236 LIMTTS AND FLUXIONS 



be, applied ; and having taken notice of the same 

 Method, in a small Performance, written in Latin, 

 and printed the i6th of July, 1776, I now proceed 

 to fulfil my promise with as much conciseness as 

 perspicuity and precision will admit of." In his 

 A?itecedental Calculus^ p. io, he says of Newton : 

 * I am perfectly satisfied, that had this great Man, 

 discovered the possibility of investigating a general 

 Geometrica! Method of reasoning, without introduc- 

 ing the ideas of Motion and Time, ... he would 

 have greatly preferred it, since Time and Motion 

 have no naturai or inseparable connection with 

 pure Mathematics. The fluxionary and differential 

 Caculi are only branches of general arithmetical 

 proportion." 



Glenie speaks (p. 3) of '' the excess of the magni- 

 tude, which has to B a ratio having to the ratio of 

 A + N to B the ratio of R to Q (when R has to O 

 any given ratio whatever), above the magnitude, 

 which has to B a ratio having to the ratio of A to B 

 the same ratio of R to 0, is geometrìcally expressed 

 by " a complicated fraction vvhose denominator is 

 B(R-Q)/Q^ and whose numerator is the result of ex- 

 panding by the binomial theorem (A -f N)^^^ and 

 then subtracting A^^^ therefrom. 



A similar expression is given for the case in which 

 A — N takes the place of A + N: '*The excess of 

 the magnitude, which has to B a ratio, having to the 

 ratio of A to B the ratio of R to Q, above the magni- 

 tude, which has to B a ratio, having to the ratio of 

 A — N to B the ratio of R to Q, is geometrically 



