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Greek Sexagesimals and Zeros

  • Alexander Jones
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Tools, Techniques, and Technologies
This chapter is in the book Tools, Techniques, and Technologies

Abstract

Starting (so far as we know) in the Hellenistic Period, and continuing through the Byzantine Period, Greek astronomy widely employed a sexagesimal (base-60) place-value notation for numerical quantities both in calculations and in presentation of numerical data. The Greek sexagesimal notation was modelled on the Babylonian cuneiform sexagesimal notation, which was prevalent in Babylonian mathematical astronomy during the last several centuries BCE and in Babylonian mathematics at least as early as the Old Babylonian Period (early second millennium BCE). The Greek zero also had a counterpart in the Babylonian notation in its later phases. There are, however, important differences between Greek and Babylonian practices in writing and manipulating sexagesimal numerals. The Greek zero also emerged from its original sexagesimal context into certain situations where non-sexagesimal Ionian numerals were the norm, coming even to express the quantity zero in its own right.

Abstract

Starting (so far as we know) in the Hellenistic Period, and continuing through the Byzantine Period, Greek astronomy widely employed a sexagesimal (base-60) place-value notation for numerical quantities both in calculations and in presentation of numerical data. The Greek sexagesimal notation was modelled on the Babylonian cuneiform sexagesimal notation, which was prevalent in Babylonian mathematical astronomy during the last several centuries BCE and in Babylonian mathematics at least as early as the Old Babylonian Period (early second millennium BCE). The Greek zero also had a counterpart in the Babylonian notation in its later phases. There are, however, important differences between Greek and Babylonian practices in writing and manipulating sexagesimal numerals. The Greek zero also emerged from its original sexagesimal context into certain situations where non-sexagesimal Ionian numerals were the norm, coming even to express the quantity zero in its own right.

Chapters in this book

  1. Frontmatter 1
  2. Acknowledgements
  3. Contents VII
  4. List of Figures and Tables IX
  5. Prologue: of Friendship and Fishponds 1
  6. Introduction 5
  7. Part I: Historiography, Disciplinary Categories, and Anachronism
  8. Greco-Roman Histories of Astronomy, Their Genres, and Their Afterlives 15
  9. When was Cosmology? The Curious History of a Disciplinary Category 33
  10. Surmise or Certainty: Women in Science in Antiquity 51
  11. Deep Reading of Kepler’s New Astronomy: An Exercise in Computational History of Science 65
  12. Part II: Scientific Writing: Genres, Authority, Authorship, and Audiences
  13. Narrative Elements in Aristotle’s Generation of Animals 83
  14. Style and Intended Readership of Theophrastus’ On Fire (De igne) 95
  15. Strategies of Moralising in the Pseudo-Vergilian Aetna 115
  16. Leonides of Alexandria’s Isopsephic Epigrams: An Astronomical Art? 131
  17. Faithful Marriages and Wild Unions: Palladius’ On Grafting 153
  18. Ancient Authority in Arabic-Islamic Scientific Writing and Practice 169
  19. “A Cabinet of Many Rare Secrets”: The Uses and Abuses of Aristotle’s Masterpiece 191
  20. Part III: Counting and Measuring: Tools, Diagrams, and Replicas
  21. The Various Uses of Numbers and Mathematics in Ancient Egypt 219
  22. Greek Sexagesimals and Zeros 231
  23. The Diagrams and Replicas of Richard of Wallingford’s Clock 253
  24. Measuring Magnetism: Retrospective on Theories and Instruments from Lucretius to Blackett and Bullard 279
  25. Ancients and Moderns in Tycho Brahe’s Astronomy 295
  26. List of Contributors 317
  27. Bibliography
  28. Index
  29. Index Locorum
https://doi.org/10.1515/9783111010632-015

Chapters in this book

  1. Frontmatter 1
  2. Acknowledgements
  3. Contents VII
  4. List of Figures and Tables IX
  5. Prologue: of Friendship and Fishponds 1
  6. Introduction 5
  7. Part I: Historiography, Disciplinary Categories, and Anachronism
  8. Greco-Roman Histories of Astronomy, Their Genres, and Their Afterlives 15
  9. When was Cosmology? The Curious History of a Disciplinary Category 33
  10. Surmise or Certainty: Women in Science in Antiquity 51
  11. Deep Reading of Kepler’s New Astronomy: An Exercise in Computational History of Science 65
  12. Part II: Scientific Writing: Genres, Authority, Authorship, and Audiences
  13. Narrative Elements in Aristotle’s Generation of Animals 83
  14. Style and Intended Readership of Theophrastus’ On Fire (De igne) 95
  15. Strategies of Moralising in the Pseudo-Vergilian Aetna 115
  16. Leonides of Alexandria’s Isopsephic Epigrams: An Astronomical Art? 131
  17. Faithful Marriages and Wild Unions: Palladius’ On Grafting 153
  18. Ancient Authority in Arabic-Islamic Scientific Writing and Practice 169
  19. “A Cabinet of Many Rare Secrets”: The Uses and Abuses of Aristotle’s Masterpiece 191
  20. Part III: Counting and Measuring: Tools, Diagrams, and Replicas
  21. The Various Uses of Numbers and Mathematics in Ancient Egypt 219
  22. Greek Sexagesimals and Zeros 231
  23. The Diagrams and Replicas of Richard of Wallingford’s Clock 253
  24. Measuring Magnetism: Retrospective on Theories and Instruments from Lucretius to Blackett and Bullard 279
  25. Ancients and Moderns in Tycho Brahe’s Astronomy 295
  26. List of Contributors 317
  27. Bibliography
  28. Index
  29. Index Locorum
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