Why can E and I propositions be converted simply in Aristotelian logic?

In Aristotelian logic, to "convert" a proposition means to interchange its subject and predicate terms. Propositions of forms E (universal negative) and I (particular affirmative) are said to be converted "simply" (simpliciter) because the truth of the original statement necessitates the truth of the statement with the terms reversed.12

Specifically, the validity of this conversion relies on the following logical relationships:
* E propositions: If "no $\beta$ is an $\alpha$," it follows necessarily that "no $\alpha$ is a $\beta$."12
* I propositions: If "some $\beta$ is an $\alpha$," it follows necessarily that "some $\alpha$ is a $\beta$."12

In contrast, other forms do not allow for such simple conversion. An A proposition (universal affirmative) cannot be converted simply because "every $\beta$ is an $\alpha$" does not imply "every $\alpha$ is a $\beta$," requiring instead a "limited" conversion (per accidens) to a particular form. An O proposition (particular negative) cannot be converted at all, as the relationship between the terms does not hold when their order is reversed.132