Robert Hatch

1. The ‘usual’ example of the ‘Barbara’ syllogism:
   
   All men are mortal,
   Socrates is a man,
   therefore
   Socrates is mortal.
   
2. Another (inference) form:
   
   All men are mortal,
   All Greeks are men,
   therefore
   All Greeks are mortal.
   
3. The same, in the form of an implication:
   
   If all men are mortal
   and all Greeks are men,
   then all Greeks are mortal.
   
4. Generalized:
   
   If all B is A
   and all C is B,
   then all C is A.
   
5. The actual Aristotelian syllogism:
   
   If A is predicated of all B
   and B is predicated of all C,
   then A is predicated of all C.
   

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A thorough discussion of Aristotle’s logic may be found in:
Jan Lukasiewicz. Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic. Oxford, 1951.