ATTEMPTS AT ARITHMETISATION 235 



other than Sir Isaac Newton's method of differences ; 

 and it is well known, that if the differences are 

 diminished so as to vanish, their vanishing ratio 

 becomes that of fluxions " (p. 560), ''that his pre- 

 tended Residuai Analysis renders the investigations 

 more tedious and obscure than any other. " Landen 

 wrote a reply in the July number, from which 

 we quote only the part relating to the word 

 **function." Says Landen : ''He objects to prime 

 nuinber\ function, etc, as terms never heard before. — 

 Alas ! hovv egregiously does he betray his ignor- 

 ance ! " 



James G lenze ^ 1793 



205. James Glenie graduated from the University 

 of St. Andrews, and became a military engineer. 

 He was a prominent Fellow of the Royal Society of 

 London. In his Antecedental Calculus,^ 1793, he 

 begins with the statement, " Having, in a Paper, 

 read before the Royal Society, the 6th of March, 

 1777, and pubhshed in the Philosophical Trans- 

 actions of that Year, promised to deliver, without 

 any consideration of Motion or Velocity, a Geo- 

 metrica! Method of Reasoning applicable to every 

 purpose, to which the much celebrated Doctrine of 

 Fluxions of the illustrious Newton has been or can 



^ 7'he Antecedental Calculus^ or a Geometrical Method of Reasoning, 

 without any Consideratiojt of Motion or Velocity applicable to every 

 Purpose^ to which Fluxions have been or can be applied. By James 

 Glenie, Esq., M.A. and F.R.S. London, 1793. According to G. 

 Vivant! (see M. Cantor's Vorlesungen uber Geschichte der Mathematik, 

 voi. iv, Leipzig, 1908, p. 667), James Glenie (1750-1817) was an 

 artillery officer in the war of the American Revolution, later professor 

 of mathematics in the military school of the East India Company. 



