All men are mortal (Major premiss).
Socrates is a man (Minor premiss).
Therefore: Socrates is mortal (Conclusion).
or
No Greeks are black, some men are Greeks,
therefore some men are not black.

Aristotle's doctrine of the syllogism was the beginning of formal logic. Aristotle was the recognized authority in logic for over two thousand years. He thought that by setting out any suggested argument in syllogistic form, it should be possible to avoid all fallacies.

It was not until the 20th century, that the philosopher Bertrand Russell discovered several formal errors in the doctrine of syllogism. (see Bertrand Russell 'History of Western Philosophy')