Let B represent the middle term, C the minor term and A the major term. The third-figure arrangement is:
Minor premise: B — C
Major premise: B — A
Conclusion: Some C — A
The predicate C of the minor premise becomes the subject of the conclusion; predicate A of the major becomes its predicate.
In “All horses are animals,” animal is the minor term. In “All horses are living beings,” living being is the major term. The conclusion joins these predicates. A term’s role depends on the conclusion, not simply the order in which premises are written.