112 GREAT MEN OF SCIENCE 



He developed the calculus of fluxions or infinitesimals. 

 This method of calculation, which was specially designed for 

 the prosecution of scientific investigation, and has become 

 fundamentally important for it, deals with infinitely small 

 quantities; Leibniz gave it the construction and form which 

 has remained fully adequate until to-day. In this mathe- 

 matical achievement lies his relationship to Newton; to 

 Guericke he is related by his extensive services to his coun- 

 try,^ and the latter were to him, as for Guericke, decisive as 

 regards his external life, his undertakings, and his manifold 

 travels. 



Leibniz was born in Leipzig; his father, whom he lost at the 

 age of six, was professor of moral philosophy at the Uni- 

 versity there, and at the same time a notary. In his earliest 

 years he already began to read in the library of his father, far 

 in advance of his school Latin, the old historians and classics 

 with great enjoyment, and at fifteen he entered the university 

 of his birthplace. Here, and then at times also in Jena, he 

 first turned to mathematics; Descartes and Euclid were his 

 studies, but he soon decided upon practical law as a career. 

 At nineteen years he obtained his doctorate in law, at Altdorf, 

 near Nuremburg, since his youth caused difficulties for him 

 in Leipzig. As in his schooldays, so at the University, he 

 made great progress, mainly by thinking for himself and 

 using books chosen by himself, in everything at that time 

 called science; he always arrived very quickly at the point 

 at which he was able to go beyond the limits of existing 

 knowledge on his own account, and he valued nothing 

 more highly than the power and freedom to do so, as opposed 

 to the advice frequently given that one should not attempt 

 to do something new in matters which one has not yet 

 studied fully. 



^ The latter are fully described in G. W. Leibniz, by Pfleiderer (Leip- 

 zig, 1870). There is an English biography of Leibniz by J. M. Mackay, 

 published in 1845. 



