Download Mathematizing Space: The Objects of Geometry from Antiquity by Vincenzo De Risi PDF
By Vincenzo De Risi
This publication collects the papers of the convention held in Berlin, Germany, 27-29 August 2012, on 'Space, Geometry and the mind's eye from Antiquity to the fashionable Age'. The convention used to be a joint attempt via the Max Planck Institute for the background of technological know-how (Berlin) and the Centro die Ricerca Matematica Ennio De Giorgi (Pisa).
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Additional resources for Mathematizing Space: The Objects of Geometry from Antiquity to the Early Modern Age
Example text
Euclid, the only one of these to use ‘room (χώρα)’, uses it for the region where the North Star turns. So he keeps place to the horizon. , the regions of Greece), ‘place’ is used only five times, but in ways different from the others here. 25 Here, Mugler identifies two principal uses. The first is a region defined by lines or surfaces, while the second, technical sense is the familiar, locus use, although the two uses can be merged. In the technical sense, in a ‘locus (τόπος)’ theorem, a place or locus is a given point, line, area or region, solid or region, such that every object of a determined sort within the locus has certain additional properties (συμπτώματα).
Cf. Long and Sedley (1987, p. 296). De Harven (2012, p. 29) takes extension to be a mode of incorporeals and so not something distinct. 47 For Chrysippus, cf. inter alia Arius Didymus, fr. 25 in Dox. Graec. 503). For Stoics and Posidonius in contrast on this point, cf. Aetius in Dox. Graec. 338a16–19, b16–21. If Cleomedes is relying on Posidonius for the argument of Caelestia I 1, that void is unlimited, this report might be incorrect. 48 Cf. Fr. 54–67 (Werhli) and Algra (1995, pp. 58–70). 49 One might expect, as a result, some terminological care.
Yet, we have a bevy of triples of definitions, but mostly unremarkable, as is clear from a comparison with Euclid, Elements I Definitions 1–3, 5, 6 (or any perusal of definitions in Aristotle). So the order in Diogenes is from three to no-dimensions and with each (except for the point): the ontologically correct definition, the privative definition, the definition by a list of dimensions. 69 So the only thing of note here is that Diogenes gives both the privative and list forms, which Euclid seems not to distinguish.