Skip to main content

The Overshadowing of Euclid’s Geometry by Legendre’s Géométrie in the Modern Greek Education

  • Chapter
  • First Online:
Exploring Mathematical Analysis, Approximation Theory, and Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 207))

  • 163 Accesses

Abstract

Euclid’s Elements is an important heritage of the Neo-Hellenic civilization. Despite this fact Euclid is very difficult to be found in the Greek mathematics education as it was developing after the liberation from the Ottoman Empire.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Traditionally, at some universities of Northern Italy, there had been a Medical-Physics Faculty, composed of two Departments: a preparatory one, for Physics-Mathematics and a Medical-Surgical (see [36], p. 97).

  2. 2.

    To this category belong the books-translations of Anthracites, Theotokis, Voulgaris and Benjamin of Lesvos (see [39]).

  3. 3.

    These types of books were translations of Razi and Kouma (see [39]).

  4. 4.

    The Greek translation of this concept was according to the 12th edition of the Legendre’ Géométrie, in 1823.

  5. 5.

    He was an aristocrat (he had the title of Count), educated with medical and philosophical studies in Padua, Italy, and a high degree of political prestige, due to his role in Russian diplomacy as a leading adviser in foreign policy for Tsar.

  6. 6.

    He was great spiritual leader of modern Greece. Through his work in Classical philology, Corais aimed at inculcating in Greeks a sense of their ancient heritage. His emphasis on the need to resurrect Greece’s ancient glory stemmed in large part from his intense hatred of the Orthodox higher clergy whom he blamed for the degraded state of the populace. For Corais, then, the model for a new Greece should be ancient Athens rather than medieval Byzantium (see [11], p. 10).

  7. 7.

    Sarazin, L.-Ch.: Manuel des écoles élémentaires, ou Exposé de la method d” enseignement mutual; suivi des ordonnances, arrêtes,règlements concernantl” instruction primaire, Paris, 1829.

  8. 8.

    Skarlatos Soutsos (1806–1887) was an aristocrat; he studied on scholarship of King Ludwig I at the Military School of Munich. He served as an officer of the Greek army; he joined the Greek military school, worked in politics and served as Minister of War, http://el.wikipedia.org/wiki/Σκαρλάτος_Σούτσος

  9. 9.

    Alexandros Rizos Ragavis (1809–1892) was an aristocrat; he studied at the Military School in Munich where he had the support of King Ludwig I. He first served as an officer in the Greek army, and later as a secretary of the Ministry of Education and Ministry of Interior. He became Professor of Archaeology at the University of Athens. He undertook as a Ministry of Foreign Affairs in the period 1856–1859, and in 1867. Afterwards he served as Ambassador of Greece to the U.S., Istanbul, Paris and Berlin. Important was also his contributions in Greek Literature.

  10. 10.

    George A. Gerakis, was one of the first scholars of the Greek government to study in Germany, circa 1837. Afterwards he taught mathematics in “Hellenic” school and Gymnasium of Patras, from 1841. He published several mathematics textbooks and translated into Greek respective textbooks of F. W.D. Snell and C. Koppe (see [50], p.202]).

  11. 11.

    In the late 1830’s there were three high schools, one in Nafplion, one in Athens and one in Syros island.

  12. 12.

    Before Kondis, at the Gymnasium of Nauplion were teaching mathematics, Dimitrios Stavridis (1803–1866), who graduated from the Polytechnic of Vienna, and Ch. Vernardos (see [7]).

  13. 13.

    See (in Greek) in Journal Pandora, 8, 1857–58, p. 181.

  14. 14.

    Specifically, this research was an attempt that can be seen as the second Greek mathematical research effort, with the first one this of Carandinos in the late 1820s.

  15. 15.

    The original that was used for this summary is unknown.

  16. 16.

    He studied Law in Paris and graduated with a doctorate in 1860.

  17. 17.

    Greeks, apart from the independent Greece.

  18. 18.

    Who was the uncle of the eminent mathematician, Constantinos Caratheodory (1873–1950).

References

  1. D. Antoniou, The Beginnings of Educational Planning in the Greek State: The Plan Commission of 1833 (in Greek) (Pataki, Athens, 1992)

    Google Scholar 

  2. L. Belloni, Italian medical education after 1600, in The History of Medical Education, An International Symposium held February 5–9, 1968, ed. by C.D. O’Malley, (University of California Press, Berkeley, Los Angeles, London, 1970), pp. 105–119

    Google Scholar 

  3. A.S. Caratheodory, About secondary education (in Greek), vol I (Greek Literary Association of Constantinople, 1863), pp. 174–189

    Google Scholar 

  4. R. Clogg, A Concise History of Greece (Cambridge University Press, 1992)

    Google Scholar 

  5. A. Damascinos, Response to the Criticism of My Arithmetic by Mr B. Lakon, Full Professor in the National University (in Greek) (Brochure, Athens, 1867), 36 pages

    Google Scholar 

  6. A. Damascinos, Response to the Rejoinder by Mr B. Lakon, Full Professor in the National University (in Greek) (Brochure. (Athens, 1868), 24 pages

