LEIBNIZ IIS 



about it from any side up to that time. Leibniz also 

 contented himself, like Newton before him and as was com- 

 mon among learned men of the time, with communications 

 to smaller circles, to London and of course in Paris; his first 

 printed publication of the differential calculus, 'a new 

 method for maxima, minima and tangents, which avoids 

 fractional and irrational quantities, and a peculiar method 

 of calculation relating to these,' appeared in 1684. 



Here we have for the first time the method, which quickly 

 became general, of describing infinitely small quantities 

 (diff'erentials); the rules of differentiation are developed, 

 which to-day belong to the fundamentals of higher mathe- 

 matics. This terminology was the secret of the easy applic- 

 ability of the new method of calculation. Leibniz says him- 

 self on this point in a letter of 1678, that terminological 

 expressions in mathematics are most helpful 'when they ex- 

 press the inmost nature of the matter shortly, and as it were 

 give a picture of it.' Tn this way the labour of thought is 

 reduced in a wonderful manner.' In actual fact, mathe- 

 matics, as far as it serves natural science, has the task of 

 keeping the labour of thought directed entirely towards 

 discovering the inmost nature of things, and then of forming 

 such an image of the discovery, that it is preserved faithfully 

 and unfalsified by means of the rules of calculation, and can 

 assume almost any desired variety of forms, which are 

 necessary for its application in complicated cases. ^ 



Leibniz was soon interrupted in the prosecution of his 

 mathematical labours by again entering into active political 

 work. The Kurfiirst of Mainz, in whose service Leibniz 

 had hitherto been, died in the year 1673. Three years later, 



^ It happens in the case of more recent applications of mathematics 

 that the labour of thought has been directed not so much to the discovery 

 of the actual behaviour of nature, as rather to arbitrary interference with 

 the course of calculation, whereby the picturing of the inmost nature of 

 the thing can only be falsified. This is obviously a misuse of the ad- 

 vantage of reduction of the labour of thought, since what has been saved 

 is applied at the wrong point. 



