NEWTON S PRINCIP1A. 7 



calculus somewhat of the relation which that bears to 

 the calculus of fixed and finite or unvarying quantities. 



It is wonderful how very near Bernouilli, when he 

 solved the problem of finding the line of swiftest 

 descent, came to finding out this calculus ; if, indeed, he 

 may not be said to have actually employed it when he 

 supposed, not as in the case of the differential calculus, 

 two ordinates of a known curve infinitely near one an 

 other, but three ordinates infinitely near, including two 

 branches of an unknown curve, each infinitely small ; 

 for he certainly made the relation of these ordinates to 

 the abscissa vary. Euler used the calculus more sys 

 tematically in the solution of various problems; but he 

 was much impeded for want of an algorithm. This 

 important defect was supplied by Lagrange, who reduced 

 the method to a system and laid down its general prin 

 ciples ; but had Euler gone on a little step further, or 

 had Bernouilli been bent on finding out a general method 

 instead of solving particular problems, or had Emerson, 

 who has one or two similar investigations in his book 

 on Fluxions, reduced the method by which he worked 

 them to a system by giving one general rule (which, writing 

 a book on the subject, he was very likely to have done), 

 the fame of that discovery would have been theirs, which 

 now redounds so greatly and so justly to the glory of 

 Lagrange. 



The discovery of Gravitation as the governing prin 

 ciple of the heavenly motions, is no exception to the rule 

 which we have stated of continuity or gradual progress. 

 When Copernicus had first clearly stated the truth to 

 which near approaches had been made by his pre 

 decessors, from Pythagoras downwards, that the planets 

 move round the sun, and that the earth also moves on 

 its axis while the moon revolves round the earth, he yet 



