Article ID: CBB001551396

Figures Real, Imagined, and Missing in Poncelet, Plücker, and Gergonne (2015)

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Lorenat, Jemma (Author)


Historia Mathematica
Volume: 42, no. 2
Issue: 2
Pages: 155-192

In the early nineteenth century debate over geometric methodology, Jean-Victor Poncelet characterized pure geometry as reasoning in which the figure is never lost from view. Whether illustrated, described or constructed, Poncelet presented the figure as the primary form of geometrical evidence, a means of justification based in sensory perception. In Poncelet's pure geometry, the objects of geometry were emphatically representational and tangible. By contrast, though classified as analytic geometry, Julius Plücker's contemporary research treated coordinate equations as visual geometric objects---evidence---by focusing on their form and endeavouring to avoid calculations. Working from Poncelet's division between pure and analytic geometries we focus on five versions by three different geometers, of a single conic section construction written between 1817-1826. Despite the similarity of their results, Poncelet, Plücker, and Joseph Diaz Gergonne each addressed the problem from contrasting methodological perspectives. We examine how the figure-based distinction materialized in contemporary geometric practices, and what constituted geometric evidence when the figure was lost from view.

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Authors & Contributors
Lorenat, Jemma
Del Centina, Andrea
Michael Wiescher
Hiebert, Erwin N.
Chatzis, Konstantinos
Zhang, Hong-mei
Journals
Archive for History of Exact Sciences
British Society for the History of Mathematics Bulletin
Historia Mathematica
Bulletin de la Société des Amis de la Bibliothèque de l'École Polytechnique
Journal of Dialectics of Nature
Revue d'Histoire des Mathématiques
Concepts
Geometry
Mathematics
Mathematicians
Conic sections
Visual representation; visual communication
Scientific illustration
People
Poncelet, Jean Victor
Plücker, Julius
Gergonne, Joseph Diaz
Steiner, Jakob
Newton, Isaac
Chasles, Michel
Time Periods
19th century
18th century
Enlightenment
Places
France
Germany
Great Britain
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