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Apollonius'un Koni Kesitlerine Tarihsel bir Bakış

Year 2021, Issue: 19, 95 - 123, 30.06.2021

Abstract

Pergeli Apollonius, Eukleides ile birlikte geometri tarihinin en önemli iki isminden biridir. Onu bu denli önemli kılan elbette ki çağının çok ötesindeki eseri, Konika’dır. Antik dönem koni kesitleri tarihi kelimenin tam manasıyla, Apollonius öncesi ve Apollonius sonrası olmak üzere ikiye ayrılmaktadır. Literatürde Apollonius öncesi dönem “Dikey Konjügasyon Teorisi”, Apollonius sonrası dönem “Eğimli Konjügasyon Teorisi” olarak geçmektedir. Bu makalede bu çizgiyi takiben öncelikle Apollonius’un bu devasa eserinin oluşmasına kaynak sağlayan Antik Yunan bilginlerinin çalışmaları incelenmiştir. Apollonius’un tarihsel ve matematiksel arka planı serimledikten sonra, Apollonius’un ismiyle anılan teorisi sunulmuştur ve eseri hakkında detaylı bilgi verilmiştir. Koni kesitleri çalışmaları ve Antik Yunan’ın üç meşhur probleminin çözümü arasında ilginç bağlantılar tespit edilmiş ve bu konuda çeşitli matematiksel örnekler sunulmuştur.

References

  • Allman, G. J. (1889). Greek Geometry From Thales to Euclid. Dublin - Londra: Dublin University Press.
  • Bulmer - Thomas, I. (1981a). Menaechmus. Dictionary of Scientific Biography (C. 9, s. 269). New York: Charles Scribner’s Sons.
  • Bulmer - Thomas, I. (1981b). Eutocius of Ascalon. Dictionary of Scientific Biography (C. 4, s. 489 - 491). New York: Charles Scribner’s Sons.
  • Bulmer - Thomas, I. (1981c). Pappus of Alexandria. Dictionary of Scientific Biography (C. 10, s. 293 - 304). New York: Charles Scribner’s Sons.
  • Cajori, F. (2014). Matematik Tarihi. Ankara: ODTÜ yayıncılık.
  • Cohen ve Drabkin. (1966) A Source Book in Greek Science. Cambridge: Harvard University Press.
  • Coolidge, J. L. (1968). A History of the Conic Sections and Quadratic Surfaces. New York Dover Publications.
  • Dörrie, H. (1965). 100 Great Problems of Elementary Mathematics Their History and Solution. New York: Dover Publications.
  • Fried, M. N. (2011). Edmond Halley’s Reconstruction of the Lost Book of Apollonius’s Conics Translation and Commentary. New York: Springer-Verlag.
  • Glenn R. (1992). A Commentary on the First Book of Euclid’s Elements, Proclus. Princeton: Princeton University Press.
  • Hann, J. (1850). A Rudimentary Treatise on Analytical Geometry and Conic Section. Londra: J. Weale.
  • Heath, T. L. (1896). Apollonius of Perga Treatise on Conic Sections. Cambridge: Cambridge University Press.
  • Heath, T. L. (1897). The Works of Archimedes. Cambridge: Cambridge at the University Press.
  • Heath, T. L. (1921). A History of Greek Mathematics (C. 1, C. 2). Londra: Oxford at the Clarendon Press.
