Purpose of this chapter

The second and third editions of the Principia appeared in 1713 and 1726 respectively. The emendation and variations between these editions are remarkable and have been studied in detail by scholars such as Hall and Cohen. However, in broad outline, the structure of the first edition remained unaltered. The number and order of the propositions, as well as the methods of proof, remained almost unchanged.

Thanks to the recent edition of Newton's Mathematical Papers, we now know that more radical restructurings were considered from the early 1690s up to the late 1710s. Despite the fact that nothing of these projects appeared in print during Newton's lifetime, it is interesting to consider them since they reveal Newton's evaluations of his own mathematical methods for natural philosophy. For instance we know of projects of gathering all the mathematical Lemmas in a separate introductory section. From David Gregory's retrospective memorandum of a visit he paid to Newton in May 1694 we learn about projects of expanding the geometrical Sections 4 and 5, Book 1, into a separate appendix on the ‘Geometria Veterum’, and of adding a treatise on the quadrature of curves as a second mathematical appendix in order to show the method whereby ‘curves can be squared’. In 1712 Newton was still thinking of adding a treatise on series and quadratures as an appendix to the Principia.