    Google Scholar 

  7. J. Demoiris, History of the Gymnasium of Nafplio (Athens, 1939)

    Google Scholar 

  8. T. Evaggelidou, The Education during the Turkish Occupation (in Greek), vol A (Athens, 1936)

    Google Scholar 

  9. A. Fatseas, Reflections on the Public and Private Education of Young Greeks (in Greek) (Athens, 1856)

    Google Scholar 

  10. H. Fotopoulos, Military Academy. The first higher education institution founded by the governor of Greece Ioannis Capodistrias, (in Greek), Stratiotiki Epitheorisi [Military Review], September–October, pp. 146–157 (2003)

    Google Scholar 

  11. T. Gallant, Modern Greece (Arnold, London, 2001)

    Google Scholar 

  12. K. Gardika-Alexandropoulou, Archive of Alexandros St.Caratheodory (in Greek) (Center for Neohellenic Research, National Research Foundation, Athens, 1981)

    Google Scholar 

  13. Y. Hamilakis, The Nation and its Ruins: Antiquity, Archeology, and National Imagination in Greece (Oxford University Press, Oxford, 2007)

    Google Scholar 

  14. G. Henderson, The Revival of Greek Thought, 1620–1830 (State University of New York Press, Albany, 1970)

    Google Scholar 

  15. Y. Karas, G. Vlachakis, Sciences in the Southeastern Europe during the 19th Century. Greece, Serbia-Montenegro (National Hellenic Research Foundation, Athens, 2004)

    Google Scholar 

  16. A. Kastanis, The teaching of mathematics in the Greek military academy during the first year of its foundation (1828–1834). Hist. Math. 30, 123–139 (2003)

    Article  MathSciNet  Google Scholar 

  17. A. Kastanis, The teaching of mathematics at the military academy at first Otto (in Greek), in History & Mathematics Education (in Greek), ed. by C. Thomaidis, N. Kastanis, K. Tzanakis, (Ziti, Thessaloniki, 2006), pp. 131–151

    Google Scholar 

  18. I. Kastanis, N. Kastanis, The transmission of mathematics into Greek education, 1800-1840: From individual initiatives to institutionalization. Paedagog. Hist. 42(4&5), 515–534 (2006)

    Article  Google Scholar 

  19. N. Kastanis, “Euclid must go - we shall not be national underbidders”. A historicdidactical approach of this contradiction in our school (in Greek). Mathematiki Epitheorisi [Math. Rev.] 31, 3–18 (1986)

    Google Scholar 

  20. N. Kastanis, Aspects of Modern Mathematics Education (in Greek) (Ekdoseis Mathematiki Bibliothiki, Thessaloniki, 1998)

    Google Scholar 

  21. N. Kastanis, An Introduction to Modern Mathematics Education (in Greek) (Mathematics Department, Aristotle University of Thessaloniki, 2004). http://users.auth.gr/~nioka/ebook/neo_elliniki_3.pdf

  22. C. Katsikas, K. Therianos, History of Modern Education. From the Founding of the Greek State to 2004 (in Greek) (Savalas, Athens, 2004)

    Google Scholar 

  23. P. Kitromilides, Modern Greek Enlightenment, National Bank Cultural Foundation (in Greek) (MIET, Athens, 1996) [It is a Greek translation of Kitromilides PM: Tradition Enlightenment and Revolution, Ph.D., Harvard University, 1978]

    Google Scholar 

  24. A. Koumarianou, L. Droulia, E. Layton, The Greek Book, 1476–1830 (in Greek) (National Bank of Greece, Athens, 1986)

    Google Scholar 

  25. P. Kyprianos, Comparative History of Greek Education (in Greek) (Bibliorama, Athens, 2004)

    Google Scholar 

  26. Lakon, B. (1867): Criticism under Mr. Antonios Damascinos published Arithmetic (in Greek), Ephimeris ton Philomathon, October 14, 15th year, No. 647, pp.1353–1358

    Google Scholar 

  27. B. Lakon, Examination by Mr. Ch. Vafa’s proof of Euclid’s V axiom (in Greek). Athena 1, 378–381 (1872)

    Google Scholar 

  28. S. Manet, Cultural mixing of Western Europe and modern Greece through the “construction” of the Greek state (1821-1862). The role of Greek antiquity (in Greek), in The Greek world between East and West (1453–1981), ed. by A. Argyriou, K.A. Demadis, A.D. Lazaridis, vol. II., (in Greek), (Greek Letters, Athens, 1999), pp. 459–672

    Google Scholar 

  29. D. Mauroskoufis, The education 1821–1832 (in Greek), in Rejuvenating Care in the Years of Struggle in the History of Modern Hellenism, 1700–2000, (in Greek), ed. by V. Panagiotopoulos, vol. 3, (Greek Letters, Athens, 2003), pp. 289–310

    Google Scholar 

  30. C. Phili, Jean Carandinos (1784-1834): Initiateur des Mathématiques Francaises en Gréce. Archives Internationales d 'Histoires des Sciences 56(167–157), 81–125 (2006)

