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Shaping the Sciences of the Ancient and Medieval World: An Introduction

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Shaping the Sciences of the Ancient and Medieval World

Part of the book series: Archimedes ((ARIM,volume 69))

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Abstract

This introductory chapter gives an overview of the research questions raised in the book as much for historians of science as for anyone working with, or producing editions of, ancient scholarly texts. It highlights the benefits that flow from a worldwide history of textual criticism and editions as well as from a focus on texts dealing with science—two key options that are taken in this book. Following the book’s scheme, the introduction first concentrates on ancient editorial practices, in particular examining their potential impact on modern editions. We then highlight how, through time, perceptions changed concerning what a text is, and how this influenced in turn how scholarly texts were made accessible. We offer an analysis of the ways historical, political and social contexts shaped editions and translations of ancient scientific works and documents, using the case studies offered in this book, before turning to an analysis of the specifics of editions and translations that bear on scholarly documents rather than on literary or religious sources. Finally, this introduction looks at how some elements specific to texts dealing with science—such as diagrams and numbers—have been edited and the specific work that has been done editing mathematical and astronomical texts of the past. All these threads help us reflect on how editorial practices have heavily mediated the way we have access to ancient sources dealing with science. The scholarship displayed here lays the foundation for further studies on the history of critical editions. It also raises questions for those who make scholarly translations and critical editions today.

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Notes

  1. 1.

    Heiberg’s edition of the Elements (1883–1888) was published as part of that of Euclid’s complete works by Heiberg and Heinrich Menge (1838–1904) (Heiberg and Menge 1883–1916). (Knorr 2001), published posthumously, returns to the same issue.

  2. 2.

    Decorps’s chapter in this book outlines a history of editions of Greek mathematical texts of antiquity. She points out that Friedrich Hultsch’s critical edition of Pappus’ Collection (1876–1878) likewise considered several passages as spurious ‘on the grounds of an ideal representation of what a Greek mathematical treatise should be’ (see note 91).

  3. 3.

    For the case of Archimedes, Netz (2012) offers a reflection on this issue.

  4. 4.

    Chemla (2005) argues that Zhao uses these diagrams as paradigms.

  5. 5.

    See, e.g., for the Elements, (Vitrac 1990, volume I: 200–202) and, for The Gnomon of the Zhou [Dynasty], the critical edition by Guo Shuchun 郭書春 and Liu Dun 劉鈍 (1998: 2). Note that, in the latter edition, the vertical presentation of the sequence of diagrams given by Qian was transformed into a horizontal one.

  6. 6.

    Fowler (1992) upholds this thesis. In an earlier publication, Knorr (1982) had also highlighted this point.

  7. 7.

    Fowler and Turner (1983) provide a systematic description of the notation of integers and fractions in the papyrus Hibeh I 27.

  8. 8.

    See notably (Judet de La Combe 1990), (Cerquiglini 1999), (Chartier 2021).

  9. 9.

    Here again, we are not alone in striving to broaden the discipline in this way. See, notably, (Suarez and Woudhuysen 2013), (Pollock et al. 2015), (Grafton and Most 2016) as well as the contributions to the journal Philological Encounters, for instance (Dayeh et al. 2018) and (Pecchia et al. 2021).

  10. 10.

    See this book, Chap. 4, to which we return below. (Chu 2010: 147–151) outlines more generally Dai Zhen’s restoring of the Chinese mathematical ‘canon’ in the context of his work for the Complete Library of the Four Branches.

  11. 11.

    Biot had access to The Gnomon of the Zhou [Dynasty] by means of the Ming edition included in the Jindai mishu 津逮祕書 (Biot 1841: 596–597). On this edition, see (Chemla 2020: 286). (Biot 1841) gives a translation of the text, and is complemented by (Biot 1842), which relies on astronomical data and computation to analyze The Gnomon of the Zhou [Dynasty] further.

  12. 12.

    On Biot’s literal approach, see (Chemla 2021: 49–57). (Martija-Ochoa 2001–2002) has analyzed Biot’s translation more broadly.

