Ménélaüs: un mathématicien proto-intuitionniste ?
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 i...
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Éditions Kimé
2025-06-01
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| Series: | Philosophia Scientiæ |
| Online Access: | https://journals.openedition.org/philosophiascientiae/4767 |
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| author | Roshdi Rashed |
| author_facet | Roshdi Rashed |
| author_sort | Roshdi Rashed |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6273e2f2a66449dc9cfb1034161571bb |
| institution | OA Journals |
| issn | 1281-2463 1775-4283 |
| language | deu |
| publishDate | 2025-06-01 |
| publisher | Éditions Kimé |
| record_format | Article |
| series | Philosophia Scientiæ |
| spelling | doaj-art-6273e2f2a66449dc9cfb1034161571bb2025-08-20T02:26:33ZdeuÉditions KiméPhilosophia Scientiæ1281-24631775-42832025-06-01292172410.4000/13yi3Ménélaüs: un mathématicien proto-intuitionniste ?Roshdi RashedThis 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.https://journals.openedition.org/philosophiascientiae/4767 |
| spellingShingle | Roshdi Rashed Ménélaüs: un mathématicien proto-intuitionniste ? Philosophia Scientiæ |
| title | Ménélaüs: un mathématicien proto-intuitionniste ? |
| title_full | Ménélaüs: un mathématicien proto-intuitionniste ? |
| title_fullStr | Ménélaüs: un mathématicien proto-intuitionniste ? |
| title_full_unstemmed | Ménélaüs: un mathématicien proto-intuitionniste ? |
| title_short | Ménélaüs: un mathématicien proto-intuitionniste ? |
| title_sort | menelaus un mathematicien proto intuitionniste |
| url | https://journals.openedition.org/philosophiascientiae/4767 |
| work_keys_str_mv | AT roshdirashed menelausunmathematicienprotointuitionniste |