Summary
In this paper, the problem of the origin of the algorithm of extraction is discussed. It is shown that the same algorithm, despite different mathematical cultures, existed in ancient China and Greece. The algorithm of extraction in China is algebraic and mechanical, in Greece geometric. The authors contrast the algorithm of extraction in China to that of Līlāvatī in India, though mathematics in ancient China and India both belong to the system of algorithms. In addition, the authors make use of the original literature of Greece, and at the same time, new results on the mathematics in the pre-Qin period, the outline of the algorithm of extraction in the pre-Nine Chapters.
Duan Yao-Yong is a professor of the Chinese People’s Armed Police Force Academy. He specializes in the history of mathematics in China and India, and mathematical education.
Konstantinos Nikolantonakis is Lecturer in the Science of Education, Department of the University of West Macedonia, Florina Epistemologie, History of Exact Sciences et Technology, Paris-VII University. He specializes in the field of history of Ancient Greek Mathematics.
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Notes
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[[7pp.146–147]].
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It is like the method from India, probably influenced by it.
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It is not method of Liu Hui, but in the Nine Chapters.
References
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\(\Gamma \iota \acute{\alpha }\nu \nu \eta \varsigma \ \Theta \omega \mu \alpha \acute{\ddot{\iota }}\delta \eta \varsigma,\ \grave{O}\ A\lambda \gamma \acute{o}\rho \iota \theta \mu o\varsigma \ \nu \pi o\lambda o\gamma \iota \sigma \mu o\acute{\upsilon }\ \tau \epsilon \tau \rho \alpha \gamma \omega \nu \iota \acute{\eta }\varsigma \ \rho \acute{\iota }\zeta \alpha \varsigma,Z\eta \tau \acute{\eta }\mu \alpha \tau \alpha \ I\sigma \tau o\rho \acute{\iota }\alpha \varsigma \ \tau \omega \nu \ M\alpha \theta \eta \mu \alpha \tau \iota \kappa \acute{\omega }\nu,\ \acute{}O\mu \iota \lambda o\varsigma \ \delta \iota \alpha \ \tau \eta \nu \ I\sigma \tau o\rho \acute{\iota }\alpha \ \tau \omega \nu M\alpha \theta \eta \mu \alpha \tau \iota \kappa \acute{\omega }\nu \), Thessaloniki, Vol. 7, May 1987.
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Yao-Yong, D., Nikolantonakis, K. (2009). The Algorithm of Extraction in Greek and Sino-Indian Mathematical Traditions. In: Yadav, B., Mohan, M. (eds) Ancient Indian Leaps into Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4695-0_11
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