Two Traces of Two-Step Eudoxan Proportion Theory in Aristotle: a Tale of Definitions in Aristotle, with a Moral

Mendell, Henry

doi:10.1007/s00407-006-0114-8

Cited by 38 publications

(3 citation statements)

References 10 publications

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“…35 Although Ṭūsī makes no mention of any textual basis for the lemma in his edition, its similarity with the Greek version indicates that it was probably based on some transmission of this proof into the Arabic tradition. On the other hand, there are some differences of conception and approach between the Greek scholium and Ṭūsī's insertion that may indicate that he, or someone before him in the Arabic transmission, 31 Knorr (1978); Mendell (2007). 32 Heiberg (1910Heiberg ( -1915.…”

Section: Lemma To Spher III 10mentioning

confidence: 99%

Naṣīr al-Dīn al-Ṭūsī’s revision of Theodosius’s Spherics

Sidoli¹,

Kusuba²

2017

New Perspectives on the History of Islamic Science

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We examine the Arabic edition of Theodosius's Spherics composed by Naṣīr al-Dīn al-Ṭūsī. Through a comparison of this text with earlier Arabic and Greek versions and a study of his editorial remarks, we develop a better understanding of al-Ṭūsī editorial project. We show that al-Ṭūsī's goal was to revitalize the text of Theodosius's Spherics by considering it firstly as a product of the mathematical sciences and secondarily as a historically contingent work. His editorial practices involved adding a number of additional hypotheses and auxiliary lemmas to demonstrate theorems used in the Spherics, reworking some propositions to clarify the underlying mathematical argument and reorganizing the proof structure in a few propositions. For al-Ṭūsı, the detailed preservation of the words and drawings was less important than a mathematically coherent presentation of the arguments and diagrams. 1 A list of Ṭūsī's editions is given by Krause (1936a, 499-504). 2 See Lorch (1996, 164-165) for a stemma of the early Arabic versions. 3 See al-Ṭūsī (1940a); Aghayanī-Chavoshī (2005). For Ṭūsī's revision of Theodosius's Spherics, the text in T. 3484 occupies pp. 23-56 but the beginning of the treatise is in disarray.

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Section: Lemma To Spher III 10mentioning

confidence: 99%

Naṣīr al-Dīn al-Ṭūsī’s revision of Theodosius’s Spherics

Sidoli¹,

Kusuba²

2017

New Perspectives on the History of Islamic Science

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“…for a similar passage in the Metaphysics, see PRITCHARD 1997. On Aristotle and the theory of proportions, see MENDELL 2007 andRABOUIN 2016. On Eudoxus' theory of proportions, see the classic KNORR 1975.…”

Section: §1 Introduction: Common Axioms and Universal Sciencementioning

confidence: 99%

Aristotle on Common Axioms

Risi

2022

Thinking and Calculating

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Aristotle claimed that each science is grounded in principles that are proper to it. He also recognized, however, the existence of principles that are common to many sciences, that he called axioms. The sources of Aristotle's theory of axioms seem to have been both philosophical and mathematical, and the outcomes of the theory are some very refined views on the analogy between different scientific domains, and possibly a theory of nonsyllogistic inferences. I sketch here Aristotle's theory of axioms, its motivations, its developments, and its applications to the theory of science. Finally, I offer a tentative interpretation of axioms that may shed some light on several open interpretative questions in Aristotle's epistemology.

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“…See also Vitrac, 1990Vitrac, -2001, for a hypothetical reworking of Elements VI, 33 along these lines, and 525-26 for an appraisal of Knorr's thesis (Vitrac thinks that the alternative proportion theory is in fact Archimedean and post-Euclidean). Further arguments are provided in Saito 2003 andMendell 2007, which distinguish the theory of proportions of Book V from the techniques used in Book VI of the Elements.…”

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confidence: 99%

Euclid’s Fourth Postulate: Its authenticity and significance for the foundations of Greek mathematics

De Risi

2022

Sci Context

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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.

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Two Traces of Two-Step Eudoxan Proportion Theory in Aristotle: a Tale of Definitions in Aristotle, with a Moral

Cited by 38 publications

References 10 publications

Naṣīr al-Dīn al-Ṭūsī’s revision of Theodosius’s Spherics

Naṣīr al-Dīn al-Ṭūsī’s revision of Theodosius’s Spherics

Aristotle on Common Axioms

Euclid’s Fourth Postulate: Its authenticity and significance for the foundations of Greek mathematics

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