CHAPTER IX 
ABORTIVE ATTEMPTS AT ARITHMETISATION 
John Kirkby, 1748 
198. In the preface to his Doctrine of Ultimators 1 
the author states that his doctrine “depends upon 
scarce any Thing else but a due Application of the 
Cypher o to the analogous Office in Universal 
Arithmetic, which it 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 Quantities 
purely as Quantities : that is, in the same abstract 
Manner, as they are the proper Subject of Algebra, 
exclusive of every other Consideration ; and con- 
1 The Doctrine of Ultimators. 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 all 
Mathematical Science entirely rescued from the blind and ungeometncal 
Method of Deduction which it has hitherto laboured under ; and made to 
depend upon Principles as strictly demonstrable, as the most self-evident 
Proposition in the first Elements of Geometry. By the Reverend Mr. 
John Kirkby, Vicar of Waldershare in Kent. London, MDCCXLVIII. 
Pp. 144. 
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