Search

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]