His mathematical work is worth special treat ment. lie began his work on the calculus (q.v.) about the time of his settling in Hanover in 1676, and two year?: later he had developed it into a fairly complete discipline. It was not, however, until six years after this that he published (1684) anything upon the subject. Two years earlier (1682) he and :\feneke flaunted the .leta Eruditorunt, and it was in this celebrated jour nal that most of his mathematical memoirs ap peared (1682-92). The first one on the new cal eulus was his Nora Methodus pro hnonnbs et Maximis (16S4). Newton (q.v.) had known and used the principles of the fluxional calculus as early as 1665, and hail made them public, al though not in print, in 1669. Leibnitz hail access to certain letters of Newton's in 1676. lie also had the oppo•timity of knowing of the theory when lie was in London in 1673, and with the mathenmtieal acquaintances he met there it might be expeetsd that the new theory would be discussed. ']'here is, however, no exact evidence That he knew anything of Newton's discovery at the time he began his own work. It should, how ever, be stated that the germs of the theory of the calculus are to be found in the works of Fermat. Wallis, and Cavalieri, all of which were well known at that time in the mathematical world.
The essential differences in the two systems lie in the notation and the method of attack. New ton used .r where Leibnitz used dx, and based his treatment on the notion of velocity of material substances where the latter proceeded from the concept of the infinitesimal. As mathematics developed. the differential notation proved greatly superior to the fluxional. and in the first quarter of the nineteenth century it was adopted in Eng land, as it had been adopted a hundred years earlier on the Continent. With this change of notation the so-called fluxional calculus dis appeared and the differential calculus took its place.
The further mathematical work of Leibnitz was not of a high order. His contributions to analytic geometry were noteworthy only for lay ing the foundation (1692) for the theory of envelopes, and for introducing the terms 'co ordinates' and 'axes of eoiirdinates! lie con tributed a little to the theory of mechanics, but his work was often inaccurate, and he made no great discoveries.
In addition to Leibnitz's works already re ferred to, special mention should be made of Syst('Ille ?IOU veau de la naPure (1665) ; Principes de be nature et de la grace ( 1719 ) ; Nou vet( ux CSSfilis SlI• l'entouleinent humain (1765) ; and it Collection of Learned Papers ll'hich Passed Between the Late :U•. Leibnitz and Dr. Clarke in the Years 171,3 and 1 716 (London, 1717). his Latin and French philosophical works have been many times collected, edited, and published. The of a complete edition of all Leib nitz's works was undertaken by Pertz. This edition, as it now stands, contains 4 vols. of history (Hanover, 1343-47) ; 7 vols. of mathe matics. edited by Gerhardt (Berlin and Halle, 1349-63) ; hut of the philosophical portion only one volume appeared. In the of Speculative Philosophy are to be found transla tions of the Nonadologie, and many of the tosser writings; and some of the important philosophi cal works have been translated by G. 1\1. Duncan (New Haven, 1390) ; the NoureauX essais by A. G. Langley (London, 1394) ; The illonadoloyy and Other Philosophical Writings, Eng. by R. Latta (Oxford, 1398).
The literature on Leibnitz is immense. The following works deserve special mention: Dill mann, Eine 7telle Darstellung der Leibnizschen MonadcnIchre ( Leipzig, 1891) ; Felierbaeli, Dar stellung, Entwirkelany und Kritik der Leilmix. schen Philosophic (Ansbach, 18:37 ) ; Non rrisson, La philosophic de Leibniz (Paris, 1860) ; R. Zimmermann, Leibnizx Monadologic (Vienna, 1847) ; 1\le•z. Leibnitz (London, 1884); Har nack, Leibnizs Berleutnimg in der fIcschiehte der ilathemalik (Stade, 18S7). See, also, History of Modern Philosophy (London, 1900), and Dewey, Leibnitz's New Essays Concerning the Iluman Understanding (Chicago, ISS8). Shiny biographies of Leibnitz have been written. Among these may he named Guhraue•, Gottfried Wilhelm Freiherr von Leibniz (Breslau, 1842 46; Eng. trans. Boston, 1845) ; Plleiderer, G. IV. Lcibniz, als Patriot, Staalsmann und Rildungstriiger (Leipzig, 1370).