数学史
參考資料

1 2  (Boyer 1991，"Euclid of Alexandria" p. 119)
↑  J. Friberg, "Methods and traditions of Babylonian mathematics. Plimpton 322, Pythagorean triples, and the Babylonian triangle parameter equations", Historia Mathematica, 8, 1981, pp. 277—318.
↑  Neugebauer, Otto.  2. Dover Publications. 1969 [1957]. ISBN 978-0-486-22332-2.  Chap. IV "Egyptian Mathematics and Astronomy", pp. 71–96.
↑  Heath. . : 5.
↑  Sir Thomas L. Heath, A Manual of Greek Mathematics, Dover, 1963, p. 1: "In the case of mathematics, it is the Greek contribution which it is most essential to know, for it was the Greeks who first made mathematics a science."
↑  George Gheverghese Joseph, The Crest of the Peacock: Non-European Roots of Mathematics,Penguin Books, London, 1991, pp.140—148
↑  Georges Ifrah, Universalgeschichte der Zahlen, Campus, Frankfurt/New York, 1986, pp.428—437
↑  Robert Kaplan, "The Nothing That Is: A Natural History of Zero", Allen Lane/The Penguin Press, London, 1999
↑  "The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. the importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of Antiquity, Archimedes and Apollonius." - Pierre Simon Laplace http://www-history.mcs.st-and.ac.uk/HistTopics/Indian_numerals.html （页面存档备份，存于）
↑  A.P. Juschkewitsch, "Geschichte der Mathematik im Mittelalter", Teubner, Leipzig, 1964
↑  《周  礼·地官司徒·保氏》：「保氏掌谏王恶而养国子以道。乃教之六艺：一曰五礼，二曰六乐，三曰五射，四曰五驭，五曰六书，六曰九数。」东汉的郑玄在他的《周 礼注疏·地官司徒·保氏》中引郑司农（郑众）所言：「九数：方田、粟米、差分、少广、商功、均输、方程、赢不足、旁要，今有重差、夕桀、勾股也。」
1 2  (Boyer 1991，"Origins" p. 3)
↑   (PDF).   [2016-05-02]. （原始内容 (PDF)存档于2012-02-07）.
↑  Williams, Scott W. . Mathematicians of the African Diaspora. SUNY Buffalo mathematics department. 2005  [2006-05-06]. （原始内容存档于2015-03-25）.
↑  Marshack, Alexander (1991): The Roots of Civilization, Colonial Hill, Mount Kisco, NY.
↑  Rudman, Peter Strom. . Prometheus Books. 2007: 64. ISBN 978-1-59102-477-4.
↑  Marshack, A. 1972. The Roots of Civilization: the Cognitive Beginning of Man’s First Art, Symbol and Notation. New York: McGraw-Hil
↑  Thom, Alexander, and Archie Thom, 1988, "The metrology and geometry of Megalithic Man", pp 132-151 in C.L.N. Ruggles, ed., Records in Stone: Papers in memory of Alexander Thom. Cambridge University Press. ISBN 0-521-33381-4.
↑  (Boyer 1991，"Mesopotamia" p. 24)
1 2 3 4 5 6  (Boyer 1991，"Mesopotamia" p. 26)
1 2 3  (Boyer 1991，"Mesopotamia" p. 25)
1 2  (Boyer 1991，"Mesopotamia" p. 41)
↑  Duncan J. Melville (2003). Third Millennium Chronology （页面存档备份，存于）, Third Millennium Mathematics. St. Lawrence University.
1 2  (Boyer 1991，"Mesopotamia" p. 27)
↑  Aaboe, Asger. . New York: Random House. 1998: 30–31.
↑  (Boyer 1991，"Mesopotamia" p. 33)
↑  (Boyer 1991，"Mesopotamia" p. 39)
↑  (Boyer 1991，"Egypt" p. 11)
↑  Egyptian Unit Fractions （页面存档备份，存于） at MathPages
↑  （页面存档备份，存于） Egyptian Unit Fractions
↑  .   [2016-05-02]. （原始内容存档于2012-02-19）.
↑  .   [2016-05-02]. （原始内容存档于2009-04-16）.
↑  (Boyer 1991，"Egypt" p. 19)
↑  .   [2016-05-02]. （原始内容存档于2015-04-07）.
