The concept of given in Greek mathematics

Sidoli, Nathan

doi:10.1007/s00407-018-0211-5

Cited by 9 publications

(5 citation statements)

References 26 publications

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“…To begin with, Ptolemy's Almagest gives propositions such as those found in Euclid's Data a major role (Sidoli 2018). Does this practice come from Hipparchus' approach or not?…”

Section: Selectingmentioning

confidence: 99%

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Forward … to the nineteenth century: Historiographic concerns about Reviel Netz’s ‘The Place of Archimedes in World History’

Chemla

2022

Interdisciplinary Science Reviews

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In this response I argue that Netz' essay adopts nineteenth-century theses on the history of mathematics, one of the uses of which was to highlight an alleged difference between Europe and "the others". The debasement of certain facets of mathematical work devoted to numbers and computation has played a key role in perpetuating these theses. Such a devaluation applies notably to decimal place-value numeration systems, which Reviel perceives as representing no "significant contribution to mathematical science." I counter this view by showing the continued theoretical impact that numeration systems of this type have had. I also discuss two historiographic operations that I identify in Reviel's argument and whose use requires revision: selecting and purifying. My conclusion emphasizes how in the post World War II period historians such as Lucien Febvre invited their colleagues to focus, in contrast, on the hybrid character of cultural artefacts.

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“…To begin with, Ptolemy's Almagest gives propositions such as those found in Euclid's Data a major role (Sidoli 2018). Does this practice come from Hipparchus' approach or not?…”

Section: Selectingmentioning

confidence: 99%

“…In this respect, Ptolemy's Almagest can be compared with Hero's Metrica(Sidoli 2018;Cuomo 2019). 26 I thank Serafina Cuomo for this remark.…”

mentioning

confidence: 99%

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Forward … to the nineteenth century: Historiographic concerns about Reviel Netz’s ‘The Place of Archimedes in World History’

Chemla

2022

Interdisciplinary Science Reviews

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“…The thesis was argued in Sidoli's important paper (Sidoli 2018b, 422-23), which also offers in footnote 45 a subtle argument on how to transform the proof of Elements I, 46 in order to make P4 unnecessary in it, even though the procedure cannot be generalized (the footnote also claims, I think wrongly, that Elements I, 14 and 15 do not need P4). For a fuller treatment of the notion of givenness, see also Sidoli 2018a. conclude that two triangles having equal sides are equal. When Euclid further applies this theorem (for instance in Elements I, 9), the triangles under consideration are given in position in a certain configuration, and nonetheless Euclid does not hesitate to make use of Elements I, 8 to conclude the demonstration-and similarly in all other cases.…”

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confidence: 99%

“… 40 The thesis was argued in Sidoli’s important paper (Sidoli 2018b, 422–23), which also offers in footnote 45 a subtle argument on how to transform the proof of Elements I, 46 in order to make P4 unnecessary in it, even though the procedure cannot be generalized (the footnote also claims, I think wrongly, that Elements I, 14 and 15 do not need P4). For a fuller treatment of the notion of givenness, see also Sidoli 2018a.…”

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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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Uses of construction in problems and theorems in Euclid’s Elements I–VI

Sidoli

2018

Arch. Hist. Exact Sci.

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The concept of given in Greek mathematics

Cited by 9 publications

References 26 publications

Forward … to the nineteenth century: Historiographic concerns about Reviel Netz’s ‘The Place of Archimedes in World History’

Forward … to the nineteenth century: Historiographic concerns about Reviel Netz’s ‘The Place of Archimedes in World History’

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

Uses of construction in problems and theorems in Euclid’s Elements I–VI

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