7 décembre 2023
Ce document est lié à :
info:eu-repo/semantics/altIdentifier/doi/10.1017/S0269889723000145
info:eu-repo/semantics/OpenAccess
Vincenzo De Risi, « Euclid's Fourth Postulate: Its authenticity and significance for the foundations of Greek mathematics », HAL-SHS : histoire, philosophie et sociologie des sciences et des techniques, ID : 10.1017/S0269889723000145
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.