↑  Howard Eves, An Introduction to the History of Mathematics, Saunders, 1990, ISBN 0-03-029558-0
↑  (Boyer 1991，"The Age of Plato and Aristotle" p. 99)
↑  Martin Bernal, "Animadversions on the Origins of Western Science", pp. 72–83 in Michael H. Shank, ed., The Scientific Enterprise in Antiquity and the Middle Ages, (Chicago: University of Chicago Press) 2000, p. 75.
↑  Bill Casselman. . University of British Columbia.   [2008-09-26]. （原始内容存档于2012-06-04）.
↑  (Boyer 1991，"Ionia and the Pythagoreans" p. 43)
↑  (Boyer 1991，"Ionia and the Pythagoreans" p. 49)
↑  Eves, Howard, An Introduction to the History of Mathematics, Saunders, 1990, ISBN 0-03-029558-0.
↑  Kurt Von Fritz. . The Annals of Mathematics. 1945.
↑  James R. Choike. . The Two-Year College Mathematics Journal. 1980.
↑  (Boyer 1991，"The Age of Plato and Aristotle" p. 86)
1 2  (Boyer 1991，"The Age of Plato and Aristotle" p. 88)
↑  Calian, George F.  (PDF). New Europe College. 2014. （原始内容 (PDF)存档于2015-10-15）.
↑  (Boyer 1991，"The Age of Plato and Aristotle" p. 87)
↑  (Boyer 1991，"The Age of Plato and Aristotle" p. 92)
↑  (Boyer 1991，"The Age of Plato and Aristotle" p. 93)
↑  (Boyer 1991，"The Age of Plato and Aristotle" p. 91)
↑  (Boyer 1991，"The Age of Plato and Aristotle" p. 98)
↑  (Boyer 1991，"Euclid of Alexandria" p. 100)
1 2  (Boyer 1991，"Euclid of Alexandria" p. 104)
↑  Howard Eves, An Introduction to the History of Mathematics, Saunders, 1990, ISBN 0-03-029558-0 p. 141: "No work, except The Bible, has been more widely used...."
↑  (Boyer 1991，"Euclid of Alexandria" p. 102)
↑  (Boyer 1991，"Archimedes of Syracuse" p. 120)
1 2  (Boyer 1991，"Archimedes of Syracuse" p. 130)
↑  (Boyer 1991，"Archimedes of Syracuse" p. 126)
↑  (Boyer 1991，"Archimedes of Syracuse" p. 125)
↑  (Boyer 1991，"Archimedes of Syracuse" p. 121)
↑  (Boyer 1991，"Archimedes of Syracuse" p. 137)
↑  (Boyer 1991，"Apollonius of Perga" p. 145)
↑  (Boyer 1991，"Apollonius of Perga" p. 146)
↑  (Boyer 1991，"Apollonius of Perga" p. 152)
↑  (Boyer 1991，"Apollonius of Perga" p. 156)
↑  (Boyer 1991，"Greek Trigonometry and Mensuration" p. 161)
1 2  (Boyer 1991，"Greek Trigonometry and Mensuration" p. 175)
↑  (Boyer 1991，"Greek Trigonometry and Mensuration" p. 162)
↑  S.C. Roy. Complex numbers: lattice simulation and zeta function applications, p. 1  （页面存档备份，存于）. Harwood Publishing, 2007, 131 pages. ISBN 1-904275-25-7
↑  (Boyer 1991，"Greek Trigonometry and Mensuration" p. 163)
↑  (Boyer 1991，"Greek Trigonometry and Mensuration" p. 164)
↑  (Boyer 1991，"Greek Trigonometry and Mensuration" p. 168)
↑  (Boyer 1991，"Revival and Decline of Greek Mathematics" p. 178)
↑  (Boyer 1991，"Revival and Decline of Greek Mathematics" p. 180)
1 2  (Boyer 1991，"Revival and Decline of Greek Mathematics" p. 181)
↑  (Boyer 1991，"Revival and Decline of Greek Mathematics" p. 183)
↑  (Boyer 1991，"Revival and Decline of Greek Mathematics" pp. 183–90)
↑  .   [2016-05-02]. （原始内容存档于2014-08-14）.