  13. 13.

    On the genesis of the philological method associated with the name of Karl Lachmann (1793–1851), see (Timpanaro 2005). Interestingly, the history of the production of sources that Timpanaro assumes in his reflections shows a clear bias due to the type of works to which philological endeavor was first applied in Europe. Indeed, sources are assumed to have been produced by copying, and copyists are assumed either to have made mistakes or to have produced copies following specific types of scenario.

  14. 14.

    The assertions, taken from Thibaut’s preface (p. v) to (Thibaut and Dvivedin 1889), were quoted in (Keller 2012: 265).

  15. 15.

    For the political implications behind this choice, see (Singh 2018: 472–474), which also writes a larger international history of the printing of Devanagarī in the twentieth century.

  16. 16.

    Preisendanz notes that to this day, the edition and publication of ancient works are deemed important and relevant to readers and editors in India. The sheer number of published books runs contrary to the feelings expressed by editors that Caraka’s compendium would be a forgotten, neglected, text.

  17. 17.

    In the three annexes appended to (Chemla et al. 2022), the reader will find information on the conventions used in this volume to deal with numbers, measurement units and measurement values in, respectively, cuneiform, Chinese and Sanskrit sources.

  18. 18.

    Proust notes that transliterations and transcriptions are historical constructions. She uses here the definitions given by the Cuneiform Digital Library Initiative (CDLI), which itself relies on the definitions of these categories given at the twenty-first congress of Orientalists in Paris in 1948. For instance, Neugebauer’s ‘transcription’ corresponds to what is now for the CDLI a ‘transliteration’. In practice, Assyriologists have also used other modes (hybrids of both notably) of representation of the tablet in Latin script. For the sake of simplicity, in what follows we will stick to the CDLI definitions.

  19. 19.

    As Proust also notes, these remarks further extend to the treatment of computations. After all, transliterations cannot always convey the fact that the addition of quantities of goods to which some tablets attest could have been obtained by bringing together and regrouping the numerical signs representing the addends. The use of Arabic numerals in transliterations might even at times encourage artificial interpretations of numerical relations.

  20. 20.

    (Proust 2002) and (Chambon 2012) consider that this system is centesimal. See also (Chemla in dialogue with Keller and Proust 2022: 31, 42). What follows is based on these publications.

  21. 21.

    The status of Bhāskara II’s Līlāvatī and Algebra in relation to his astronomical Crown of Theoretical Astronomical Treatises is still under investigation. In the wake of Colebrooke’s publication, which follows some Sanskrit commentators, they were often thought of as chapters extracted from the astronomical treatise, and having had a more or less autonomous life. Recent studies of the inner coherence of these texts have suggested that these chapters might have been from the beginning three independent treatises (Ramasubramanian et al. 2019: xxi sqq). An edition of all three works taking into account the different strata of editorial work on the texts is thus in need.

  22. 22.

    See Sect. 1.1.4.

  23. 23.

    (Charette 2012), (Smadja 2016).

  24. 24.

    Note that this assertion is true for China, but not for Korea or for Japan, where some of these works were the objects of earlier editions. Moreover, this statement implies that we do not consider as ‘editions’ works based on thirteenth-century works like Gu Yingxiang’s 顧應祥 (1483–1565) works based on Li Ye’s Measuring the circle on the Sea-Mirror (Ceyuan haijing 測圓海鏡, 1248) and Wu Jing’s 吳敬 Great Compendium of The Nine Chapters on Mathematical Methods with Analogies (Jiuzhang suanfa bilei daquan 九章算法比類大全, 1450). On these works, see, respectively, (Guo Shirong 2015) and (Zhou Xiaohan 2018).

  25. 25.

    On the way in which mathematical and astronomical works were edited, drawing on that earlier project, see (Chu 2010: 148–149; 160–162 (Tables 3 and 4)).

  26. 26.

    (Pollock 2009), (Pollock 2016).

References

  • Acerbi, Fabio. 2007. Euclide, Tutte le Opere, Il Pensiero Occidentale. Bompiani.

    Google Scholar 

  • August, Ernst Ferdinand. 1826–1829. Eukleidou stoicheia. Euclidis Elementa. Berolini: Impensis T. Trautweinii.

    Google Scholar 

  • Qian Baocong 錢寶琮. 1963. Suanjing shishu 算經十書 (Qian Baocong jiaodian 錢寶琮校點) (Critical punctuated edition of The Ten Classics of Mathematics). Beijing 北京: Zhonghua shuju 中華書局.

    Google Scholar 

  • Biot, Edouard. 1841 (juin). Traduction et examen d’un ancien ouvrage chinois intitulé TCHEOU-PEI, littéralement “Style ou signal dans une circonférence”; par M. Edouard BIOT. Journal Asiatique 3e série, 11: 593–639.

    Google Scholar 

  • ———. 1842 (février). Note supplémentaire à la traduction du Tcheou-pei. Journal Asiatique 3e série, 13: 198–202.

    Google Scholar 

  • Cerquiglini, Bernard. 1999. In Praise of the Variant: a Critical History of Philology. Baltimore: John Hopkins University Press. Originally published as Éloge de la variante: Histoire critique de la philologie. Paris: Éditions du Seuil, 1989.

    Google Scholar 

  • Chambon, Grégory. 2012. Notations de nombres et pratique de calcul en Mésopotamie: Réflexions sur le système centésimal de position. Revue d’histoire des mathématiques 18: 5–36.

    Google Scholar 

  • Charette, François. 2012. The Logical Greek Versus the Imaginative Oriental: On the Historiography of ‘Non-Western’ Mathematics During the Period 1820–1920. In The History of Mathematical Proof in Ancient Traditions, ed. K. Chemla, 274–293. Cambridge: Cambridge University Press.

    Google Scholar 

  • Chartier, Roger. 2021. Éditer et traduire. Mobilité et matérialité des textes (XVIe–XVIIIe siècle). Paris: EHESS, Gallimard et Seuil, Hautes Etudes.

    Google Scholar 

  • Chemla, Karine. 1999. Commentaires, éditions et autres textes seconds: quel enjeu pour l’histoire des mathématiques ? Réflexions inspirées par la note de Reviel Netz. Revue d’histoire des mathématiques 5: 127–148.

    Google Scholar 

  • ———. 2004. Editing the earliest extant mathematical figures from China. Paper presented at the Conference “Diagrams and Images criticism in mathematical textual traditions,” Pisa (Italy), 11-2004.

    Google Scholar 

  • ———. 2005. Geometrical figures and generality in ancient China and beyond: Liu Hui and Zhao Shuang, Plato and Thabit ibn Qurra. Science in context 18: 123–166.

    Article  Google Scholar 

  • ———. 2020. On the Diagrammaticity of Ancient Texts and its Importance for the History of Science, Based on the Example of the Early Chinese Mathematical Text The Gnomon of the Zhou. EASTS (East Asian Science, Technology and Society) 14: 279–308. https://doi.org/10.1215/18752160-8538529.

  • ———. 2021. From Reading Rules to Reading Algorithms: Textual Anachronisms in the History of Mathematics and their Effect on Interpretation. In Anachronisms in the History of Mathematics. Essays on the Historical Interpretation of Mathematical Texts, ed. Niccolò Guicciardini, 42–82. Cambridge, UK: Cambridge University Press.

    Chapter  Google Scholar 

  • ——— (in dialogue with Agathe Keller and Christine Proust). 2022. Cultures of computation and quantification in the ancient world: An introduction. In Cultures of computation and quantification in the ancient world. Numbers, measurements, and operations in documents from Mesopotamia, China and South Asia, eds. Karine Chemla, Agathe Keller, and Christine Proust, 1–140. Cham: Springer Nature.

    Google Scholar 

  • Chemla, Karine, Agathe Keller, and Christine Proust, eds. 2022. Cultures of computation and quantification in the ancient world. Numbers, measurements, and operations in documents from Mesopotamia, China and South Asia. Cham: Springer Nature.

