ATTEMPTS AT ARITHMETISATION 229 



the Ultimator of the Abscissa is to the Ultimator of 

 the Semiordinate ; so is the Semiordinate itself to 

 the Subnormal " (p. 51). 



The author has occasion to use second and third 

 ultimators afid to consider ultimators as variable or 

 invariable. He lets (p. 60) i'° be the invariable of 



the first ultimator ;ir°, x the invariable of the second 



ultimator x^ etc. , and warns the reader that his 

 dot does not mean a fluxion. In the more involved 

 applications to curves he lets an infinitely small arch 

 equal ;ir° = i-°. Our impression of the book is that 

 the author's intentions were good when he attempted 

 an arithmetisation. But there is a total lack of clear 

 and rigorous exposition. 



200. The Ladies' Diary^ London, 1750, p. 45, 

 contains a hostile criticism of the Doctrine of 

 Ultimators by an anonymous writer (probably the 

 editor, Robert Heath), in which the author of this 

 doctrine is said to declare that fluxions, as explained 

 by Newton, are " absurd and unintelligible," and to 

 place confidence in '* the Authority of a certain Irish 

 B — p, a Mathematician as wise as himself. For 

 you must know that this pious B — p (the sagacious 

 Author of the Analyst, as he stiles him) out of his 

 religious Zeal against Mathematical Learning, had 

 been engaged in the same senseless Attempt with 

 himself, of degrading the noblest Science. . . . 

 Having thus, as he [the author of ''Ultimators"] 

 thinks, overturn'd the Doctrine of Fluxions . . . 

 he has given us instead of it . . . a new Science of 



