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3 results

  • Chapter 13 - Concepts in Greek Mathematics

  • Edited by Gábor Betegh, University of Cambridge, Voula Tsouna, University of California, Santa Barbara
  • Book:
    Conceptualising Concepts in Greek Philosophy
    Published online:
    25 April 2024
    Print publication:
    02 May 2024, pp 307-329

  • Summary

    The chapter ‘Concepts in Greek Mathematics’ by Reviel Netz problematises a set of assumptions commonly encountered in the literature on Greek mathematics, which typically derive from a supposedly objective, a-historical conception of mathematical theory and practice. In sharp opposition to that tradition, Netz raises the possibility that the purpose of engaging with mathematical concepts may have been different in antiquity than what it has been taken to be. He asks central questions afresh, for instance: why do mathematical texts begin with definitions, and what is the purpose of mathematical definitions and of axioms. In connection to these issues, he highlights new aspects of the relationship between Greek mathematics and Greek philosophy, between engaging with mathematical concepts and philosophical thinking. He also advances the thesis that the relations between mathematics and philosophy changed through the various eras of antiquity, as did mathematical concepts and the role of mathematical definitions. We should seriously entertain the idea that even mathematical concepts need to be viewed within a given historical and cultural context.

  • Euclid’s Fourth Postulate: Its authenticity and significance for the foundations of Greek mathematics

  • Vincenzo De Risi
  • Journal:
    Science in Context / Volume 35 / Issue 1 / March 2022
    Published online by Cambridge University Press:
    07 December 2023, pp. 49-80
    Print publication:
    March 2022
    • Article
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  • The Fourth Postulate of Euclid’s Elements states that all right angles are equal. This principle has always been considered problematic in the deductive economy of the treatise, and even the ancient interpreters were confused about its mathematical role and its epistemological status. The present essay reconsiders the ancient testimonies on the Fourth Postulate, showing that there is no certain evidence for its authenticity, nor for its spuriousness. The paper also considers modern mathematical interpretations of this postulate, pointing out various anachronisms. It further discusses the validity of the ancient proof by superposition of the Fourth Postulate. Finally, the article proposes an interpretation of the history of the concept of angle in Greek geometry between Euclid and Apollonius, and puts forward a conjecture on the interpolation of the Fourth Postulate in the Hellenistic age. The essay contributes to a general reassessment of the axiomatic foundations of ancient mathematics.

  • 11 - THE EXACT SCIENCES

  • Edited by R. N. Frye
  • Book:
    The Cambridge History of Iran
    Published online:
    28 March 2008
    Print publication:
    26 June 1975, pp 378-395

  • Summary

    This chapter describes scientific activity in Iran during the four centuries beginning about 30/650. Early ‘Abbāsid scientists tended to be astronomer-astrologers whose techniques and theories were inherited from Indian and Sāsānian forebears and whose role as innovators was small. Their sole major contribution was in the form of numerous and meticulous astronomical observations. Present knowledge of the scribal arithmetic is due largely to study of a textbook for the use of government employees written by Abu'l-Wafā' al-Buzjānī, a thinker of great originality and power. Computational mathematics did not reach the degree of sophistication it achieved later, in Mongol and Timurid times, but numerical tables of functions were considerably more extensive and precise than those produced by the Greeks and the Indians. Among the more complicated arithmetic processes, the operation of root extraction received considerable attention in ‘Abbāsid times.