    Google Scholar 

  • Chu, Pingyi (祝平一 Zhu Pingyi). 2010. Scientific Texts in Contest, 1600–1800. In Looking at it from Asia: The processes that shaped the sources of history of science, ed. Florence Bretelle-Establet, 141–166. Dordrecht: Springer.

    Google Scholar 

  • Colebrooke, Henry Thomas. 1824. On the Philosophy of the Hindus [Part II]. Transactions of the Royal Asiatic Society of Great Britain and Ireland 1: 92–118.

    Google Scholar 

  • Dayeh, Islam, Umar Ryad, and Pascale Rabault-Feuerhahn. 2018. Nineteenth and Twentieth Century Philological Encounters. Philological Encounters 3 (1–2): 1–2. https://doi.org/10.1163/24519197-12340044.

    Article  Google Scholar 

  • De Young, Gregg. 2005. Diagrams in the Arabic Euclidean tradition: a preliminary assessment. Historia mathematica 32: 129–179.

    Article  Google Scholar 

  • ———. 2012. Mathematical diagrams from manuscript to print: examples from the Arabic Euclidean transmission. Synthese 186: 21–54.

    Article  Google Scholar 

  • ———. 2020. On “Overspecification” in Medieval Mathematical Diagrams. In Diagrammatic Representation and Inference, eds. Peter Chapman Ahti-Veikko Pietarinen, Leonie Bosveld-de Smet, Valeria Giardino, James Corter, and Sven Linker, 3–9. Cham: Springer International Publishing.

    Chapter  Google Scholar 

  • Fowler, David. 1987. The Mathematics of Plato’s academy. A new reconstruction. Oxford: Clarendon Press.

    Google Scholar 

  • ———. 1992. Logistic and fractions in early Greek mathematics. In Histoire de Fractions, Fractions d’Histoire, ed. Paul Benoit, Karine Chemla, and Jim Ritter, 133–147. Stuttgart: Birkhaüser.

    Google Scholar 

  • Fowler, David H., and E.G. Turner. 1983. Hibeh Papyrus I 27: An Early Example of Greek Arithmetical Notation. Historia Mathematica 10: 344–359.

    Article  Google Scholar 

  • Ganeri, Jonardon. 1996. The Hindu syllogism: Nineteenth-century perceptions of Indian logical thought. Philosophy East and West 46: 1–16.

    Article  Google Scholar 

  • Grafton, Anthony, and Glenn W. Most, eds. 2016. Canonical Texts and Scholarly Practices: A Global Comparative Approach. Cambridge: Cambridge University Press.

    Google Scholar 

  • Grenfell, Bernard P., and Arthur S. Hunt. 1898. Oxyrhynchus Papyri. Part I: Edited with Translations and Notes. London: Egypt Exploration Fund.

    Google Scholar 

  • ———. 1906. Hibeh Papyri. Part I: Edited with Translations and Notes. London: Egypt Exploration Fund.

    Google Scholar 

  • Guo Shirong 郭世榮. 2015. Gu Yingxiang’s Method of Solving Numerical Equations with the Abacus. In A Delicate Balance: Global Perspectives on Innovation and Tradition in the History of Mathematics. A Festschrift in Honor of Joseph W. Dauben, eds. David E. Rowe, and Horng Wann-Sheng, 343–359. Cham: Birkhäuser-Springer.

    Google Scholar 

  • Guo Shuchun 郭書春, and Liu Dun 劉鈍. 1998. Suanjing shishu 算經十書 (The Ten Canonical Texts of Mathematics). Guo Shuchun, Liu Dun dianjiao 郭書春,劉鈍 點校 (Punctuated critical edition by Guo Shuchun and Liu Dun). Shenyang 瀋陽: Liaoning jiaoyu chubanshe 遼寧教育出版社.

    Google Scholar 

  • Heath, Thomas. 1897. The Works of Archimedes. London: Cambridge University Press.

