10 



Grease by the addition of the least part, it is in their nature» 

 therefore to be progressive, and since the grounds of com- 

 parison are innumerable, and the circumstances of relation 

 infinitely diversified, their progress knows np assignable li- 

 mit. If the extent of number considered in one direct line 

 transcend the utmost efi'orts of thought, and outstrip the- 

 Kiost rapid methods of calculation, what are we to think if 

 this infinity be propagated on every side by the inexhaustible 

 power of combination, each successive change presenting a 

 new order of the whole system, resolvable into an indetermit- 

 nate number of new dispositions among its elementary parts, 

 and every different mode of juxtaposition susceptible of an 

 endless variety of relations undiscovered during the contencb. 

 plation of former arrangements ? Again, if on account of 

 the innumerable variations in the length, the number,^ and 

 mutual inclination of lines and surfaces, pure geometEy ^one 

 afford such a vast field for speculation, that the human intel>- 

 lect, after having exspatiated there for near three thousand 

 years, finds still new tracts aboundiog in objects! unnoticed 

 by former inquiries, what bounds can now be prescribed to 

 diseo^very, when new and extensive principles have been 

 adopted, new modes of investigation applied, when regions, 

 hitherto unknown, even in name, or considered incapable of 

 being rendered subject to mathematical research, have been 

 added to the dominions of science ? In scientific subjects 

 every new discovery, however noble in itself, however admir- 

 able for the skill and ingenuity displayed in the research. 