↑  (Boyer 1991，"China and India" p. 201)
1 2  (Boyer 1991，"China and India" p. 196)
↑  Katz 2007，第194–199頁 harvnb模板錯誤: 無指向目標: CITEREFKatz2007 (幫助)
↑  (Boyer 1991，"China and India" p. 198)
↑  Needham, Joseph. . 3, Mathematics and the Sciences of the Heavens and the Earth. Taipei: Caves Books Ltd. 1986.
1 2 3  (Boyer 1991，"China and India" p. 202)
↑  清阮元撰《畴人传》：“后祖冲之更创密法，仍是割之又割耳，未能于徽注之外，别立新术也”
↑  吴文俊主编《中国数学史大系》第二卷 219页
↑  Zill, Dennis G.; Wright, Scott; Wright, Warren S.  3. Jones & Bartlett Learning. 2009: xxvii  [2016-05-02]. ISBN 0-7637-5995-3. （原始内容存档于2016-05-03）.  Extract of page 27 （页面存档备份，存于）
1 2 3  (Boyer 1991，"China and India" p. 205)
↑  (Boyer 1991，"China and India" p. 206)
↑  Rowlett, Russ, , University of North Carolina at Chapel Hill, 2004-07-04  [2009-06-22], （原始内容存档于2018-07-31）
1 2 3 4  (Boyer 1991，"China and India" p. 207)
↑  T. K. Puttaswamy, "The Accomplishments of Ancient Indian Mathematicians", pp. 411–2, in Selin, Helaine; D'Ambrosio, Ubiratan (编). . Springer. 2000. ISBN 1-4020-0260-2.
↑  R. P. Kulkarni, "The Value of π known to Śulbasūtras 的存檔，存档日期2012-02-06.", Indian Journal for the History of Science, 13 1 (1978): 32-41
↑  J.J. Connor, E.F. Robertson. The Indian Sulba Sutras Univ. of St. Andrew, Scotland  （页面存档备份，存于） The values for π are 4 x (13/15)2 (3.0044...), 25/8 (3.125), 900/289 (3.11418685...), 1156/361 (3.202216...), and 339/108 (3.1389).
↑  J.J. Connor, E.F. Robertson. The Indian Sulba Sutras Univ. of St. Andrew, Scotland  （页面存档备份，存于）
↑  Bronkhorst, Johannes. . Journal of Indian Philosophy (Springer Netherlands). 2001, 29 (1–2): 43–80. doi:10.1023/A:1017506118885.
↑  Sanchez, Julio; Canton, Maria P. . Boca Raton, Florida: CRC Press. 2007: 37. ISBN 0-8493-7189-9.
↑  W. S. Anglin and J. Lambek, The Heritage of Thales, Springer, 1995, ISBN 0-387-94544-X
↑  Hall, Rachel W.  (PDF). Math Horizons. 2008, 15: 10–11  [2016-05-02]. （原始内容 (PDF)存档于2012-02-12）.
↑  (Boyer 1991，"China and India" p. 208)
1 2  (Boyer 1991，"China and India" p. 209)
↑  (Boyer 1991，"China and India" p. 210)
↑  (Boyer 1991，"China and India" p. 211)
↑  Boyer. . . 1991: 226. By 766 we learn that an astronomical-mathematical work, known to the Arabs as the Sindhind, was brought to Baghdad from India. It is generally thought that this was the Brahmasphuta Siddhanta, although it may have been the Surya Siddhanata. A few years later, perhaps about 775, this Siddhanata was translated into Arabic, and it was not long afterwards (ca. 780) that Ptolemy's astrological Tetrabiblos was translated into Arabic from the Greek.
↑  Plofker 2009 182-207
↑  Plofker 2009 pp 197 - 198; George Gheverghese Joseph, The Crest of the Peacock: Non-European Roots of Mathematics, Penguin Books, London, 1991 pp 298 - 300; Takao Hayashi, Indian Mathematics, pp 118 - 130 in Companion History of the History and Philosophy of the Mathematical Sciences, ed. I. Grattan.Guinness, Johns Hopkins University Press, Baltimore and London, 1994, p 126
↑  Plofker 2009 pp 217 - 253
↑  P. P. Divakaran, The first textbook of calculus: Yukti-bhāṣā, Journal of Indian Philosophy 35, 2007, pp 417 - 433.
