CHAPTER IX 

 ABORTIVE ATTEMPTS AT ARITHMETISATION 



John Kirkby, 1748 



198. In the preface to his Doctrine of Ultirnators ^ 

 the author states that his doctrine **depends upon 

 scarce any Thing else but a due Application of the 

 Cypher to the analogous Office in Universal 

 Arithmetic, which ìt is always known to occupy in 

 Common Arithmetic." He argues that -'the super- 

 lative impropriety of the Word Fluxion, when 

 applied to this Purpose, will fully appear ; when we 

 come to consider, that it is put to express an Idea, 

 which arises from the Contemplation of Ouantities 

 purely as Quantities : that is, in the same abstract 

 Manner, as they are the proper Subject of Algebra, 

 exclusive of every other Considerati on ; and con- 



^ The Doctrine of Ultirnators. Containing a new Acquisition to 

 Mathematical Literature, naturally resulting from the Consideration of 

 an Equation, as reducible from its variable to its ultimate State : Or, a 

 Discovery of the true and genuine Foundation of what has hitherto mis- 

 takenly prevailed under the improper Names of Fluxions and the Differ- 

 ential Calculus. By means of which we now have that Apex of ali 

 Mathematical Science entirely rescued from the blind and ungeometrical 

 Method of Deduction which it has hitherto laboured under ; andmade to 

 depend upon Principles as strici ly demonstrable, as the most selfevident 

 Proposition in the first Elements of Geometry. By the Reverend Mr. 

 John Kirkby, Vicar of Waldershare in Reni. London, MDCCXLVIIl. 

 Pp. 144. 



225 15 



