,ect. i] DISSERTATION SECOND. 35 



germs of the new analysis, and as being the work of men 

 always inspired by genius, sometimes warmed by opposi- 

 tion, and generally animated by the success which accom- 

 panied their researches. 



But we must now look at the original works of the 

 earliest inventor. Newton, besides his letters published in 

 the Commercium Epistolicum, is the author of three tracts 

 on the new analysis that have all been occasionally men- 

 tioned. None of them, however, appeared nearly so soon 

 as a great number of the pieces which have just been 

 enumerated. The Quadrature of Curves, written as early 

 as 1665 or 1666, did not appear till 1704; and though it 

 be a treatise of great value, and containing very impor- 

 tant and very general theorems concerning the quadrature 

 of curves, it must be allowed, that it is not well adapted 

 to make known the spirit and the views of the infinitesi- 

 mal analysis. After a short introduction, which is indeed 

 analytical, and which explains the idea of a fluxion with 

 great brevity and clearness, the treatise sets out with pro- 

 posing to find any number of curves that can be squared ; 

 and here the demonstrations become all synthetical, with- 

 out any thing that may be properly called analytical in- 

 vestigation. By synthetical demonstrations I do not mean 

 reasonings where the algebraic language is not used, but 

 reasonings, whatever language be employed, where the 

 solution of the proposed question is first laid down, and 

 afterwards demonstrated to be true. Such is the method 

 pursued throughout this work, and it is wonderful how 

 many valuable conclusions concerning the areas of curves, 

 and their reduction to the areas of the circle and hyper- 

 bola, are in that manner deduced. But though truths can 

 be very well conveyed in the synthetical way, the methods 

 of investigating truth are not communicated by it, nor tne 

 powers of invention directed to their proper objects. As 