    Article  Google Scholar 

  31. B.A. Rosenfeld, A History of Non-Euclidean Geometry. Evolution of the Concept of a Geometric Space (Springer-Verlag, New York Inc. 1988), p. 103

    Book  Google Scholar 

  32. A. Roussopoulos, A Guide for Students of the University Otto (in Greek) (Nicholaos Angelidis, Athens, 1857)

    Google Scholar 

  33. D. Sakkis, Newly Established Greek State, 1833–1848 (in Greek) (Typothito, Athens, 2001)

    Google Scholar 

  34. G. Schubring, Changing cultural and epistemological views on mathematics and different institutional contexts, in nineteenth-century Europe, in Mathematical Europe. History, Myth, Identity, ed. by C. Goldstein et al., (Éditions de la Maison des sciences de l’Homme, Paris, 1996), pp. 361–388

    Google Scholar 

  35. G. Schubring, Neues über Legendre in Italien, in Mathematik im Fluß der Zeit, ed. by W. Hein, P. Ullrich, (Rauner, Augsburg, 2004), pp. 256–274

    Google Scholar 

  36. A. Sideri, Greek Students at the University of Pisa (1806–1861) (in Greek), vol A΄ (General Secretariat for Youth, Athens, 1980)

    Google Scholar 

  37. T. Sklavelitis, Anthonios Fatseas (1821-1872): Ideological pursuits (in Greek), in Issues History of Modern Letters. Tribute to K.Th. Dimara (in Greek), (Paratiritis, Thessaloniki, 1994), pp. 161–170

    Google Scholar 

  38. M. Stephanides, Centenary 1837–1937. History of Physics and Mathematics Faculty (in Greek), vol II (Athens, 1952)

    Google Scholar 

  39. M. Terdimou, Euclidean geometry, in History and Philosophy of Science in the Greek Area (17th–19th Cent.) (in Greek), ed. by G. Karas, (Metaichmio, Athens, 2003), pp. 196–216

    Google Scholar 

  40. M. Terdimou, The confrontation of mathematics on behalf of the eastern orthodox church during the ottoman period (in Greek), in Multicultural Science in the Ottoman Empire, ed. by E. Ihsanoglu, K. Chatzis, E. Nikolaidis, (Brepols Publishers, Turnhout, 2003), pp. 53–63

    Chapter  Google Scholar 

  41. P. Thanailaki, America and Protestantism (in Greek) (Kastaniotis, Athens, 2005)

    Google Scholar 

  42. E. Theodossiou, T. Grammenos, V. Manimanis, Theophilos Kairis: The creator and initiator of theosebism in Greece. Eur. Leg. 9(6), 783–797 (2004)

    Article  Google Scholar 

  43. F. Thiersch, De l’ État Actuel de la Gréce et des Moyens d’ Arriver à sa Restauration (Deuxième Partie, F.A. Brockhaus, Leipzig, 1833)

    Google Scholar 

  44. C. Toumasis, The epos of Euclidean geometry in Greek secondary education (1836-1985): Pressure for change and resistance. Educ. Stud. Math. 21, 491–508 (1990)

    Article  Google Scholar 

  45. C. Vafas, Elements of Geometry in A.M. Legendre plus Additions and Adaptations M.A. Blanchet (in Greek) (Athens, 1860)

    Google Scholar 

  46. C. Vafas, Proofs fifth request of Euclid (in Greek). Athena 1, 383–390 (1872)

    Google Scholar 

  47. E. Zambeta, Religion and national identity in Greek education. Intercult. Educ. 11(2), 145–155 (2000)

    Article  Google Scholar 

  48. Th. Zervas, Resurrecting the past, constructing the future: A historical investigation on the formation of a Greek national identity in schools, 1834–1913, Ph. D, in University of Chicago, Illinois (2010)

    Google Scholar 

  49. S. Ziogou-Karastergiou, The Girls’ Secondary Education 1830–1893 (in Greek) (General Secretariat for Youth, Athens, 1986)

    Google Scholar 

  50. K. Zormbala, A Greek geometry textbook of the 19th century: Influences of mathematical science on axiomatic in school. Sudhoffs Arch. 86(2), 198–219 (2002)

    Google Scholar 

  51. K. Zormbala, Dominance aspects in Greek school geometry in the 19th century (in Greek), in History and Mathematics Education (in Greek), ed. by C. Thomaidis, N. Kastanis, K. Tzanakis, (Ziti, Thessaloniki, 2006), pp. 95–112

    Google Scholar 

  52. G. Zoubos, Mathematics in the Ionian Academy (1824–1864) (in Greek), Ph.D., Department of History, Ionian University, Corfu (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kastanis, N. (2023). The Overshadowing of Euclid’s Geometry by Legendre’s Géométrie in the Modern Greek Education. In: Daras, N.J., Rassias, M.T., Zographopoulos, N.B. (eds) Exploring Mathematical Analysis, Approximation Theory, and Optimization. Springer Optimization and Its Applications, vol 207. Springer, Cham. https://doi.org/10.1007/978-3-031-46487-4_9

Download citation

Publish with us

Policies and ethics