Advertisement

Archive for History of Exact Sciences

, Volume 68, Issue 2, pp 207–239 | Cite as

Building the stemma codicum from geometric diagrams

A treatise on optics by Ibn al-Haytham as a test case
  • Dominique RaynaudEmail author
Article

Abstract

In view of the progress made in recent decades in the fields of stemmatology and the analysis of geometric diagrams, the present article explores the possibility of establishing the stemma codicum of a handwritten tradition from geometric diagrams alone. This exploratory method is tested on Ibn al-Haytham’s Epistle on the Shape of the Eclipse, because this work has not yet been issued in a critical edition. Separate stemmata were constructed on the basis of the diagrams and the text, and a comparison showed no major differences. The greater reliability of a stemma codicum constructed on the basis of the diagrams rather than the text of a mathematical work is discussed, and preliminary conclusions are drawn.

Keywords

Susceptible Locus Critical Edition Mathematical Text True Character Ordinal Ranking 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

I gratefully acknowledge Ken Saito (Osaka Prefecture University), Gregg de Young (American University in Cairo), A. Mark Smith (University of Missouri), Len Berggren (Simon Fraser University) and anonymous referees for valuable comments on a first draft of this paper, while reserving for myself full responsibility for any remaining errors.

References

  1. Barbrook, A.C., N. Blake, and P.M.W. Robinson. 1998. The phylogeny of the Canterbury Tales. Nature 394: 839.CrossRefGoogle Scholar
  2. Barrow-Green, J. 2006. ‘Much necessary for all sortes of men:’ 450 years of Euclid’s Elements in English. BSHM Bulletin 21: 2–25.CrossRefzbMATHMathSciNetGoogle Scholar
  3. Bédier, J. 1929. La tradition manuscrite du Lai de l’ombre. Réflexions sur l’art d’éditer les anciens textes. Paris: Honoré Champion.Google Scholar
  4. Bourgain, P., and F. Vielliard. 2002. Conseils pour l’édition des textes médiévaux, III. Paris: École des Chartes.Google Scholar
  5. Brey, G. 2009. Scientific manuscripts in the digital age. Digital Proceedings of the Lawrence J. Schoenberg Symposium on Manuscript Studies in the Digital Age. Issue 1: On the Nature of Things: Modern Perspectives on Scientific Manuscripts. Art. 5: 1–7.Google Scholar
  6. Cambiano, G. 1992. La démonstration géométrique. In Les Savoirs de l’écriture en Grèce ancienne, ed. M. Detienne, 251–272. Lille: Presses universitaires de Lille.Google Scholar
  7. Cardelle de Hartmann, C., P. Schwagmeier, and P. Roelli. 2013. Petrus Alfonsi, Dialogus: Kritische Edition und Kommentar (work in progress). Universität Zürich: Philosophische Fakultät.Google Scholar
  8. Cipolla, A., M. Buzzoni, O.E. Haugen and R. Rosselli Del Turco (ed.). 2012. IV Incontro di Filologia Digitale: Constitutio Textus (Verona, 13–15 September 2012).Google Scholar
  9. Crozet, P. 2005. Editer les figures des manuscrits arabes de géométrie: l’exemple d’al Sijzī. In The problem of diagrams and drawings criticism in mathematical texts, ed. P. Mascellani, P.D. Napolitani and V. Gavagna, 33–42. A Workshop Held in Pisa, Report Version 1.0.Google Scholar
  10. Decorps-Foulquier, M. 1999. Sur les figures du traité des coniques d’Apollonios de Pergé édité par Eutocius d’Ascalon. Revue d’histoire des mathématiques 5: 61–82.zbMATHMathSciNetGoogle Scholar
  11. Dees, A. 1988. Ecdotique et informatique. In Actes du XVIIIe Congrès international de linguistique et de philologie romanes (Trier, 18–24 Mai 1986), ed. J. Kremer, VI, 18–27. Tübingen: Niemayer.Google Scholar
