i PREFACE. 



jnore. — It is fhewn, that of thcfe three terms there Is one by which 

 the two terms in the conclufion are fyllogifed or brought together, 

 and which, from thence, is called the Middle Term — That in the two- 

 Proportions this term muft one way or another be joined with each, 

 of the two terms of the conclufion, and this can be done only in 

 one or other of three ways, by being the prasdicate of both Propo- 

 fitions, the fubjed; of both, or, laftly, the praidicate of the one 

 and the fubjed of the other *. Thefe three feveral ways of conned- 

 -ing the terms of the conclufion by means of the middle term Ariftotle 

 calls Figures, alluding, as his Commentators fay, to the divifion ufed 

 by the mathematicians of the fubjeds of their Art, into Points, 

 Lines, and Figures, fimple terms {landing for Points, proportions 

 for Lines, and fyllogifms for Figures — It is further fhewn, that thefe 

 Figures are divided into Moods, according as the two proportions and 

 conclufion of the fyllogifm are affirmative or negative, univerfal or 

 particular ; the firft Figure confiiling of four Moods, the fecond of as 

 many, and the third of fix, which make altogether fourteen Moods, or 

 T^cTTo;, as they are called by Ariftotle — And laftly, that of every fyllo- 

 gifm one of the two propofitions or premifes muft neceffarily be a ge- 

 neral propofition either affirmative or negative ; and that from two 

 particular propofitions, or two negative, whether general or particular, 

 nothing can be fyllogifed. 



If I fhould go deeper into this Syllogiftical Art, very few of my 

 Readers, I doubt, could follow^ me : I wuU therefore content myfelf 

 with obferving, that Ariftotle demonftrates all his theorems in the 

 manner of geometers, either diredly or ex ahjiirdo ; and he ufes a 

 tliird method which is peculiar to Logic, I mean the converfion of 

 propofitions, by which he demonftrates, that one kind of propofition 

 is convertible into another of a different kind j and it fliould re- 

 commend 



* Of Propofitions in general, and the difference betwixt the prsedicate and fubjec 

 fee what I have faid, Vol. I. Mctaphyf. p. 375, et feq. 



