Digital Texts and Diagrams: Representing the Transmission of Euclid’s Elements
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Abstract
The Digital Euclid project aims to publish an open, digital edition of every extant witness to the text and diagrams of Euclid’s Elements. This paper discusses the required groundwork and is divided in two parts. It first covers a survey of the surviving manuscript and print sources for the Elements that intends to identify the extent of these materials, how many of these works have already been digitally imaged, and what challenges they pose to current data extraction methods. The latter part of the paper discusses the methods used to produce machine-actionable texts and diagrams and focuses especially on the development of tools for the identification and extraction of diagrammatic data.
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References
Busard (1968): H. L. L. Busard, The Translation of the Elements of Euclid from Arabic into Latin by Hermann of Carinthia(?), Leiden 1968.
Busard (1983): H. L. L. Busard, The First Latin Translation of Euclid‘s Elements commonly ascribed to Adelard of Bath. Books I–VIII and Books X.36–XV.2, Toronto1983.
Busard (1984): H. L. L. Busard, The Latin Translation of the Arabic Version of Euclid’s Elements commonly ascribed to Gerard of Cremona, Leiden 1984.
Busard (1987): H. L. L. Busard, The Mediaeval Latin translation of Euclid’s Elements Made Directly from the Greek, Stuttgart 1987.
Busard (1992): H. L. L. Busard, Robert of Chester’s Redaction of Euclid’s Elements, the so-called Adelard II Version, Birkhäuser 1992.
Busard (1996): H. L. L. Busard, A Thirteenth-Century Adaption of Robert of Chester‘s Version of Euclid‘s Elements, München 1996.
Busard (2001): H. L. L. Busard, Johannes de Tinemue‘s redaction of Euclid‘s „Elements“, the so-called Adelard III version, Stuttgart 2001.
Busard (2005): H. L. L. Busard, Campanus of Novara and Euclid‘s Elements, Stuttgart 2005.
Folkerts (1989): M. Folkerts, Euclid in Medieval Europe, The Benjamin Catalogue 1989.
Heiberg (1883–6): I. L. Heiberg, “Euclidis Elementa”, Euclidis Opera Omnia Vol.1–4, Leipzig 1883–6.
Kayas (1977): G. J. Kayas, Vingt-trois siecles de tradition euclidienne: essai bibliographique, Palaiseau 1977.
Lo Bello (2003): A. Lo Bello, Gerard of Cremona‘s Translation of the Commentary of Al-Nayrizi on Book I of Euclid‘s Elements of Geometry, Leiden 2003.
Netz (2004): R. Netz, The Works of Archimedes: Translation and Commentary, Cambridge 2004.
Riccardi (1887): P. Riccardi, Saggio di una bibliografia euclidea, Tipografia Gamberini e Parmeggiani 1887.
Saito (2009): K. Saito, “Reading ancient Greek mathematics”, The Oxford Handbook of the History of Mathematics, Oxford 2009.
Steck (1981): M. Steck, Bibliographia Euclideana: Die Geisteslinien der Tradition in den Editionen der ‘Elemente’ des Euklid um 365–300, Arbor scientiarum, Hildesheim 1981.
Weitere Ressourcen (Zuletzt aufgerufen am 29.12.2015):
ABBYY FineReader:
http://www.abbyy.com/finereader/
Autotrace:
http://autotrace.sourceforge.net/
Inkscape:
Gallica:
Google Books:
HathiTrust:
Internet Archive:
Münchner Digitalisierungszentrum (MDZ):
http://www.digitale-sammlungen.de/
OCRopus:
https://github.com/tmbdev/ocropy
Open Greek and Latin Project of the Open Philology Project:
http://www.dh.uni-leipzig.de/wo/projects/open-greek-and-latin-project/
Perseus:
SLUB Dresden:
http://www.slub-dresden.de/startseite/
Sourceforge (Find, Create, and Publish Open Source Software):
epidoc.sourceforge.net/.
Tesseract:
https://github.com/tesseract-ocr
https://code.google.com/p/tesseract-ocr/
The Gamera Project:
http://gamera.informatik.hsnr.de/
The CITE Architecture:
Supplementary Content
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Fig 1
Description
Coverage of the Elements in 354 manuscript versions of the text.
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Fig 2
Description
A selection of folio 145v of BnF Arabe 2484, showing diagrams relevant to an Arabic version of Book I, proposition 2. Source: gallica.bnf.fr.
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Fig 3 neu
Description
Languages represented in the Digital Euclid survey of print editions as of July 2015.
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Fig 4
Description
Coverage of the Elements in 425 print versions of the text.
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Fig 5
Description
Three examples of scanned diagram foldouts. The leftmost page was partially imaged, but not unfolded. The middle is an example of an unfolded page. The rightmost page remained folded, and nothing of the diagrams was captured. Source for all three images: the Internet Archive.
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Fig 6
Description
Workflows for extraction of textual and diagrammatic data from manuscript and print editions.
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Fig 7
Description
Screenshots of OCR output from the Lace Greek OCR project website. In the output for the first example, the ‘j’ at the start of the first line and ‘Β’ in the last were introduced from the diagram. The second includes ‘Λ’ at the start of the fourth line. Source: heml.mta.ca/lace.
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Fig 8
Description
Three sample pages with incorrect layout analysis by ABBYY FineReader. Source for all three original images: the Internet Archive.
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Fig 9
Description
Four pages from Simson’s edition put through the first phase of the identification process. Potential diagram components are colorized for manual review. Red: quad component; green: definite line component; blue: possible line component. Source for all four images: the Internet Archive.
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Fig 10
Description
Diagram for Elements Book I proposition 1, separated into two images containing either alphabetic or geometric components. Source: the Internet Archive.
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Fig 11
Description
Diagram from Heath’s English edition. Connected components that are identified as labels appear in grey. This diagram contains two labels, H and G, that overlap with the figure and that must be removed manually. Source: the Internet Archive.
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Fig 12
Description
Left: diagram for Elements Book I proposition 2 from Heath’s edition. Right: a segmented autotraced SVG version with endpoints and corners located and marked for manual review. Source for original image: the Internet Archive.
License
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