1727, Thomas Pellet, who was assessing Newton’s literary estate, judged this text ‘not fit to be printed’ (page i, Image 3), probably because the manuscript represented an incomplete version of the <i>Arithmetica Universalis</i>, which Whiston had already printed. Many parts of the printed <i>Arithmetica Universalis</i> cover introductory material, but its reader can find also innovative results, which are lacking in Add. 3993 (most notably, Newton’s rule for finding the number of ‘impossible’ (imaginary) roots of an equation). In Newton’s text, the rule is explained by worked-out examples. How to prove the rule was a major problem left to Newton’s readers. In the 1720s, the Scottish mathematicians George Campbell and Colin Maclaurin provided demonstrations in the <i>Philosophical Transactions</i>. Newton also treated the ‘composition of the coefficients from the roots’ and stated a set of rules, equivalent to those given by Albert Girard in 1629 but given in a more easily memorable form. Today they are known as the Newton-Girard formulae.</p><p style='text-align: justify;'>Niccolò Guicciardini, Università degli Studi di Milano, and Scott Mandelbrote, Peterhouse, Cambridge.</p>


Want to know more?

Under the 'More' menu you can find , and information about sharing this image.

No Contents List Available
No Metadata Available

Share

If you want to share this page with others you can send them a link to this individual page:
Alternatively please share this page on social media

You can also embed the viewer into your own website or blog using the code below: