روش ارشمیدس: قضایای 13 و 14

نوع مقاله: مقاله ترجمه ای

نویسندگان

1 عضو هیات علمی دانشگاه غیر انتفاعی شیخ بهائی

2 مدرس دانشگاه شیخ بهائی

چکیده

سم استوانه ای همواره موضوعی بسیار جذاب بوده است و این از زمانی آغاز شد که ارشمیدس، تنها از طریق مفاهیم هندسی ثابت کردکه حجم سم استوانه ای 1/6 حجم مکعب محاطی آن است. در این مقاله با استفاده از مثلثات و حسابگان دیفرانسیل و انتگرال، چگونگی محاسبه حجم سم استوانه ای ارائه شده است.

کلیدواژه‌ها


[1] J. L. Heiberg, Eine Neue Archimedeshandschrift, Hermes, 42 no. 2 (1907) 235–303.

[2] J. L. Heiberg and H. G. Zeuthen, Eine Neuve Schrift des Archimedes, Verlag von B. G. Teubner, Leipzig,1907 321–363.

[3] T. L. Heath, The Method of Archimedes :Recently Discovered by Heiberg, Cambridge, 1912.

[4] T. L. Heath, The Thirteen Books of Euclid’s Elements, 1, 2, 3, Dover, 1956.

[5] Great Books of The Western World, Robert Maynard Hutchins, ed., Mortimer J. Adler, Ass. ed., II: Euclid,Archimedes, Apol-lonius of Perga, Nicomachus, Encyclopedia Britannica, 1952.

[6] E. J. Dijksterhuis, Archimedes, with a new bibliographic essay by Wilbur R. Knorr, Princeton University Press, 1987 pp. 459.

[7] R. Netz, K. Saito and N. Tchernetska, A New Reading of Method Proposition 14: Preliminary Evidence from the Archimedes Palimpsest, (Part I), SCIAMSVS, 2 (2001) 9–29.

[8] A New Reading of Method Proposition 14: Preliminary Evidence from the Archimedes Palimpsest (Part 2), SCIAMSVS, 3 (2002) 109–125.

[9] R. Netz, The Works of Archimedes, 1, Cambridge, 2004.

[10] R. Netz and W. Noel, The ARCHIMEDES CODEX, Da Capo Press, 2007.

[11] R. Netz and W. Noel, Natalie Tchernetska and Nigel Wilson, The ARCHIMEDES Palimpsest, Walters Art Museum and Cam-bridge, 1,2, 2011.

[12] S. Stein, Archimedes: What Did He Do Besides Cry Eureka, Mathematical Association of America, 1999.

[13] The Archimedes Palimpsest, Christie’s (Auction catalog), 502, Park Avenue, New York, 1998.

[14] S. H. Gould, The Method of Archimedes, American Mathematical Monthly, 62 1955 473–476.

[15] J. L. Heiberg, translated by D. C. Macgregor, Mathematics and Physical Science in Classical Antiquity, Chapters in the History of Science II, Charles Singer, ed., Oxford, 1922.

[16] Archimedes Text Sold for 2 Million, The New York Times, 1998 pp. A22.

[17] Carol Vogel, Eureka, The New York Times, February 19, 1999.

[18] Big Literary Find in Constantinople, The New York Times, 1907 pp. 1.

[19] Archimedes text goes to unnamed buyer for 2.2 m, Kathimerini, Athens, 1998, pp. 1.

[20] Half-leaf of a 10th century codex, translated by Nigel Wilson, Cambridge University Library, Add.1879.23.

[21] W. R. Knorr, The Method of Indivisibles in Ancient Geometry, Vita Mathematica (R. Calinger, ed.,) Mathematical Association of American, 1996 pp. 71–74.

[22] C. H. Edwards Jr., The Historical Development of the Calculus, Springer-Verlag, 1979 68–76.

[23] Archimedes Comes to America, Science, 284 (1999) pp. 2083.

[24] I. Boserup (ed.), Københavns Universitet 1479–1979: Klassisk filologi efter 1899, 8 (1992) 367–374.

[25] S. B. Gray, A Centennial Celebration of Two Great Scholars, Notices of the American Mathematical Association, 55 (2008) 776–783.

[26] J. L. Berggren, The Archimedes Codex, Book Review, Notices of the American Mathematical Association, 55 2008 943–947.

[27] J. Stewart, Calculus, 5ed, Thomson, Brooks/Cole, 2003, pp. 888.

[28] A. Alexander, Infinitesimal, Scientific American / Farrar, Straus and Giroux, 2014 107–111.

[29] P. Lynch, “Sharing a Pint” ThatsMaths thatsmaths.com/2012/12/13/sharing-a-pint/.

[30] PBS (2003) Infinite Secrets, NOVA Science Programming, Original PBS Date: September 30, 2003