The geometry of burning mirrors in Greek antiquity. Analysis, heuristic, projections, lemmatic fragmentation

The article analyzes in detail the assumptions and the proofs typical of the research field of the geometry of burning mirrors. It emphasizes the role of two propositions of the Archimedean Quadratura parabolae, never brought to bear on this subject, and of a complex system of projections reducing a...

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Bibliographic Details
Published inArchive for history of exact sciences Vol. 65; no. 5; pp. 471 - 497
Main Author Acerbi, Fabio
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer 01.09.2011
Springer-Verlag
Subjects
Antiquity
Astronomy
Conic sections
Diodes
Geometry
Heuristics
History
History and Philosophical Foundations of Physics
History of Mathematical Sciences
History of Science
History of science and technology
Mathematical sciences and techniques
Mathematics
Mathematics and Statistics
Observations and Techniques
Parabolas
Parabolic reflectors
Philosophy of Science
Property lines
Tangents
Triangles
Vertices
Antiquity
Greek Antiquity
Vertex Versus
Locus Theorem
Conic Section
Equal Angle
Burning
Archimedes
Geometry
Diocles
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Summary:The article analyzes in detail the assumptions and the proofs typical of the research field of the geometry of burning mirrors. It emphasizes the role of two propositions of the Archimedean Quadratura parabolae, never brought to bear on this subject, and of a complex system of projections reducing a sumptōma of a parabola to some specific linear lemmas. On the grounds of this case-study, the much-debated problem of the heuristic role of analysis is also discussed.
ISSN:0003-9519
1432-0657
DOI:10.1007/s00407-010-0076-8