How did Aristotle use variables in his logical arguments?

Aristotle was the first logician to utilize variables, an innovation that allowed him to achieve a high level of abstraction and generality in his syllogistic theory.12

In his term logic, Aristotle used variables as placeholders for terms or names within logical schemas. For example, in the schema "If every $\beta$ is an $\alpha$ and every $\gamma$ is a $\beta$, then every $\gamma$ is an $\alpha$," the Greek letters $\alpha$, $\beta$, and $\gamma$ function as variables. By replacing these placeholders with specific terms—such as "substance" for $\alpha$, "animal" for $\beta$, and "dog" for $\gamma$—one can generate a valid syllogism in the form known as Barbara.12

This systematic use of variables enabled Aristotle to define valid patterns of reasoning independently of the specific content of the arguments, establishing the foundation for deductive systems.123