III. A Jhort Paper on the Principles of the Antecedental 

 Calculus. By James Glenie, E/qj M. A. F. R. S. Lond, 

 & Edin. 



[Read Dec. i. 1794.] 



SEVERAL of my friends have fuggefted to me the propriety 

 of publifhing fomething of the kind now offered to 

 the Society, obferving, that the great brevity with which the 

 Antecedental Calcidus is written, and the very concife form in 

 which it is deUvered to the ptibUc, may lead fome to form 

 erroneous opinions refpedling the principles on which it is 

 founded. In compliance partly with their requefk, I have 

 drawn up this fliort paper, which I hope will remove even the 

 poflibility of mifconception on that head, and convince every 

 intelligent reader, that the antecedental calculus has the fame 

 geometrical principles for its ground-work, that the formulae in 

 the Univerfal Comparifon themfelves ha^i-e, from which I origi- 

 nally derived it more than twenty years ago. 



In the third page of that treatife, I have fliewn from the 

 firft formula in the third theorem of my Univerfal Comparifon^ 

 that, when R and Q_are any two given magnitudes of the fame 

 kind, and A, N, B are any homogeneous magnitudes, the ex- 

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

 ratio of A-f-N to B the ratio of R to Q^ above the magnitude, 



Vol. IV. I which 