  12. De Young, G. 2004. The Latin translation of Euclid’s Elements attributed to Gerard of Cremona in relation to the Arabic transmission. Suhayl 4: 311–383.Google Scholar
  13. De Young, G. 2005. Diagrams in the Arabic Euclidean tradition. Historia Mathematica 32: 129–179.CrossRefzbMATHMathSciNetGoogle Scholar
  14. De Young, G. 2012. Mathematical diagrams from manuscript to print: Examples from the Arabic Euclidean transmission. Synthese 186: 21–54.CrossRefzbMATHMathSciNetGoogle Scholar
  15. Dom Quentin, H. 1922. Mémoire sur l’établissement du texte latin de la Vulgate. Rome: Desclée et Cie.Google Scholar
  16. Edgerton, S.Y. 1985. The renaissance development of scientific illustration. In Science and the arts in the renaissance, ed. J.W. Shirley and F.D. Hoeniger, 168–197. Washington D.C.: Folger Books.Google Scholar
  17. Felsenstein, J. 2009. Phylip. Phylogeny Inference Package. Version 3.69. http://evolution.genetics.washington.edu/phylip.html
  18. Glenisson, J. (ed.). 1979. La Pratique des ordinateurs dans la critique des textes. Actes du Colloque international (Paris, 29–31 mars 1978). Paris: Éditions du CNRS.Google Scholar
  19. Heath, T.L. 1956. The thirteen books of Euclid’s elements, Translated from the text of Heiberg with introduction and commentary. New York: Dover.Google Scholar
  20. Hennig, W. 1950. Grundzüge einer Theorie der phylogenetischen Systematik. Berlin: Deutscher Zentralverlag.Google Scholar
  21. Huygens, R.B.C. 2001. Ars edendi. Introduction pratique à l’édition des textes latins du Moyen Age. Turnhout: Brepols.Google Scholar
  22. Jardine, B., and N. Jardine. 2010. Critical editing of early modern astronomical diagrams. Journal for History of Astronomy 41(3): 393–414.MathSciNetGoogle Scholar
  23. Khalidov, A.B. 1986. Arabskie rukopisi Instituta vostokovedenija kratkij katalog, chast’ 2: Ukazateli i priloženie. Moskva: Izdatel’stvo Nauka.Google Scholar
  24. Kitching, I., et al. 1998. Cladistics. The theory and practice of parsimony analysis. Oxford: Oxford University Press.Google Scholar
  25. Krause, M. 1936. Stambuler Handschriften islamischer Mathematiker. Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Studien 3: 437–532.Google Scholar
  26. Lachmann, K. 1850. Caroli Lachmanni in T. Lucretii Cari De rerum natura libros commentarius. Berolini: Impensis G. Reimeiri.Google Scholar
  27. Loth, O. 1877. A catalogue of the Arabic manuscripts in the library of the India Office. London.Google Scholar
  28. Maas, P. 1958. Textual criticism. Oxford: Clarendon Press.Google Scholar
  29. Maas, P. 2010. Computer Aided Stemmatics. The Case of Fifty-Two Text Versions of Carakasasahitā Vimānasthāna 8.67-157. Wiener Zeitschrift für die Kunde Südasiens 52/53: 63–120.Google Scholar
  30. Macé, C., T. Schmidt, and J.F. Weiler. 2001. Le classement des manuscrits par la statistique et la phylogénétique: les cas de Grégoire de Nazianze et de Basile le Minime. Revue d’Histoire des Textes 31: 241–273.Google Scholar
  31. Macé, C., and Baret, P.V. 2006. Why phylogenetic methods work: The theory of evolution and textual criticism. In The evolution of texts. Confronting stemmatological and genetical methods, ed. C. Macé et al., 89–108. Roma-Pisa: Istituti editoriali e poligrafici internazionali.Google Scholar
  32. Mahoney, M.S. 1985. Diagrams and dynamics: Mathematical perspectives on Edgerton’s thesis. In Science and the arts in the renaissance, ed. J.W. Shirley, and F.D. Hoeniger, 198–220. Washington, D.C.: Folger Books.Google Scholar
  33. Manders, K. 2008. The Euclidean diagram. In The philosophy of mathematical practice, ed. P. Mancosu, 80–133. Oxford: Oxford University Press.CrossRefGoogle Scholar
  34. Mascellani, P., P.D. Napolitani, V. Gavagna (ed). 2005. The problem of diagrams and drawings criticism in mathematical texts. A Workshop Held in Pisa, Report Version 1.0.Google Scholar
  35. Mooney, L.R., A.C. Barbrook, C.J. Howe, and M. Spencer. 2001. Stemmatic analysis of Lydgate’s Kings of England: A test case for the application of software developed for evolutionary biology to manuscript stemmatics. Revue d’Histoire des Textes 31: 275–297.Google Scholar
  36. Mumma, J., M. Panza, and G. Sandu, eds. 2013. Diagrams in mathematics: History and philosophy. Synthese 186(1): 7–20.Google Scholar
  37. Murdoch, J.E. 1984. Album of science: Antiquity and the middle ages. New York: Scribner’s Sons.Google Scholar
  38. Naẓīf, M. 1942/1943. Al-Ḥasan Ibn al-Haytham wa-buḥūthuhu wa-kushūfuhu al-naẓariyya, 2 vols. Cairo: University of Cairo.Google Scholar
  39. Netz, R. 1999. The shaping of deduction in Greek mathematics: A study in cognitive history. Cambridge: Cambridge University Press.CrossRefzbMATHGoogle Scholar
  40. Pietquin, P. 2010. Le Septième livre du traité De aspectibus d’Alhazen, traduction latine médiévale de l’Optique d’Ibn al-Haytham. Bruxelles: Académie royale de Belgique.Google Scholar
  41. Rashed, R. 1993. Les Mathématiques infinitésimales du IXe au XIe siècle, vol. II. Ibn al-Haytham. London: al-Furqān Islamic Heritage Foundation.Google Scholar
  42. Rashed, R. 2005. Geometry and dioptrics in classical Islam. London: al-Furqān Islamic Heritage Foundation.Google Scholar
  43. Rashed, R. 2006. Les Mathématiques infinitésimales du IXe au XIe siècle, vol. V: Astronomie, géométrie sphérique et trigonométrie. London: al-Furqān Islamic Heritage Foundation.Google Scholar
  44. Rider, R.E. 1993. Early modern mathematics in print. In Non-verbal communication in science prior to 1900, ed. R.G. Mazzolini, 91–113. Firenze: Leo S. Olschki.Google Scholar
  45. Robinson, P.M.W. 1996. Computer-assisted analysis and ‘best-text’ historical editing. In Studies in stemmatology, ed. P. van Reenen et al., 123–134. Amsterdam: John Benjamins.Google Scholar
  46. Robinson, P.M.W., and R.J. O’Hara. 1996. Cladistic analysis of an Old Norse manuscript tradition. Research in Humanities Computing 4: 115–137.Google Scholar
  47. Robinson, P.M.W. 1998. New methods of editing, exploring, and reading the Canterbury Tales. A talk given at the conference ’I nuovi orizzonti della filologia’. Accademia Nazionale dei Lincei (Rome, May 28, 1998).Google Scholar
  48. Roos, T., and T. Heikkilä. 2009. Evaluating methods for computer-assisted stemmatology using artificial benchmark data sets. Literary and Linguistic Computing 24: 417–433.CrossRefGoogle Scholar
  49. Sabra, A.I. 1972. Ibn al-Haytham. In Dictionary of scientific biography VI, ed. C.C. Gillispie, 189–210. New York: Scribner’s Sons.Google Scholar
  50. Sabra, A.I., and N. Shehaby. 1971. Ibn al-Haytham, al-Shukūk ‘alā Baṭlamyūs (Dubitationes in Ptolemaeum). Cairo: The National Library Press.Google Scholar
  51. Saito, K. 2005. The diagrams in codex P of Euclid’s elements. In The problem of diagrams and drawings criticism in mathematical texts, ed. P. Mascellani, P.D. Napolitani and V. Gavagna, 19–28. A Workshop Held in Pisa, Report Version 1.0.Google Scholar
  52. Saito, K. 2006. A preliminary study in the critical assessment of diagrams in Greek mathematical works. Sciamvs 7: 81–144.Google Scholar
  53. Saito, K. ed. 2011. Diagrams in Greek mathematical texts. kakenhi, Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science. Report Version 2.03.Google Scholar