  • Heath, T. L. (1931). A Manual of the Greek Mathematics. Londra: Oxford at the Clarendon Press.
  • Heath, T. L. (1952). The Thirteen Books of Euclid’s Elements; Great Books of the Western World. Chicago: Encyclopaedia Britannica.
  • Heath, T. L. (1956). The Thirteen Books of Euclid’s Elements (C. 1, C. 2, C. 3). New York: Dover Publications.
  • Hogendijk, J. P. (1979). On The Trisection of an Angle and The Construction of a Regular Nonagon by means of Conic Sections in Medieval Islamic Geometry. Utrecht: Utrecht University.
  • Hogendijk, J. P. (1985). Ibn AI-Haytham’s Completion of the Conics. New York: Springer-Verlag.
  • Holme, A. (2010). Geometry Cultural Heritage. Berlin-Heidelberg: Springer-Verlag.
  • Huxley, G. L. (1981). Anthemius of Tralles. Dictionary of Scientific Biography (C. 1, s. 169 - 170). New York: Charles Scribner’s Sons.
  • Jones, A. (1986). Pappus of Alexandria Book VII of the Collection (C. 1, C. 2). New York Springer-Verlag.
  • Katz, V. J. (1993). A History of Mathematics (an Introduction). New York: Harper Collins College Publishers.
  • Kline, Moris. (1972). Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press.
  • Knorr, W. R. (1982). Observations on Early History of Conics. Centaurus 26 (s. 1 - 24).
  • Kökçü, A. (2019). Bir Zamanlar Geometri. Ankara: Nobel.
  • Kramer, E. (1983). The Nature and Growth of Modern Mathematics. New York: Hawthorn Books Inc Publishers.
  • Loomis, E. (1878). Elements of Analytical Geometry. New York: New York Harper.
  • Morrow, Glenn R. 1981. Proclus. Dictionary of Scientific Biography (C. 11, s. 160 - 162). New York: Charles Scribner’s Sons. Ostermann, A. ve Wanner, G. (2012). Geometry by It’s History. Berlin-Heidelberg: Springer-Verlag.
  • Smith, D. E. (1958). History of Mathematics. New York: Dover Publications.
  • Terzioğlu, N. ve İlker, A. N. (1960). Modern Geometri, Konikler (Teorem ve Problemler). İstanbul: Şirketi Mürettibiye Basımevi.
  • Toomer, G. J. (1981a). Apollonius of Perga. Dictionary of Scientific Biography (C. 1, s. 179 - 192). New York: Charles Scribner’s Sons.
  • Toomer, G. J. (1981b). Ptolemy. Dictionary of Scientific Biography (C. 11, s. 186 - 206). New York: Charles Scribner’s Sons.
  • Toomer G. J. (1990). Apollonius Conics Books V to VII: The Arabic Translation of the Lost Greek Original in the Version of the Banu Musa. New York: Springer- Verlag.
  • Young, J. R. (1871). A Rudimentary Treatise on Analytical Geometry and Conic Section. Londra: Crosby Lockwood.
  • Zacharies, M. (1947). Düzlemde ve Uzayda Elementer Geometri. İstanbul: Kenan Matbaası.
Year 2021, Issue: 19, 95 - 123, 30.06.2021