    Google Scholar 

  • ———. 1908. Euclid. The Thirteen Books of the Elements. Translated with introduction and commentary by Sir Thomas Heath. Cambridge: Cambridge University Press.

    Google Scholar 

  • ———. 1926. Euclid. The Thirteen Books of the Elements. Translated with introduction and commentary by Sir Thomas Heath. 2nd ed. Cambridge: Cambridge University Press.

    Google Scholar 

  • ———. 1956. The Thirteen Books of Euclid’s Elements. New York: Dover Publications.

    Google Scholar 

  • Heiberg, Johan Ludvig. 1880–1881. Archimedis Opera Omnia cum Commentariis Eutocii. Leipzig: B. G. Teubner.

    Google Scholar 

  • ——————. 1883–1888. Euclidis Elementa edidit et latine interpretatus I. L. Heiberg, vol. I. Elementa I-IV (1883); II. Elementa V-IX (1884); III. Elementa X (1886); IV. Elementa XI-XIII (1885); V. Elementa XIV-XV, Scholia, Prolegomena critica (1888). Book series: Euclidis Opera omnia, eds. I. L. Heiberg, and H. Menge. Leipzig: B. G. Teubner.

    Google Scholar 

  • —————. 1910–1915. Archimedis Opera Omnia cum Commentariis Eutocii Iterum Edidit. Leipzig: B. G. Teubner.

    Google Scholar 

  • Heiberg, J.L., and H. Menge, eds. 1883–1916. Euclidis Opera omnia. Leipzig: Teubner.

    Google Scholar 

  • Hultsch, Friedrich. 1876–1878. Pappi Alexandrini Collectionis quae supersunt (3 vols.). Berlin: Weidmann.

    Google Scholar 

  • Judet de La Combe, P. 1990. Philologie classique et légitimité. Quelques questions sur un ‘modèle’. In Philologiques I. Contribution à l’histoire des disciplines littéraires en France et en Allemagne au XIXe siècle, eds. M. Espagne and M. Werner, 23–42. Paris: Éditions de la Maison des Sciences de l’homme.

    Google Scholar 

  • Keller, Agathe. 2012. Overlooking mathematical justifications in the Sanskrit tradition: the nuanced case of G. F. W. Thibaut. In The History of Mathematical Proof in Ancient Traditions, ed. Karine Chemla, 260–273. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Knorr, Wilbur R. 1982. Techniques of Fractions in the Ancient Egypt and Greece. Historia Mathematica 9: 133–141.

    Google Scholar 

  • ————. 1996. The Wrong Text of Euclid: On Heiberg’s Text and Its Alternatives. Centaurus: International Magazine of the History of Mathematics, Science, and Technology 38: 208–276.

    Article  Google Scholar 

  • ———. 2001. On Heiberg’s Euclid. Science in context 14: 133–143.

    Article  Google Scholar 

  • Lee, Eunsoo. 2018. Let the Diagram Speak: Compass Arcs and Visual Auxiliaries in Printed Diagrams of Euclid’s Elements. Endeavour 42: 78–98.

    Article  Google Scholar 

  • ———. 2020. Visual Agency in Euclid’s Elements: A Study of the Transmission of Visual Knowledge. Ph.D.: Stanford University.

    Google Scholar 

  • Li Jimin 李繼閔. 1990. Dongfang shuxue dianji Jiuzhang suanshu ji qi Liu Hui zhu yanjiu 東方數學典籍九章算術及其劉徽注研究 (Research on the Oriental mathematical Classic The Nine Chapters on Mathematical Procedures and on its Commentary by Liu Hui). Xi’an.: Shaanxi renmin jiaoyu chubanshe.

    Google Scholar 

  • Martija-Ochoa, Isabelle. 2001–2002. ‘Edouard et Jean-Baptiste Biot. L’astronomie chinoise en France au XIXe siècle’. Master Thesis, University Paris Diderot.

