Between Theoretical and Practical Geometry: A New Interpretation of Heron's Metrica

Doctoral Dissertation uoadl:2337659 222 Read counter

Unit:
Department of History and Philosophy of Science
Library of the School of Science
Deposit date:
2017-12-12
Year:
2017
Author:
Touliatou Theodora
Dissertation committee:
Ιωάννης Χριστιανίδης, Καθηγητής, Τμήμα Ιστορίας και Φιλοσοφίας της Επιστήμης, ΕΚΠΑ
Δήμητρα Χριστοπούλου, Επίκουρη Καθηγήτρια, Τμήμα Μαθηματικών, ΕΚΠΑ
Θεόδωρος Αραμπατζής, Καθηγητής, Τμήμα Ιστορίας και Φιλοσοφίας της Επιστήμης, ΕΚΠΑ
Ευστάθιος Αραποστάθης, Επίκουρος Καθηγητής, Τμήμα Ιστορίας και Φιλοσοφίας της Επιστήμης, ΕΚΠΑ
Ευθύμιος Νικολαΐδης, Διευθυντής Ερευνών, Τομέας Νεοελληνικών Ερευνών, ΕΙΕ
Εμμανουήλ Πατηνιώτης, Αναπληρωτής Καθηγητής, Τμήμα Ιστορίας και Φιλοσοφίας της Επιστήμης, ΕΚΠΑ
Μιχάλης Σιάλαρος, Επίκουρος Καθηγητής, Τμήμα Ιστορίας και Φιλοσοφίας της Επιστήμης, ΕΚΠΑ
Original Title:
Μεταξύ Θεωρητικής και Πρακτικής Γεωμετρίας: Μια Νέα Ανάγνωση των Μετρικών του Ήρωνα του Αλεξανδρινού
Languages:
Greek
Translated title:
Between Theoretical and Practical Geometry: A New Interpretation of Heron's Metrica
Summary:
The present dissertation is a research project on the Mertrica, a work of Heron of Alexandria. Heron’s Metrica is one of the most important works of metrological content preserved by antiquity. It has a form of a series of problems accompanied by their solutions in the form of computational procedure. The development of a sequence of geometrical arguments related to, and preceding the computational procedure, which concludes the solution of each problem, is what differentiates the Metrica from other metrological treatises. The coexistence of geometrical demonstrative elements and arithmetical computations defines and classifies the Mertrica between the “theoretical” and “practical” geometry. This dissertation surveys the content of the Metrica and explores the role the geometrical component plays in each solution. The unfolding of the geometrical component, in the form of deductive reasoning, appertains to the classical demonstrative texts preserved by antiquity; so the geometrical component has been interpreted by some contemporary historians of mathematics as “proof” of the computational procedures. Then, focusing on this interpretive point, they claim that the crucial aim of Heron’s Metrica is the creation proper “demonstrative ground” for the justification of the computational procedures. Contrary to the above interpretation, we suggest that the geometrical discourse functions as a heuristic tool when looking for the appropriate computational procedures. The substantiation of this claim leads us to a new interpretation of the didactic dimension of Heron’s treatise, which consists of providing to the reader heuristic means by which he will be able to devise the appropriate computational procedures for solving metrological problems.
Main subject category:
Science
Other subject categories:
Mathematics
History
Keywords:
computational procedure, epilogismos, geometrical analysis, arithmetized geometry, heuristic character
Index:
No
Number of index pages:
0
Contains images:
Yes
Number of references:
189
Number of pages:
224

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