2018
DOI: 10.1007/s00407-018-0212-4
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Uses of construction in problems and theorems in Euclid’s Elements I–VI

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Cited by 11 publications
(5 citation statements)
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“…Many have pointed to this as evidence that Euclid's constructions do not correspond to actual ruler and compasses, since no actual compasses are collapsible (Sidoli, 2018b, 422, Acerbi, 2010b. This conclusion clashes with the operationalist reading of geometry.…”
Section: The "Collapsible" Compassmentioning
confidence: 99%
“…Many have pointed to this as evidence that Euclid's constructions do not correspond to actual ruler and compasses, since no actual compasses are collapsible (Sidoli, 2018b, 422, Acerbi, 2010b. This conclusion clashes with the operationalist reading of geometry.…”
Section: The "Collapsible" Compassmentioning
confidence: 99%
“…This means essentially Postulates 1-3 and 5 of Book I, with some minor accommodations for informal assumptions that Euclid does not articulate explicitly. See, e.g., [Sidoli 2018], where, in particular, Euclid's postulates (419-424) and problems (426-431) are both interpreted as functions introducing certain geometrical entities.…”
Section: Analysis As Justification Of Meansmentioning
confidence: 99%
“…Euclid seems never to question the universal replicability of his constructions, and many scholars have advanced hypotheses on the role of constructive schemata in the process of universal generalization of the theorems. The most refined and subtle attempts towards a constructivist reading of the Elements have been made by Ferreirós (2016, 130), Sidoli (2018b, 434), and Blåsjö (2022).…”
mentioning
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.…”
mentioning
confidence: 99%