The popular explanations of Maclaurin, Pemberton, and Voltaire are too widely known to need description ; they do not much help the mathematical student. Many so-called explanations of Newtonian philosophy (such as Benjamin Martin's, 1751) are literally nothing but treatises on general physics.
The additions to Madame du Chastelleee translation consist of a popular resume and the mathematical treatment of various questions of the Prineipia. The latter must be considered as emanating from Claimant, since they were his lessons to his pupil. Some have supposed that Voltaire's work belongs in the same sense to Madams du Chastellet.
In the '316canique Mesta,' book 16, cap. 2, Laplace has exhibited the results of Newton's lunar theory, and connected them with the modern analysis of the subject to a certain extent. The preciseness of the manner of compressing Newton's results renders this chapter valuable, and likely to assist the student of the Principia.
Mr. Airy's development and extension of the results of the eleventh section (which forms the article GRAVITATION in this work) places one of the methods of the Principia, and one which ought to last, within the reach of every student. It is unique, the difficulties of the eleventh section having left it almost without a commentator, and altogether without an explainer ; and it takes in several of the dis coveries of the present time.
Many commentaries on the Principia have been written at Cambridge by private tutors for the use of their pupils, of which some have been printed. Of the following we have never seen more than the title : ' Excerpts quadam e Prim. Phil. Nat., cum notis variorum,' Cambridge, 1765. There is Carr's three sections of Newton, a modern work, and an exposition of various parts of the Principia contained in the second edition of Professor W'hewell's Dynamics' We believe that several recent Cambridge works contain some help on the subject.
To give a view of the foreign objections to Newton's system, at the time of its first introduction, the following works may serve: 1, Collection of Papers which passed between Mr. Leibnitz and Dr. Clarke, in 1715 and 1716,' by Dr. Samuel Clarke ; Loudon, 1717. 2, ' Traitk de Felix entre Des Cartes et Newton,' by the Jesuit Aim:5 Henri-Paulian ; Avignon, 1763. 3, Le vrai Systkme de Phyaiquo Onerale de M. Isaac Newton, expossi et analysti en parallel° avec eclui de Des Cartes,' by the Jesuit Louis Castel ; Paris, 1743 (a defence of Descartes). 4, ' Anti-Newtonianismus,' by Cclestini Cominale, 31.D.; Naples, 1754. 5, Discours sur les diff6rentes Figures des Astres, by 31aupertuis, the first assertor of Newton's doctrines in France; Paris, 1732, and in the collection of his works. 6, 'Letters to a German Princess,' by Euler (first published in 1770, translated into English by Dr. H. Ilunter, 1795).
Tho moat celebrated comments in the way of objection are those of Lansein, Jona BERNOULLI, and Iltiveneas (see Moo. Div.]; the first and third real admirers of the genius of Newton, the second also an admirer after his fashion. Many of their remarks may be found in the published correspondence of the first two, but the history of the effect produced by the Prineipia in the years following its publication is scattered in too many places for us to attempt to give the particular publications which should be consulted.