{"title":"欧几里得第四公设:其真实性及其对希腊数学基础的意义。","authors":"Vincenzo De Risi","doi":"10.1017/S0269889723000145","DOIUrl":null,"url":null,"abstract":"<p><p>The Fourth Postulate of Euclid's <i>Elements</i> 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.</p>","PeriodicalId":49562,"journal":{"name":"Science in Context","volume":" ","pages":"49-80"},"PeriodicalIF":0.3000,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Euclid's Fourth Postulate: Its authenticity and significance for the foundations of Greek mathematics.\",\"authors\":\"Vincenzo De Risi\",\"doi\":\"10.1017/S0269889723000145\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>The Fourth Postulate of Euclid's <i>Elements</i> 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.</p>\",\"PeriodicalId\":49562,\"journal\":{\"name\":\"Science in Context\",\"volume\":\" \",\"pages\":\"49-80\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Science in Context\",\"FirstCategoryId\":\"98\",\"ListUrlMain\":\"https://doi.org/10.1017/S0269889723000145\",\"RegionNum\":4,\"RegionCategory\":\"哲学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2023/12/7 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"Arts and Humanities\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Science in Context","FirstCategoryId":"98","ListUrlMain":"https://doi.org/10.1017/S0269889723000145","RegionNum":4,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2023/12/7 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"Arts and Humanities","Score":null,"Total":0}
Euclid's Fourth Postulate: Its authenticity and significance for the foundations of Greek mathematics.
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.
期刊介绍:
Science in Context is an international journal edited at The Cohn Institute for the History and Philosophy of Science and Ideas, Tel Aviv University, with the support of the Van Leer Jerusalem Institute. It is devoted to the study of the sciences from the points of view of comparative epistemology and historical sociology of scientific knowledge. The journal is committed to an interdisciplinary approach to the study of science and its cultural development - it does not segregate considerations drawn from history, philosophy and sociology. Controversies within scientific knowledge and debates about methodology are presented in their contexts.