I 



of Infinitesimals in England. 325 



with LeibuitZj the relation of the infinitely small increments is 

 itself the object of determination. That the difference between 

 the two did rest mainly upon a difference in the idea generationis 

 quantitatum is perfectly true : the fault to be found vtdth the 

 alteration of the scholium is that the reader is left to infer that 

 the difl'ereucc of the ideas of generation of quantity vras as visible 

 to Newton as the difference of symbols^ from the moment 

 when he received Leibnitz's communication. This might easily 

 have escaped notice in making the alteration. The fluxional 

 idea was not, so far as I can find, in the mind of Cavalieri, Fer- 

 mat, or Leibnitz : I shall have occasion elsewhere to notice its 

 occurrence among the schoolmen. 



Before 1693, no one could know anything of Newton's flux- 

 ions except from private communication. Before 1704, no one, 

 except in the same way, could know that Newton jireferred the 

 method of limits to that of infinitesimals, in algebraical calculus. 



Of the English contemporaries of Newton, the first who wrote 

 on the differential calculus of Leibnitz was John Craig, This 

 writer, though in one* respect of absurd memory, had original 

 power, and capacity for assimilating the various apparently dif- 

 ferent systems of the day. His earliest work was Methodas 

 Figurarum .... Quadraturas determinandi, London, 1685, 4to 

 (pp. iv-|-43 + i(plate)). Some additions are made to this tract 

 in the Phil. Trans. Nos. 183 and 232. In the preface of 1718 

 (presently mentioned), Craig informs us that in 1685 he was a 

 resident t at Cambridge, and that Newton, at his request, read 

 his writing before it was sent to press. Here, however, we shall 

 see reason to think that lie spoke of the wrong tract. After 

 some exemplifications of Barrow and Sluse — not referring to 

 Newton as having any method of quadratures, but only as to 

 the binomial theorem — he proceeds to say that nothing is want- 

 ing to extend his method to all but transcendental curves, except 

 only the removal of two difficulties. The first difficulty is the 

 extraction of roots, which he gets over by a series of Newton's, 

 which he hears that Dr. Wallis has sent to })ress, but which New- 



* In 1 r)99 lie published his Theologias Christians Principia Mathematica, 

 an ill-judged imitiition of Newton's title, in which he calculates that the 

 evidence of Christianity will be reduced to nothing by lapse of time in 

 A.D. .3i.'30, at which time therefore a renewal of revelation will take place. 

 Craig is now better kno^^■n by this tract (which is said to have been rei)ub- 

 lished and answered in Germany as late as 1755) than by his other writings. 



t Cantahrifjiat commnratus means, I suppose, that he was a member of 

 the University; but I cannot find his name in tlie list of graduates. He 

 was afterwar(ls a clergyman in Dorsetshire, and was a Scotchman by birth. 

 His diocesan was Burnet, to whom he expresses unusual obligation : and 

 Burnet's son, who was afterwards a member of the Comm. Epist. Com- 

 mittee, was his pupil. 1 cannot (ind the date of his death, but by the list 

 of subscribers to De Moivre's Misc. Amilyt. 1 sec that he was alive in 17-W. 