    Google Scholar 

  • McKenzie, D.F. 1999. Bibliography and the Sociology of Texts. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Mugler, Charles. 1970–1972. Archimède. I. De la sphère et du cylindre, La mesure du cercle, Sur les conoides et sphéroïdes; II. Des spirales, De l’équilibre des figures planes, L’arénaire, La quadrature de la parabole; III. Des corps flottants, Stomachion, La méthode, Le livre des lemmes, Le problème des bœufs; IV. Commentaires d’Eutocius et fragments. Texte établi et traduit par Charles Mugler. Paris: Les Belles Lettres.

    Google Scholar 

  • Netz, Reviel. 1999. The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. West Nyack, NY, USA: Cambridge University Press.

    Book  Google Scholar 

  • ———. 2004. The works of Archimedes. Translation and commentary. Volume 1: The two books On the sphere and the cylinder. Cambridge: Cambridge University Press.

    Google Scholar 

  • ———. 2012. The Texture of Archimedes’ Arguments: through Heiberg’s Veil. In The History of Mathematical Proof in Ancient Traditions, ed. Karine Chemla, 163–205. Cambridge: Cambridge University Press.

    Google Scholar 

  • ———. 2013. Authorial Presence in the Ancient Exact Sciences. In Writing Science: Medical and Mathematical Authorship in Ancient Traditions, ed. Markus Asper, 217–254. Berlin/Boston: De Gruyter.

    Chapter  Google Scholar 

  • ———. 2020. Why Were Greek Mathematical Diagrams Schematic? Nuncius 35: 506–535.

    Article  Google Scholar 

  • Pecchia, Cristina, Johanna Buss, and Alaka A. Chudal. 2021. Print Cultures in the Making in 19th- and 20th-Century South Asia: Beyond Disciplinary Boundaries. Philological Encounters 6 (1–2): 1–14. https://doi.org/10.1163/24519197-bja10019.

    Article  Google Scholar 

  • Plofker, Kim. 2021. Anachronism and anachorism in the study of mathematics in India. In Anachronisms in the History of Mathematics. Essays on the Historical Interpretation of Mathematical Texts, ed. Niccolò Guicciardini, 83–104. Cambridge, UK: Cambridge University Press.

    Chapter  Google Scholar 

  • Pollock, Sheldon. 2009. Future Philology? The Fate of a Soft Science in a Hard World. In The Fate of Disciplines, eds. J. Chandler and A. I. Davidson. Critical Inquiry 35 (4): 931–961.

    Article  Google Scholar 

  • ———. 2016. Philology and Freedom. Philological Encounters 1 (1-4): 4–30. https://doi.org/10.1163/24519197-00000012.

    Article  Google Scholar 

  • Pollock, Sheldon, Benjamin A. Elman, and Ku-ming Kevin Chang, eds. 2015. World Philology. Harvard: Harvard University Press.

    Google Scholar 

  • Proust, Christine. 2002. Numération centésimale de position à Mari. In Recueil d’études à la mémoire d’André Parrot, Florilegium Marianum 6 = Mémoires de Nabu 7, eds. D. Charpin and J.-M. Durand, 513–516. Paris.

    Google Scholar 

  • Ramasubramanian, K., Takao Hayashi, and Clemency Montelle. 2019. Introduction. In Bhāskara Prabhā, eds. K. Ramasubramanian, Takao Hayashi, and Clemency Montelle, XV-XXXIV. New Delhi/Singapore: Hindustan Book Agency and Springer Nature.

    Google Scholar 

  • Saito, Ken. 2006. A preliminary study in the critical assessment of diagrams in Greek mathematical works. SCIAMVS 7: 81–144.

    Google Scholar 

  • ———. 2011 (April 3). The Diagrams of Book II and III of the Elements in Greek Manuscripts. In Diagrams in Greek Mathematical Texts (May 8, 2008, last update April 3, 2011). Report version 2.03, ed. Ken Saito, 39–80. Online publication: https://www.greekmath.org/diagrams/Diagrams_in_Greek_Mathematical_Texts_Report_Ver_2_03_20110403.pdf. Accessed 26 Apr 2023.