↑  Pingree, David, , Isis, December 1992, 83 (4): 562, JSTOR 234257, doi:10.1086/356288, One example I can give you relates to the Indian Mādhava's demonstration, in about 1400 A.D., of the infinite power series of trigonometrical functions using geometrical and algebraic arguments. When this was first described in English by Charles Whish, in the 1830s, it was heralded as the Indians' discovery of the calculus. This claim and Mādhava's achievements were ignored by Western historians, presumably at first because they could not admit that an Indian discovered the calculus, but later because no one read anymore the Transactions of the Royal Asiatic Society, in which Whish's article was published. The matter resurfaced in the 1950s, and now we have the Sanskrit texts properly edited, and we understand the clever way that Mādhava derived the series without the calculus; but many historians still find it impossible to conceive of the problem and its solution in terms of anything other than the calculus and proclaim that the calculus is what Mādhava found. In this case the elegance and brilliance of Mādhava's mathematics are being distorted as they are buried under the current mathematical solution to a problem to which he discovered an alternate and powerful solution.
↑  Bressoud, David, , College Mathematics Journal, 2002, 33 (1): 2–13, doi:10.2307/1558972
↑  Plofker, Kim, , Historia Mathematica, November 2001, 28 (4): 293, doi:10.1006/hmat.2001.2331, It is not unusual to encounter in discussions of Indian mathematics such assertions as that 'the concept of differentiation was understood [in India] from the time of Manjula (... in the 10th century)' [Joseph 1991, 300], or that 'we may consider Madhava to have been the founder of mathematical analysis' (Joseph 1991, 293), or that Bhaskara II may claim to be 'the precursor of Newton and Leibniz in the discovery of the principle of the differential calculus' (Bag 1979, 294).... The points of resemblance, particularly between early European calculus and the Keralese work on power series, have even inspired suggestions of a possible transmission of mathematical ideas from the Malabar coast in or after the 15th century to the Latin scholarly world (e.g., in (Bag 1979, 285)).... It should be borne in mind, however, that such an emphasis on the similarity of Sanskrit (or Malayalam) and Latin mathematics risks diminishing our ability fully to see and comprehend the former. To speak of the Indian 'discovery of the principle of the differential calculus' somewhat obscures the fact that Indian techniques for expressing changes in the Sine by means of the Cosine or vice versa, as in the examples we have seen, remained within that specific trigonometric context. The differential 'principle' was not generalized to arbitrary functions—in fact, the explicit notion of an arbitrary function, not to mention that of its derivative or an algorithm for taking the derivative, is irrelevant here
↑  Katz, Victor J.,  (PDF), Mathematics Magazine, June 1995, 68 (3): 163–174  [2016-05-02], JSTOR 2691411, doi:10.2307/2691411, （原始内容存档 (PDF)于2016-03-04）
↑  (Boyer 1991，"The Arabic Hegemony" p. 230) "The six cases of equations given above exhaust all possibilities for linear and quadratic equations having positive root. So systematic and exhaustive was al-Khwārizmī's exposition that his readers must have had little difficulty in mastering the solutions."
↑  Gandz and Saloman (1936), The sources of Khwarizmi's algebra, Osiris i, pp. 263–77: "In a sense, Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers".
↑  (Boyer 1991，"The Arabic Hegemony" p. 229) "It is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the translation above. The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word muqabalah is said to refer to "reduction" or "balancing" - that is, the cancellation of like terms on opposite sides of the equation."
↑  Rashed, R.; Armstrong, Angela. . Springer. 1994: 11–12. ISBN 0-7923-2565-6. OCLC 29181926.
↑  Sesiano, Jacques. . . Springer: 4–5. 1997-07-31.
↑  Victor J. Katz (1998). History of Mathematics: An Introduction, pp. 255–59. Addison-Wesley. ISBN 0-321-01618-1.
↑  F. Woepcke (1853). Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi. Paris.
↑  Katz, Victor J. . Mathematics Magazine. 1995, 68 (3): 163–74. doi:10.2307/2691411.
↑  約翰·J·奧康納; 埃德蒙·F·羅伯遜, ,  （英语）
↑  《智慧篇》, 11:20
↑  Caldwell, John (1981) "The De Institutione Arithmetica and the De Institutione Musica", pp. 135–54 in Margaret Gibson, ed., Boethius: His Life, Thought, and Influence, (Oxford: Basil Blackwell).
