Euclid’s Fourth Postulate
Its authenticity and significance for the foundations of Greek mathematics
Datos Bibliográficos
| ID | 11658293 |
|---|---|
| Autores | Vincenzo De Risi (0000-0003-3100-8411, methodS in Patient-centered outcomes and HEalth ResEarch, autor de correspondencia) |
| Año | 2022 |
| Volumen | 35 |
| Número | 1 |
| Páginas | 49-80 |
| Fecha de publicación | 2022-03-01 |
| Peer Reviewed | Sí |
| Open Access | Sí |
| Tipo | ARTICLE |
| Revista | Science in Context (JOURNAL) |
| Identificadores de la revista | ISSN: 0269-8897 • E-ISSN: 1474-0664 |
| Editorial | Cambridge University Press (CUP) (PUBLISHER) |
| DOI | 10.1017/s0269889723000145 |
| PMID | 38058179 |
| OpenAlex | W4389443948 |
| Idioma | EN |
| Citas recibidas | 2 |
| Referencias citadas | 43 |
Argument The Fourth Postulate of Euclid’s Elements states that all right angles are equal. This principle has always been considered problematic in the deductive economy of the treatise, and even the ancient interpreters were confused about its mathematical role and its epistemological status. The present essay reconsiders the ancient testimonies on the Fourth Postulate, showing that there is no certain evidence for its authenticity, nor for its spuriousness. The paper also considers modern mathematical interpretations of this postulate, pointing out various anachronisms. It further discusses the validity of the ancient proof by superposition of the Fourth Postulate. Finally, the article proposes an interpretation of the history of the concept of angle in Greek geometry between Euclid and Apollonius, and puts forward a conjecture on the interpolation of the Fourth Postulate in the Hellenistic age. The essay contributes to a general reassessment of the axiomatic foundations of ancient mathematics
Anachronism · Ancient Greek · Argument (complex analysis · Axiom · Calculus (dental · Conjecture · Epistemology · Geometry · Interpretation (philosophy · Interpreter · Linguistics · Pure mathematics · Computer Science · History and Theory of Mathematics · Law · Mathematics · Mathematics and Applications · Mathematics Education and Teaching Techniques · Philosophy
Uses of construction in problems and theorems in Euclid’s Elements I–VI
Were There Epicurean Mathematicians?
Mathematics in Aristotle
On Certain Mathematical Terms in Aristotle's Logic
Theory Change, Ancient Axiomatics, and Galileo’s Methodology
Two Traces of Two-Step Eudoxan Proportion Theory in Aristotle
The Shaping of Deduction in Greek Mathematics
The twofold role of diagrams in Euclid’s plane geometry
Translation and Transmission
Phantom Theories of pre-Eudoxean Proportion
Two Approaches to Foundations in Greek Mathematics
Minimal Parts in Epicurean Atomism
| Velocidad de citación | historical |
|---|---|
| Altamente citado | No |