Terugverwijzingen en nieuwe stappen in Griekse wiskundige bewijzen

Both δέδεικται and ἐδείχθη are used by Greek mathematical authors in their proofs to refer to something that has already been proved. In this master’s thesis, the use of the passive aorist and the middle perfect in ancient Greek mathematical texts is discussed. The modern interpretations of the verbal aspects in (literary) Greek by Rijksbaron, Sicking and Stork serve as a theoretical framework. I intend to demonstrate that mathematical Greek, despite its dense, formulaic language, does follow the rules of Greek grammar that hold for conventional language use. This research focusses on metacommunicative verbs, that refer to the procedure of a proof, as opposed to verbs that are used in the construction of a diagram. The indicative forms and participles of a selection of verbs (δείκνυμι, ἐπιτάσσω, προτίθημι, εὑρίσκω, λέγω and δίδωμι) were analyzed in a confined corpus including works of Euclid, Archimedes, and Apollonius. The aim was to explain the distribution of the aorist and...Show moreBoth δέδεικται and ἐδείχθη are used by Greek mathematical authors in their proofs to refer to something that has already been proved. In this master’s thesis, the use of the passive aorist and the middle perfect in ancient Greek mathematical texts is discussed. The modern interpretations of the verbal aspects in (literary) Greek by Rijksbaron, Sicking and Stork serve as a theoretical framework. I intend to demonstrate that mathematical Greek, despite its dense, formulaic language, does follow the rules of Greek grammar that hold for conventional language use. This research focusses on metacommunicative verbs, that refer to the procedure of a proof, as opposed to verbs that are used in the construction of a diagram. The indicative forms and participles of a selection of verbs (δείκνυμι, ἐπιτάσσω, προτίθημι, εὑρίσκω, λέγω and δίδωμι) were analyzed in a confined corpus including works of Euclid, Archimedes, and Apollonius. The aim was to explain the distribution of the aorist and perfect forms. This analysis led to the conclusion that the aorist emphasizes the performed action and marks a new step in a proof. The perfect, on the other hand, stresses the attained result of an action and is therefore used to refer to a finished proof or a completed construction of figures. In the conclusion, a hypothesis will be offered on the interpretation of the perfect imperative, a heavily debated phenomenon that is frequently encountered in Greek mathematics.Show less

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Terugverwijzingen en nieuwe stappen in Griekse wiskundige bewijzen