↑  Folkerts, Menso, "Boethius" Geometrie II, (Wiesbaden: Franz Steiner Verlag, 1970).
↑  Marie-Thérèse d'Alverny, "Translations and Translators", pp. 421–62 in Robert L. Benson and Giles Constable, Renaissance and Renewal in the Twelfth Century, (Cambridge: Harvard University Press, 1982).
↑  Guy Beaujouan, "The Transformation of the Quadrivium", pp. 463–87 in Robert L. Benson and Giles Constable, Renaissance and Renewal in the Twelfth Century, (Cambridge: Harvard University Press, 1982).
↑  Grant, Edward and John E. Murdoch (1987), eds., Mathematics and Its Applications to Science and Natural Philosophy in the Middle Ages, (Cambridge: Cambridge University Press) ISBN 0-521-32260-X.
↑  Clagett, Marshall (1961) The Science of Mechanics in the Middle Ages, (Madison: University of Wisconsin Press), pp. 421–40.
↑  Murdoch, John E. (1969) "Mathesis in Philosophiam Scholasticam Introducta: The Rise and Development of the Application of Mathematics in Fourteenth Century Philosophy and Theology", in Arts libéraux et philosophie au Moyen Âge (Montréal: Institut d'Études Médiévales), at pp. 224–27.
↑  Clagett, Marshall (1961) The Science of Mechanics in the Middle Ages, (Madison: University of Wisconsin Press), pp. 210, 214–15, 236.
↑  Clagett, Marshall (1961) 中世纪数学科学 (Madison:Wisconsin 大学出版社), p. 284.
↑  Clagett, Marshall (1961) 中世纪数学科学, (Madison: University of Wisconsin Press), pp. 332–45, 382–91.
↑  Nicole Oresme, "Questions on the Geometry of Euclid" Q. 14, pp. 560–65, in Marshall Clagett, ed., Nicole Oresme and the Medieval Geometry of Qualities and Motions, (Madison: University of Wisconsin Press, 1968).
↑  Heeffer, Albrecht: On the curious historical coincidence of algebra and double-entry bookkeeping, Foundations of the Formal Sciences, Ghent University, November 2009, p.7  （页面存档备份，存于）
↑  della Francesca, Piero. De Prospectiva Pingendi, ed. G. Nicco Fasola, 2 vols., Florence (1942).
↑  della Francesca, Piero. Trattato d'Abaco, ed. G. Arrighi, Pisa (1970).
↑  della Francesca, Piero. L'opera "De corporibus regularibus" di Pietro Franceschi detto della Francesca usurpata da Fra Luca Pacioli, ed. G. Mancini, Rome, (1916).
↑  Alan Sangster, Greg Stoner & Patricia McCarthy: "The market for Luca Pacioli’s Summa Arithmetica" （页面存档备份，存于） (Accounting, Business & Financial History Conference, Cardiff, September 2007) p. 1–2
↑  Grattan-Guinness, Ivor. . W.W. Norton. 1997. ISBN 0-393-32030-8.
↑  
Kline, Morris. . Great Britain: Pelican. 1953: 150–151.
↑  Struik, Dirk.  3rd. Courier Dover Publications. 1987: 89. ISBN 9780486602554.
↑  Eves, Howard, An Introduction to the History of Mathematics, Saunders, 1990, ISBN 0-03-029558-0, p. 379, "...the concepts of calculus...(are) so far reaching and have exercised such an impact on the modern world that it is perhaps correct to say that without some knowledge of them a person today can scarcely claim to be well educated."
↑  Maurice Mashaal, 2006. Bourbaki: A Secret Society of Mathematicians. American Mathematical Society. ISBN 0-8218-3967-5, ISBN 978-0-8218-3967-6.
↑  Alexandrov, Pavel S., , Brewer, James W; Smith, Martha K  (编), , New York: Marcel Dekker: 99–111, 1981, ISBN 0-8247-1550-0 .
↑   (PDF).   [2016-05-02]. （原始内容存档 (PDF)于2016-03-04）.
↑  Sevryuk
↑   (PDF).   [2013-11-30]. （原始内容存档 (PDF)于2012-11-03）.
↑  . BBC News. 22 August 2006  [16 June 2011]. （原始内容存档于2019-03-31）.