32 DISSERTATION SECOND. [farti. 



utilissimum et generalissimum esse, sed etiam eorura quae in 

 geomefria scire unquam desideraveriin." l This passage is 

 not a little characteristick of Descartes, who was very much 

 disposed to think well of what he had done himself, and 

 even to suppose that it could not easily be rendered more 

 perfect. The truth, however, is, that his method of draw- 

 ing tangents is extremely operose, and is one of those hasty 

 views which, though ingenious and even profound, require 

 to be vastly simplified, before they can be reduced to 

 practice. Fermat, the rival and sometimes the superiour 

 of Descartes, was far more fortunate with regard to this 

 problem, and his method of drawing tangents to curves, is 

 the same, in effect, that has been followed by all the geome- 

 ters since his time, — while that of Descartes, which could 

 only be valued when the other was unknown, has been long 

 since entirely abandoned. The remainder of the second 

 book is occupied with the consideration of the curves, which 

 have been called the ovals of Descartes, and with some in- 

 vestigations concerning the centres of lenses; the whole in- 

 dicating the hand of a great master, and deserving the most 

 diligent study of those, who would become acquainted with 

 this great enlargement of mathematical science. 



The third book of the geometry treats of the construc- 

 tion of equations by geometrick curves, and it also contains 

 a new method of resolving biquadratick equations. 



The leading principles of algebra were now unfolded, 

 and the notation was brought, from a mere contrivance for 

 abridging common language, to a system of symbolical 

 writing, admirably fitted to assist the mind in the exercise 

 of thought. 



The happy idea, indeed, of expressing quantity, and the 

 operations on quantity, by conventional symbols, instead of 



1 Cartesii Geometria, p. 40. 