Abstract

References

  • Allman, G. J. (1889). Greek Geometry From Thales to Euclid. Dublin - Londra: Dublin University Press.
  • Bulmer - Thomas, I. (1981a). Menaechmus. Dictionary of Scientific Biography (C. 9, s. 269). New York: Charles Scribner’s Sons.
  • Bulmer - Thomas, I. (1981b). Eutocius of Ascalon. Dictionary of Scientific Biography (C. 4, s. 489 - 491). New York: Charles Scribner’s Sons.
  • Bulmer - Thomas, I. (1981c). Pappus of Alexandria. Dictionary of Scientific Biography (C. 10, s. 293 - 304). New York: Charles Scribner’s Sons.
  • Cajori, F. (2014). Matematik Tarihi. Ankara: ODTÜ yayıncılık.
  • Cohen ve Drabkin. (1966) A Source Book in Greek Science. Cambridge: Harvard University Press.
  • Coolidge, J. L. (1968). A History of the Conic Sections and Quadratic Surfaces. New York Dover Publications.
  • Dörrie, H. (1965). 100 Great Problems of Elementary Mathematics Their History and Solution. New York: Dover Publications.
  • Fried, M. N. (2011). Edmond Halley’s Reconstruction of the Lost Book of Apollonius’s Conics Translation and Commentary. New York: Springer-Verlag.
  • Glenn R. (1992). A Commentary on the First Book of Euclid’s Elements, Proclus. Princeton: Princeton University Press.
  • Hann, J. (1850). A Rudimentary Treatise on Analytical Geometry and Conic Section. Londra: J. Weale.
  • Heath, T. L. (1896). Apollonius of Perga Treatise on Conic Sections. Cambridge: Cambridge University Press.
  • Heath, T. L. (1897). The Works of Archimedes. Cambridge: Cambridge at the University Press.
  • Heath, T. L. (1921). A History of Greek Mathematics (C. 1, C. 2). Londra: Oxford at the Clarendon Press.
  • Heath, T. L. (1931). A Manual of the Greek Mathematics. Londra: Oxford at the Clarendon Press.
  • Heath, T. L. (1952). The Thirteen Books of Euclid’s Elements; Great Books of the Western World. Chicago: Encyclopaedia Britannica.
  • Heath, T. L. (1956). The Thirteen Books of Euclid’s Elements (C. 1, C. 2, C. 3). New York: Dover Publications.
  • Hogendijk, J. P. (1979). On The Trisection of an Angle and The Construction of a Regular Nonagon by means of Conic Sections in Medieval Islamic Geometry. Utrecht: Utrecht University.
  • Hogendijk, J. P. (1985). Ibn AI-Haytham’s Completion of the Conics. New York: Springer-Verlag.
  • Holme, A. (2010). Geometry Cultural Heritage. Berlin-Heidelberg: Springer-Verlag.
  • Huxley, G. L. (1981). Anthemius of Tralles. Dictionary of Scientific Biography (C. 1, s. 169 - 170). New York: Charles Scribner’s Sons.
  • Jones, A. (1986). Pappus of Alexandria Book VII of the Collection (C. 1, C. 2). New York Springer-Verlag.
  • Katz, V. J. (1993). A History of Mathematics (an Introduction). New York: Harper Collins College Publishers.
  • Kline, Moris. (1972). Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press.
  • Knorr, W. R. (1982). Observations on Early History of Conics. Centaurus 26 (s. 1 - 24).
  • Kökçü, A. (2019). Bir Zamanlar Geometri. Ankara: Nobel.
  • Kramer, E. (1983). The Nature and Growth of Modern Mathematics. New York: Hawthorn Books Inc Publishers.
  • Loomis, E. (1878). Elements of Analytical Geometry. New York: New York Harper.
  • Morrow, Glenn R. 1981. Proclus. Dictionary of Scientific Biography (C. 11, s. 160 - 162). New York: Charles Scribner’s Sons. Ostermann, A. ve Wanner, G. (2012). Geometry by It’s History. Berlin-Heidelberg: Springer-Verlag.
  • Smith, D. E. (1958). History of Mathematics. New York: Dover Publications.
  • Terzioğlu, N. ve İlker, A. N. (1960). Modern Geometri, Konikler (Teorem ve Problemler). İstanbul: Şirketi Mürettibiye Basımevi.
  • Toomer, G. J. (1981a). Apollonius of Perga. Dictionary of Scientific Biography (C. 1, s. 179 - 192). New York: Charles Scribner’s Sons.
  • Toomer, G. J. (1981b). Ptolemy. Dictionary of Scientific Biography (C. 11, s. 186 - 206). New York: Charles Scribner’s Sons.
  • Toomer G. J. (1990). Apollonius Conics Books V to VII: The Arabic Translation of the Lost Greek Original in the Version of the Banu Musa. New York: Springer- Verlag.
  • Young, J. R. (1871). A Rudimentary Treatise on Analytical Geometry and Conic Section. Londra: Crosby Lockwood.
  • Zacharies, M. (1947). Düzlemde ve Uzayda Elementer Geometri. İstanbul: Kenan Matbaası.
There are 36 citations in total.

Details

Primary Language Turkish
Journal Section Research Article
Authors

İrem Aslan Seyhan 0000-0003-4999-2891

Publication Date June 30, 2021
Submission Date February 23, 2021
Published in Issue Year 2021 Issue: 19

Cite

APA Aslan Seyhan, İ. (2021). Apollonius’un Koni Kesitlerine Tarihsel bir Bakış. Dört Öge(19), 95-123.