Book contents
- Ancient Greece and China Compared
- Ancient Greece and China Compared
- Copyright page
- Contents
- Figures
- Acknowledgements
- Notes on Editions
- Contributors
- Introduction: Methods, Problems and Prospects
- Part I Methodological Issues and Goals
- Part II Philosophy and Religion
- Part III Art and Literature
- Part IV Mathematics and Life Sciences
- 10 Divisions, Big and Small: Comparing Archimedes and Liu Hui
- 11 Abstraction as a Value in the Historiography of Mathematics in Ancient Greece and China: A Historical Approach to Comparative History of Mathematics
- 12 Recipes for Love in the Ancient World
- Part V Agriculture, Planning and Institutions
- Afterword
- Index
- References
10 - Divisions, Big and Small: Comparing Archimedes and Liu Hui
from Part IV - Mathematics and Life Sciences
Published online by Cambridge University Press: 21 December 2017
Book contents
- Ancient Greece and China Compared
- Ancient Greece and China Compared
- Copyright page
- Contents
- Figures
- Acknowledgements
- Notes on Editions
- Contributors
- Introduction: Methods, Problems and Prospects
- Part I Methodological Issues and Goals
- Part II Philosophy and Religion
- Part III Art and Literature
- Part IV Mathematics and Life Sciences
- 10 Divisions, Big and Small: Comparing Archimedes and Liu Hui
- 11 Abstraction as a Value in the Historiography of Mathematics in Ancient Greece and China: A Historical Approach to Comparative History of Mathematics
- 12 Recipes for Love in the Ancient World
- Part V Agriculture, Planning and Institutions
- Afterword
- Index
- References
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- Ancient Greece and China Compared , pp. 259 - 289Publisher: Cambridge University PressPrint publication year: 2018
References
Andersen, K. (1985) ‘Cavalieri’s method of indivisibles’, Archive for History of Exact Sciences 31: 291–367.Google Scholar
Caroli, M. (2007) Il titolo iniziale nel rotolo librario greco-egizio. Con un catalogo delle testimonianze iconografiche greche e di area vesuviana. Bari.Google Scholar
Chemla, K. (2005) ‘The interplay between proof and algorithm in 3rd century China: the operation as prescription of computation and the operation as argument’, in Visualization, Explanation and Reasoning Styles in Mathematics, eds. Mancosu, P., Jørgensen, K. F. and Pedersen, S. A.. Dordrecht: 123–45.Google Scholar
Chemla, K. (2013) ‘Ancient writings, modern conceptions of authorship. Reflections on some historical processes that shaped the oldest extant mathematical sources from ancient China’, in Writing Science: Medical and Mathematical Authorship in Ancient Greece, ed. Asper, M.. Berlin: 63–82.Google Scholar
Clagett, M. (1976) Archimedes in the Middle Ages, vol. II: The Translations from the Greek by William of Moerbeke. Philadelphia.Google Scholar
Cullen, C. (2002) ‘Learning from Liu Hui? A different way to do mathematics’, Notices of the AMS 49: 783–91.Google Scholar
Dauben, J. W. (2007) ‘Chinese mathematics’, in The Mathematics of Egypt, Mesopotamia, China, India and Islam: A Sourcebook, ed. Katz, V. J.. Princeton: 187–384.Google Scholar
Fu, D. 1991. ‘Why did Liu Hui fail to derive the volume of a sphere?’, Historia Mathematica 18: 212–38.Google Scholar
Hayashi, E. and Saito, K. (2009) Tenbin no Majutsushi: Arukimedesu no Sugaku (Sorcerer of the Scales: Archimedes’ Mathematics). Tokyo.Google Scholar
He, J.-H. (2004) ‘Zu-Geng’s axiom vs Cavalieri’s theory’, Applied Mathematics and Computation 152: 9–15.Google Scholar
Heath, T. L. (1912) The Method of Archimedes Recently Discovered by Heiberg. Cambridge.Google Scholar
Horng, W.-S. (1995) ‘How did Liu Hui perceive the concept of infinity: a revisit’, Historia Scientiarum 4: 207–22.Google Scholar
Knorr, W. R. (1982) ‘Observations on the early history of the Conics’, Centaurus 26: 1–24.Google Scholar
Knorr, W. R. (1996) ‘The method of indivisibles in ancient geometry’, in Vita Mathematica: Historical Research and Integration with Teaching, ed. Calinger, R.. Washington, DC: 67–86.Google Scholar
Martzloff, J. C. (1997) A History of Chinese Mathematics (orig. Histoire des mathématiques chinoises, Paris 1987). Berlin.Google Scholar
Netz, R. (2004) The Works of Archimedes, vol. I: The Two Books on the Sphere and the Cylinder. Cambridge.Google Scholar
Netz, R. (2009) Ludic Proof: Greek Mathematics and the Alexandrian Aesthetics. Cambridge.Google Scholar
Netz, R., Acerbi, F. and Wilson, N. (2004) ‘Towards a reconstruction of Archimedes’ Stomachion’, SCIAMVS 5: 67–99.Google Scholar
Netz, R., Noel, W., Tchernetska, N. and Wilson, N. (2011) The Archimedes Palimpsest. Cambridge.Google Scholar
Netz, R., Saito, K. and Tchernetska, N. (2001–2) ‘A new reading of Method proposition 14: preliminary evidence from the Archimedes Palimpsest’, SCIAMVS 2: 9–29; 3: 109–29.Google Scholar
Rufini, E. (1926) Il ‘Metodo’ di Archimede e le origini del calcolo infinitesimale nell’ Antichità. Bologna.Google Scholar
Saito, K. and Napolitani, P. D. (2014) ‘Reading the lost folia of the Archimedean Palimpsest: the last proposition of the Method’, in From Alexandria, through Baghdad: Surveys and Studies in the Ancient Greek and Medieval Islamic Mathematical Sciences, in Honor of J.L. Berggren, eds. Sidoli, N. and van Brummelen, G.. Berlin: 199–225.Google Scholar
Sato, T. (1986) ‘A reconstruction of “The Method” 17, and the development of Archimedes’ thought on quadrature – why did Archimedes not notice the internal connection in the problems dealt with in many of his works?’, Historia Scientiarum 31: 61–86.Google Scholar
Sato, T. (1987) ‘A reconstruction of “The Method” 17, and the development of Archimedes’ thought on quadrature – why did Archimedes not notice the internal connection in the problems dealt with in many of his works?’, Historia Scientiarum 32: 75–142.Google Scholar
Vardi, I. (1999) ‘What is ancient mathematics?’, The Mathematical Intelligencer 2: 38–47.Google Scholar
Volkov, A. (2012) ‘Argumentation for state examinations: demonstration in traditional Chinese and Vietnamese mathematics’, in The History of Mathematical Proof in Ancient Traditions, ed. Chemla, K.. Cambridge: 509–51.Google Scholar
Wagner, D. B. (1978) ‘Liu Hui and Tsu Keng-chih on the volume of a sphere’, Chinese Science 3: 59–79.Google Scholar
Wagner, D. B. (1979) ‘An early Chinese derivation of the volume of a pyramid: Liu Hui, third century AD’, Historia Mathematica 6: 164–88.Google Scholar
Williams, B. J. and Harvey, H. R. (1997) The Codice de Santa María Asunción: Facsimile and Commentary: Households and Lands in Sixteenth-Century Tepetlaoztoc. Salt Lake City.Google Scholar
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