third one 'THE CONCLUSION' and the whole set 'A SYLLOGISM'.

Evidently, ONE of the Attributes must occur in both Premisses; or
else one must occur in ONE Premiss, and its CONTRADICTORY in the
other.

In the first case (when, for example, the Premisses are "some m
are x" and "no m are y'") the Term, which occurs twice, is called
'THE MIDDLE TERM', because it serves as a sort of link between the
other two Terms.

In the second case (when, for example, the Premisses are "no
m are x'" and "all m' are y") the two Terms, which contain these
contradictory Attributes, may be called 'THE MIDDLE TERMS'.

Thus, in the first case, the class of "m-Things" is the Middle
Term; and, in the second case, the two classes of "m-Things" and
"m'-Things" are the Middle Terms.

The Attribute, which occurs in the Middle Term or Terms, disappears
in the Conclusion, and is said to be "eliminated", which literally
means "turned out of doors".

Now let us try to draw a Conclusion from the two Premisses--

"Some new Cakes are unwholesome;
No nice Cakes are unwholesome."

In order to express them with counters, we need to divide Cakes in
THREE different ways, with regard to newness, to niceness, and to