  54. Saito, K. ed. 2013. Reproduced diagrams from Greek and Arabic manuscripts. Research Report ‘Databasing the Manuscript Diagrams of Sources in Ancient and Medieval Mathematics’.Google Scholar
  55. Saito, K., and N. Sidoli. 2012. Diagrams and arguments in ancient Greek mathematics: Lessons drawn from comparisons of the manuscript diagrams with those in modern critical editions. In The history of mathematical proof in ancient traditions, ed. K. Chemla, 135–162. Cambridge: Cambridge University Press.Google Scholar
  56. Salemans, B.J.P. 1996. Cladistics or the resurrection of the method of Lachmann. On building the stemma of Yvain. In Studies in stemmatology, ed. P. van Reenen et al., 3–70. Amsterdam: J. Benjamins.Google Scholar
  57. Salemans, B.J.P. 2000. Building stemmas with the computer in a cladistic. Neo-Lachmannian, way. The case of fourteen text versions of Lanseloet van Denemerken. Thesis. Nijmegen: Katholieke Universiteit.Google Scholar
  58. Sidoli, N. 2007. What we can learn from a diagram: The case of Aristarchus’s on the sizes and distances of the Sun and Moon. Annals of Science 64: 527–547.CrossRefGoogle Scholar
  59. Sidoli, N., and J.L. Berggren. 2007. The Arabic version of Ptolemy’s planisphere or flattening the surface of the sphere: Text, translation, commentary. Sciamvs 8: 37–139.zbMATHMathSciNetGoogle Scholar
  60. Sidoli, N., and K. Saito. 2009. The role of geometrical construction in Theodosius’s spherics. Archive for History of Exact Sciences 63: 581–609.CrossRefzbMATHMathSciNetGoogle Scholar
  61. Sidoli, N., and C. Li. 2011. The manuscript diagrams of al-Harawī’s version of spherics. Research report for ‘Databasing the manuscript diagrams of sources in ancient and medieval mathematics’, Japan Society for the Promotion of Science Grants-in-Aid, 2009–2010, no. 2130325.Google Scholar
  62. Suzuki, T. 2011. The diagrams of the phaenomena in Greek and Arabic manuscripts. In Diagrams in Greek mathematical texts, ed. K. Saito, 15–38. kakenhi Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science. Report version 2.03.Google Scholar
  63. Swofford, D.L. 2003. PAUP \(^*\) Phylogenetic analysis using parsimony, version 4.0. Tallahassee: Florida State University.Google Scholar
  64. van Reenen, P., M. van Mulken, and J. Dyk (eds.). 1996. Studies in stemmatology. Amsterdam: John Benjamins.Google Scholar
  65. van Reenen, P., A. den Hollander, and M. van Mulken (eds.). 2004. Studies in stemmatology II. Amsterdam: John Benjamins.Google Scholar
  66. Viré, G. 1986. Informatique et classement des manuscrits. Essai méthodologique sur le ‘De astronomia’ d’Hygin. Bruxelles: Éditions de l’Université de Bruxelles.Google Scholar
  67. Wiedemann, E. 1914. Über der Camera obscura bei Ibn al Haiṭam. Sitzungsberichte phys.-med. Sozietät in Erlangen 46: 155–169.Google Scholar
  68. Wiesemiller, B., and H. Rothe. 2006. Interpretation of bootstrap values in phylogenetic analysis. Anthropologischer Anzeiger 64: 161–165.Google Scholar
  69. Windram, H.F., P. Shaw, P. Robinson, and C.J. Howe. 2008. Dante’s Monarchia as a test case for the use of phylogenetic methods in stemmatic analysis. Literary and Linguistic Computing 23: 443–463.CrossRefGoogle Scholar
  70. Woerther, F., and H. Khonsari. 2001. L’application des programmes de reconstructions phylogénétique sur ordinateur à l’étude de la tradition manuscrite d’un texte: l’exemple de l’Ars Rhetorica du Pseudo-Denys d’Halicarnasse. Revue d’Histoire des Textes 31: 227–240.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.PLCUniversité de GrenobleGrenobleFrance
  2. 2.GEMASSCNRS/Université Paris 4 SorbonneParisFrance

Personalised recommendations