III. A Jhort Paper on the Principles of the Antecedental 

 Calculus. By James Gleme^ Efqs M. A. F. R. S. Lond. 

 & Edin. 



[Read Dec. i. 1794.] 



SEVERAL of my friends have fuggefted to me the propriety 

 of pubUfhing fomething of the kind now offered to 

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

 Antecedental Calculus is written, and the very concife form in 

 which it is dehvered to the pubHc, may lead fome to form 

 erroneous opinions refpedling the principles on which it is 

 founded. In compliance partly with their requeft, I have 

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

 poilibility 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 formulse in 

 the Univerfal Comparifon themfelves have, from which I origi- 

 nally derived it more than twenty years ago. 



In the third page of that treatife, I have ihewn 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 



