Ménélaüs: un mathématicien proto-intuitionniste ? - Roshdi Rashed (Philosophia Scientiæ)
This article aims to highlight certain salient points from the Sphaerics of Menelaus, of which we have published the Arabic versions (see Menelaus’ Spherics: Early Translation and al-Māhānı̄/ al-Harawı̄’s Version. Edition, translation and commentary, Berlin; Boston, 2017). We will see how Menelaus is fully aware that he is inventing a new type of geometry which entails two fundamental decisions. These are the axiomatic decision to suspend Euclid’s fifth postulate and the logical decision to suspend the use of the excluded middle. Menelaus specifically states that he will not resort to reasoning by absurdity in his argument, which marks a date in the history of mathematics. Does this undeniable proto-intuitionist tendency make Menelaus an intuitionist mathematician in the modern sense? Not completely, since we can observe the underlying presence, here and there in his treatise, of a classically Euclidean mode of demonstration.