lit PREFACE. 



tical Reafonlng is fyllogiftical, and all the fteps of Euclid's demon- 

 ftrations arc fo many Enthymcma's, or imperfed Syllogifms, of 

 which one of the Propofitions, though abfolutely neceifary for the 

 conclufion, is not thought neceflary to be exprefled *, would much 

 exceed the bounds of a Preface, and would lead me too far from 

 what I chiefly propofed, which is to give the Hiftory of Antient 

 Philofophy, I will therefore confine what I have further to fay upon 

 the fubjedl of Syllogifra to two obfervations. 



The firft is, that the rules of the Syllogifm, v/hieh were formerly 

 fo well underftood by every man who pretended to learning, are 

 now fo little known, that though we ufe the fyllogiftical terms, and 

 talk of major and minor propofitions, yet we are not able to dif- 

 tinguifh them, but commonly call the firft propofition, according to 

 Gur manner of arranging them, the major propofition, though it be 

 truly the minor. Thus, when we fay^ 



Every man is an afiimal ; 

 Every animal is a fubjlance ; 

 Therefore every 7nan is a fubJlancCy 



We call the firft propofition the major,, whereas the fecond is truly 

 fuch ; becaufe in it the greater term or pnedlcate of the conclufion, 

 that \% fubjiancc^ is praedicated of the middle term animal \ and if 



V.'C 



* AriftoUe, in the firft Book of \i\% firji Jnalytics, Cap. 24, has taken the trouble 

 to fhew us, that all the ftens of a geometrical demonftration are Syllogifms of the kin.I 

 I have mentioned : For this purpofe he has given us a curious demonftration of the 

 fifth propofition of the firft Book of Euclid ; but it is fo fhortly exprefled, and fo ob- 

 fcurely for want of a diagram, that I fhoukl not have underftood it, if it had not beerj 

 explained by his comm.entator Philoponus, vi^ho has fupplied the diagram (Folio 62, 

 of his Commentary upon Ariftotle's Firji Analytics). But now I underftand it, I find is 

 is much fliorter, and, I thiiik, it is full as clear as that of Euclid, and therefore a bet- 

 ter demonftration. 



