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The main purpose of the present volume is to discuss, and to make generally accessible, three dissertations1 by the Scottish mathematician Colin MacLaurin (1698–1746), who was regarded both in Britain and in continental Europe as one of the leading mathematicians of his time.

On 23 June 1713, at the age of 15, Colin MacLaurin graduated with the degree of Master awarded by the Faculty of Arts of the University of Glasgow [62]. As part of the requirements for this degree he presented and defended in public his dissertation, De Gravitate, aliisque viribus Naturalibus , which is the first item in this book. As far as I have been able to ascertain, candidates were not required to submit their work in printed form. It is likely therefore that MacLaurin had his dissertation printed with a view to its later use in the advancement of his career; indeed, it was probably submitted in support of his application for the Chair of Mathematics at Marischal College, Aberdeen, which he successfully contested in August—September 1717.^15 The dissertation is affectionately dedicated to MacLaurin’s uncle, the Reverend Daniel McLaurin, who was a father-figure to his growing nephew (see Appendix I.2, p. 32).^16

I. Among the various phenomena of corporeal nature, there are two, which, as they are very greatly distinguished almost before all others, having been examined in themselves, have occupied to a very great extent the philosophers of all time. One of these is that general tendency towards its centre of all bodies moving about the surface of the earth, which is commonly called gravity; the other is the regular gyration of planets in their orbits, which recurs with definite periods. Various hypotheses have been devised by various people for the explanation in mechanical terms of those phenomena. An impartial examination of these will prepare the way for explaining and developing that general law of universal gravitation, to which, it will be established, those two most noble effects are to be referred as a common foundation, even if at first sight they seem to have nothing in common; from this we will also seize the opportunity to consider along the way certain other forces of nature, which it is necessary to put in place for the solution of certain other phenomena, which philosophers have undertaken to explain likewise by mechanical theories.

The prize-essay topics proposed by the Royal Academy of Sciences in Paris for the years 1724 and 1726 were concerned with the collision of bodies: in the competition of 1724^24 the bodies were to be perfectly hard and the prize was won by MacLaurin for his essay [66], with which this article is concerned; elastic bodies were to be considered for 1726, when the winning essay was that of Père Maziere, described as Prêtre de l’Oratoire [76]. In a Notice prefixed to the published version of MacLaurin’s essay (see Appendix II.1, p. 79) it was stated on behalf of the Academy that many of the submissions, while excellent in themselves, had not dealt with the topic as proposed. Amongst these was an extensive work by Jean Bernoulli, which had apparently been submitted in both 1724 and 1726 and had been praised on both occasions. Bernoulli’s essay [13] was also published in the volumes containing the prize essays [1]; one reason for this may have been the desire to present both sides of an on-going controversy concerning the force of a moving body (see below). In fact, MacLaurin had also transgressed the limits of the proposed question, dealing not only with the collision of perfectly hard bodies but also with cases of elastic collisions.

The prize topic proposed by the Royal Academy of Sciences for 1740 was the tides: le Flux et Reflux de la Mer . The winners, in the order in which their essays were published by the Academy, were Father Antoine Cavalleri [23], Daniel Bernoulli [12], Colin MacLaurin [68] and Leonhard Euler [38]. Cavelleri’s work was based on the Cartesian idea of vortices;47 the other three were founded on Newtonian principles and were subsequently reproduced in the “Jesuit Edition” of the Principia (1739–1742) [86] as illustrations of the Newtonian philosophy. Newton had already discussed in its earlier editions the tidal forces on the Earth which resulted from the gravitational attraction of the Sun and of the Moon; his work was of course the starting point for MacLaurin’s investigations.