Newton Papers : Treatise on Algebra and Miscellaneous Unrelated Material

Newton Papers

The hand in the early part of Add. 3995, a small-quarto notebook, is typical of Newton's early years [<a href='' onclick='store.loadPage(24);return false;'>fols 7v-18r</a>]. Subsequent pages [<a href='' onclick='store.loadPage(55);return false;'>fols 79r-84r</a>] are in the hand of Barnabas Smith, Newton’s step-father, who is citing from Quintus Curtius Rufus’s Historiae Alexandri Magni (Histories of Alexander the Great). His hand can be found in many pages of the <a href='/view/MS-ADD-04004'>Waste Book, Add. 4004</a>. There is a third hand [<a href='' onclick='store.loadPage(68);return false;'>fols 85v-94v</a>] copying out a prayer and a sermon on Leviticus 9:18 with comparisons with New Testament texts.The part in Newton’s hand consists of several versions of a short commonplace exposition on ‘quantity and muchness’. Newton lists definitions of ratios and proportions, he dwells on the notion of number and defines the elementary operations on numbers. He further expands (in some pages providing in the margin a numbering of his annotations as well as cross-references) on definitions of rational, irrational, commensurable and incommensurable, finite, infinitely great and infinitely little, definite and indefinite, affirmative and negative, ‘quanta’.It is interesting to note that Newton’s English terminology in part corresponds to the Latin of Barrow’s compact edition of Euclid’s Elements (1656), which the young Newton carefully annotated, and to the language of Barrow’s Lectiones mathematicae (most notably lectures 14-16), which were delivered in 1664-6 and printed posthumously in the 1680s. Other sources that Newton might have used in this youthful attempt to pin down the definitions of basic terms in algebra and in the theory of proportions are William Oughtred’s Clavis mathematicae (the third edition of 1652), or even John Wallis’s Operum Mathematicorum pars altera (Oxford, 1656) and François Viète’s Opera Mathematica (Leiden, 1646).The way of organizing the text of Add. 3995 and the manuscript’s subject matter appear related to parts of the Quaestiones Quaedam Philosophiae [<a href='/view/MS-ADD-03996/179'>Add. 3996, fols 88r-135r</a>] that Newton probably wrote in 1664-5, when he was still a student. Add. 3995 therefore provides important information about Newton’s early mathematical studies and his relationships with Isaac Barrow.Niccolò Guicciardini, Università degli Studi di Milano, and Scott Mandelbrote, Peterhouse, Cambridge.