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Taisbak, Christian Marinus
The Importance of Being Given
2002, 272 s., indb
Acta Historica Scientiarum Naturalium et Medicinalium, vol. 45
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Euclid's Data - The Importance of Being Given
is a scholarly contribution to an area - the history of Greek geometrical analysis - that is still insufficiently understood. At the time of Zeuthen, and even up to the middle of the last century, it was fashionable to treat the Data algebraically. Taisbak has abandoned this approach completely, arguing that it does nothing to help us understand either the development of the work or the reasons for its having been copied, studied, and quoted for more than 2 millennia. We must bear a queer sort of frustration that affects us everywhere in the Data: we get very little information, hardly any 'knowledge' of the givens. And why not? Probably because 'knowing' geometrical objects was problematic in those days when the concept of 'given' came into being, and the consequences of incommensurability were just being understood. Next to nothing is known of these items, and very little that is worth knowing: length, size, distance, - any of the attributes that can be spoken of by means of numbers.
Although there have been two recent translations of the Data, this one is unique in providing, as well, an extensive commentary, which provides the insights gained from three decades of studying the work. The book is meant as a coherent and understandable account of what could have been going on in Euclid's mind, and some reasons for believing that that is what actually was going on in his mind.
Christian Marinus Taisbak recently retired as associate professor in the Department of Greek and Latin at the University of Copenhagen. He is the author of Coloured Quadrangles. A Guide to the Tenth Book of Euclid's Elements
(Museum Tusculanum Press, 1982).
Notation and Abbreviations
Definitionsl-4: The Foundation
Three questions and one
Six parallel statements
Mathematicians Unemployed or Admitted Tools ?
The Helping Hand
By geometrical methods
Definitions 5-8: Circles
Definitions 9-12: Magnitudes by a Given Greater
Definitions 13-15: Lines and Direction
Chapter2.Magnitudes and Ratio I.Dt 1-9
Dt 1-4. Four Axiomatic (?) Fundamentals
Dt5-9.Metamorphoses of Ratios
Cbapter 3. By a Given Greater than in Ratio. Dt 10-21
Synopsis of Dt 10-21
Chapter 4. Magnitudes and Ratio II. Dt 22-24
Chapter 5. Position. Distance, Direction, Parallels. Dt 25-38
Cbapter 6. Form. Triangles and Polygons. Dt 39-55
Dt55 The Main Theorem?
Cbapter 7. Equiangular parallelograms I. Reciprocal proportion. Dt 56
Cbapter 8. Application of areas I. Dt 57-62
Cbapter 9. Ratio and Angles. Dt 63-67
Cbapter 10. Equiangular parallelograms II. Reciprocal proportion. Dt 68-75
Cbapter 11. Duplicates and Outsiders. Dt 76-83
Cbapter 12. Application of areas. II. Dt 84-85
Cbapter 13. Intersecting Hyperbolas. H. G. Zeuthen and Dt 86
Cbapter 14. Circles. Dt 87-94
Appendix A. Marinus' Commentary
Appendix B. Synopsis of Dt 39 and I.22
List of Definitions and Enunciations
Deductive Structure of Dt 1-9
Deductive Structure of Dt 10-24
Deductive Structure of Dt 25-38
Deductive Structure of Dt 39-55
Deductive Structure of Dt 56-67
Deductive Structure of Dt 68-83
Deductive Structure of Dt 84-94
Euclid's Data "paves the way to the right tree. It includes Heinrich Menge's edition of the Greek text and a faithful translation of it, it also offers a thorough historical interpretation of the Data's mathematical content and deductive steps, and above all it lays down the foundations for a positive interpretation of the Data, by putting forward a non-quantitative account of the term "given". All these features make Taisbak's book the best extant interpretation of the Data."
- Orna Hariri, Tel Aviv University, Department of Classics, International Journal of the Classical Tradition, Spring 2005.
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Christian Marinus Taisbak som forfatter
1982, ISBN 978-87-88073-46-1, hft
2010, ISBN 978-87-635-3320-1, e-publikation
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