The Algorithm of Extraction in Greek and Sino-Indian Mathematical Traditions

  • Duan Yao-YongEmail author
  • Kostas Nikolantonakis


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.


Early Writer Eleventh Century Mathematical Tradition False Position Digit Quotient 
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  1. 1.
    Chemla, K.: Should they read FORTRAN as if it were English? The Collection of the Chinese University of Hong Kong. Vol. 1(2), 1987, pp. 301–316.Google Scholar
  2. 2.
    Christopher, C.: The Suan shu shu ‘Writings on Reckoning,’, p.88.
  3. 3.
    Heath, T. L.: Greek Mathematics, Vol. II, Oxford, 1921.zbMATHGoogle Scholar
  4. 4.
    Patwardhan, K. S.: Somashekhara Amrita Naimpally, Shyam Lal Singh, Līlāvatī of Bhāskarācārya, A Treatise of Mathematics of Vedic Tradition, Delhi, 2001, pp. 23–24.Google Scholar
  5. 5.
    Schöne, H: Heronis Alexandrini Opera Quae Superunt Omnia. Vol. III, Leipzig (1903).Google Scholar
  6. 6.
    Shuchu, G.: The Collation of Suanshushu (A Book of Arithmetic), China Historical Materials of Science and Technology, Vol. 22 (2001), 3, pp. 214–215.Google Scholar
  7. 7.
    Smith, D. E.: History of Mathematics, Vol. 2: Special Topics of Elementary Mathematics, New York (1953).Google Scholar
  8. 8.
    \(\Gamma \iota \acute{\alpha }\nu \nu \eta \varsigma \ \Theta \omega \mu \alpha \acute{\ddot{\iota }}\delta \eta \varsigma,\ \grave{O}\ A\lambda \gamma \acute{o}\rho \iota \theta \mu o\varsigma \ \nu \pi o\lambda o\gamma \iota \sigma \mu o\acute{\upsilon }\ \tau \epsilon \tau \rho \alpha \gamma \omega \nu \iota \acute{\eta }\varsigma \ \rho \acute{\iota }\zeta \alpha \varsigma,Z\eta \tau \acute{\eta }\mu \alpha \tau \alpha \ I\sigma \tau o\rho \acute{\iota }\alpha \varsigma \ \tau \omega \nu \ M\alpha \theta \eta \mu \alpha \tau \iota \kappa \acute{\omega }\nu,\ \acute{}O\mu \iota \lambda o\varsigma \ \delta \iota \alpha \ \tau \eta \nu \ I\sigma \tau o\rho \acute{\iota }\alpha \ \tau \omega \nu M\alpha \theta \eta \mu \alpha \tau \iota \kappa \acute{\omega }\nu \), Thessaloniki, Vol. 7, May 1987.Google Scholar

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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.The Chinese People’s Armed Police Force AcademyLangfangChina
  2. 2.University of West MacedoniaFlorinaGreece

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