The logic rule `by contrapositive' and the Elements of Euclid (Q2717921)

In the study under review, the author analyzes, starting from Euclid's \textit{Elements}, some mathematical cases in which the demonstration of a certain theorem involves also -- likewise -- its reverse formulation, i.e., its contrapositive.NEWLINENEWLINENEWLINESeveral examples, taken especially from Book 1 of the \textit{Elements} are discussed in detail, the evaluation of each one's contrapositive being attempted. The conclusion reached by the author is that, in some situations, the contrapositive belongs to/is part of a more complex formulation while, in other cases it is quite different from the starting point of the theorem, or it is simply self-consistent. Euclid himself did not even try to demonstrate the contrapositive formulations of all his theorems, which he considered equivalent to the former ones and, consequently, theorems as such themselves. He formulated such theorems only when they could have been further utilized in their very same form.NEWLINENEWLINENEWLINEAll in all, this very interesting direction of theoretical research may be considered as anticipating and laying the foundations of a modern branch of logic -- mathematical logic.