  Aristotelian assertoric syllogistic, which is currently of growing interest,
has attracted the attention of the founders of modern logic, who approached it
in several (semantical and syntactical) ways. Further approaches were
introduced later on. These approaches (with few exceptions) are here discussed,
developed and interrelated. Among other things, different facets of soundness,
completeness, decidability and independence are investigated. Specifically
arithmetization (Leibniz), algebraization (Leibniz and Boole), and Venn models
(Euler and Venn) are closely examined. All proofs are simple. In particular
there is no recourse to maximal nor minimal conditions (with only one,
dispensable, exception), which makes the long awaited deciphering of the
enigmatic Leibniz characteristic numbers possible. The problem was how to look
at matters from the right perspective.
