skct. i] DISSERTATION SECOND. 33 



first fluxions of any variable quantity, to constitute a new se- 

 ries of variable quantities flowing with velocities, the measures 

 of which form the fluxions of the second order, from which, 

 in the same manner, are deduced fluxions of the third and of 

 still higher orders. The general principles are the same as 

 in the fluxions of the first order, but the difficulties of the 

 calculus are greater, particularly in the integrations ; for to 

 rise from second fluxions to the variable quantities them- 

 selves two integrations are necessary ; from third fluxions 

 three, and so on. 



The tract which first made known the new analysis was 

 that of Leibnitz, published as already remarked, in the first 

 volume of the Acta Eruditorum for 1684, where it occupies 

 no more than six pages, 1 and is the work of an author not 

 yet become very familiar with the nature of his own inven- 

 tion. It was sufficient, however, to explain that invention to 

 mathematicians ; but, nevertheless, some years elapsed be- 

 fore it drew much attention. The Bcrnouliis were the first 

 who perceived its value, and made themselves masters of the 

 principles and methods contained, or rather suggested, in it. 

 Leibnitz published many other papers in the Acta Eruditorum 

 and the journals of the times, full of original views and im- 

 portant hints, thrown out very briefly, and requiring the elu- 

 cidations which his friends just mentioned were always so 

 willing and so able to supply. The number of literary and 

 scientific objects which divided the attention of the author 

 himself was so great, that lie had not time to bestow on the 

 illustration and developement of the most important of his 

 own discoveries, and the new analysis, for all that he has 

 taught, would have been very little known, and very imper- 



1 Nova Mclhodus pro Maximis et Minimis, &c. Leibnitfi Opera, 

 Tom. III. p. 167. 



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