P R E P A C Ee U 



•commend the ftudy of this Science to our mathematicians, that, in 

 order to make his demonftrations univerfal, he ufes letters as uni- 

 verfal charaders, (landing for all kinds of terms or propofitions. 

 Such fymbols are ufed by algebraifts, as is well known, and alfo by 

 Euclid in his feventh Book, where he treats of numbers: And 

 however intricate all this bufmefs of the Syllogifm may appear, it 

 is reducible to this fimple axiom, Tbai the whole is greater than any 

 of Its parts, and contains them all; the necelTary confequence of 

 which is, that if any, thing contain the whole of another thing, it 

 muft contain all the parts of that other thing ; and if, on the con- 

 trary, it do not contain but exclude the whole of that other thing, 

 it muft necelTarily exclude every part of it. This axiom, which, 

 thus explained, applies both to affirmative and negative conclufions 

 of Syllogifms, is fhortly thus expreffed by the fchoolmen : ^od 

 verum eji de toto, verum cjl de omni *. This fyftem therefore of 

 Ariftotle has the greateft beauty that any fyftem of Science can have, 

 viz. that though it be fo various in its confequences, it is moft 

 fimple in its principles. 



To prove how ufeful this Sylloglftical Art is, in trying the force 

 of every argument, and evolving the moft intricate and perplexed 

 ratiocination, and to explain how every kind of Reafonlng is redu- 

 cible to the form of Syllogifm, and to fhew that even the Mathema- 



h 2 ^ical 



« The way that Ariftotle expreffes this fundamental principle of the Syllogifm is as 

 follows : *OAco? y«p o' ^r^ l<rVy cJf o^ov Trpo; ^fpof, >ca. «AAo Trpof touto cJ? (Mifoa Trpof 

 iUv, il lvSiVO<: tm To.ouTwv SuHVMtTiv H Jf.Kvuo,!;, cvh yocf yi\^xi <TvXXoyi(ri^cc.-^ 

 (Analytka Priora, Lib. I. Cap. 41.) The meaning of which is, » That where there 

 « is not one thing that has the relation of IVhole and Part to another thing, and where 

 « that other thing has not the relation to a third thing of Part to mote, there can be 



« no Syllogifm." Or, as Philoponus has cxprefTed it, " The greater term muft 



« comprehend the middle, and the middle the leffer." See his Commentary upon the 

 firft Book of the Firjl Analytks^ Folio 86. 



