PREFACE. Ix 



It is true this does not always happen to 

 the fearcher, or his contemporaries, nor 

 even, fometimes to the immediate fucceed- 

 ing generation ; but i am apt to think that 

 advantages of one kind or other always ac- 

 crue to mankind from fuch purfuits. Some 

 men are born to obferve and record what 

 perhaps by itfelf is perfedly ufelefs, but 

 yet of great importance, to another who 

 follows and goes a ftep farther ftill as ufe- 

 lefs. To him another fucceeds, and thus 

 by degrees ; till at laft one of a fuperior 

 genius comes, who laying all that has been 

 done before his time together brings on a 

 new face of things, improves, adorns, ex- 

 alts human fociety. 



All thofe fpeculations concerning lines 

 and numbers fo ardently purfued, and fo 

 exquifitely conduded by the Grecians ; 

 what did they aim at ? or what did they 

 produce for ages ? A little arithmetic, and 

 the firft elements of geometry were all 

 they had need of. This Plato aflerts, and 

 tho' as being himfelf an able mathematician 

 and remarkably fond of thefe fciences, he 



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