  • ———. 2019. Re-examination of the different origins of the arithmetical books of Euclid’s Elements. Special issue: On Mathemata: Commenting on Greek and Arabic Mathematical Texts. Historia Mathematica 47: 39–53.

    Google Scholar 

  • Saito, Ken, and Nathan 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. Karine Chemla, 135–162. Cambridge: Cambridge University Press.

    Google Scholar 

  • Shanghai Tushuguan 上海圖書館, and Beijing Daxue Tushuguan 北京大學圖書館. 1980. Songke suanjing liu zhong 宋刻算經六種 (Six mathematical Canons printed during the Song dynasty). Beijing: Wenwu chubanshe.

    Google Scholar 

  • Sidoli, Nathan, and Ken Saito. 2012. Comparative analysis in Greek geometry. Historia Mathematica 39: 1–33.

    Article  Google Scholar 

  • Singh, Vaibhav. 2018. The Machine in the Colony: Technology, Politics, and the Typography of Devanagari in the Early Years of Mechanization. Philological Encounters 3: 469–495. https://doi.org/10.1163/24519197-12340051.

    Article  Google Scholar 

  • Smadja, Ivahn. 2016. On two conjectures that shaped the historiography of indeterminate analysis: Strachey and Chasles on Sanskrit sources. Historia Mathematica 43: 241–287. https://doi.org/10.1016/j.hm.2016.04.001.

    Article  Google Scholar 

  • Suarez, Michael F., and H.R. Woudhuysen, eds. 2013. The Book: A Global History. Oxford: Oxford University Press.

    Google Scholar 

  • Thibaut, Georg, and Sudhākara Dvivedin. 1889. The Pañchasiddhântikâ, the Astronomical Work of Varâha Mihira. The Text, Edited with an Original Commentary in Sanskrit and an English Translation and Introduction. Benares: E. J. Lazarus and co, at the Medical Hall Press.

    Google Scholar 

  • Timpanaro, Sebastiano. 2005. The Genesis of Lachmann’s Method. Edited and translated by Glenn W. Most. Chicago/London: The University of Chicago Press.

    Google Scholar 

  • Ver Eecke, Paul. 1921. Les oeuvres complètes d’Archimède, traduites du grec en français avec une introduction et des notes. Paris: Desclée, De Brouwer & cie.

    Google Scholar 

  • Vitrac, Bernard. 1990–2001. Euclide: Les Eléments. Vol. 1: Introduction générale (par Maurice Caveing) et Livres I à IV (1994). Vol. 2: Livres V à IX (1994). Vol. 3: Livre X (1998). Vol. 4: Livres XI à XIII (2001). Book series Bibliothèque d’histoire des sciences. Paris: Presses Universitaires de France.

    Google Scholar 

  • Zheng, Cheng 鄭誠, and Yiwen Zhu 朱一文. 2010. Shushu Jiuzhang liuchuan xin kao: Zhao Qimei chaoben chutan 數書九章流傳新考: 趙琦美鈔本初探 (A new study on the textual transmission of Shushu Jiuzhang). Ziran Kexueshi Yanjiu 自然科學史研究 (Studies in the History of Natural Sciences) 29 (3): 319–328.

    Google Scholar 

  • Zhou, Xiaohan 周霄漢. 2018. Elements of Continuity between Mathematical Writings from the Song-Yuan (13th–14th century) Dynasties and the Ming Dynasty (15th century): Comparing Yang Hui’s Mathematical Methods (1261 CE) and Wu Jing’s Great Compendium (1450 C.E.). PhD. Dissertation, University Paris Diderot.

    Google Scholar 

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Chemla, K., Keller, A. (2024). Shaping the Sciences of the Ancient and Medieval World: An Introduction. In: Keller, A., Chemla, K. (eds) Shaping the Sciences of the Ancient and Medieval World. Archimedes, vol 69. Springer, Cham. https://doi.org/10.1007/978-3-031-49617-2_1

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