History of calculus (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "History of calculus" in English language version.

Last modified: 15:44:45, 17 August 2026 (UTC)

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Ossendrijver, Mathieu (29 January 2016). "Ancient Babylonian astronomers calculated Jupiter's position from the area under a time-velocity graph". Science. 351 (6272): 482–484. Bibcode:2016Sci...351..482O. doi:10.1126/science.aad8085. PMID 26823423. S2CID 206644971.
Ferguson, James (2004), A Brief Survey of the History of the Calculus of Variations and its Applications, arXiv:math/0402357, Bibcode:2004math......2357F

agnesscott.edu (Global: low place; English: low place)

Unlu, Elif (April 1995). "Maria Gaetana Agnesi". Agnes Scott College.

ams.org (Global: 434^th place; English: 249^th place)

Review of J.M. Child's translation (1916) The geometrical lectures of Isaac Barrow reviewer: Arnold Dresden (Jun 1918) p.454 Barrow has the fundamental theorem of calculus

archive.org (Global: 6^th place; English: 6^th place)

Boyer, Carl B. (1991). "Archimedes of Syracuse". A History of Mathematics (2nd ed.). Wiley. pp. 127. ISBN 978-0-471-54397-8. Greek mathematics sometimes has been described as essentially static, with little regard for the notion of variability; but Archimedes, in his study of the spiral, seems to have found the tangent to a curve through kinematic considerations akin to differential calculus. Thinking of a point on the spiral ⁠ $r=a\theta$ ⁠ as subjected to a double motion – a uniform radial motion away from the origin of coordinates and a circular motion about the origin – he seems to have found (through the parallelogram of velocities) the direction of motion (hence of the tangent to the curve) by noting the resultant of the two component motions. This appears to be the first instance in which a tangent was found to a curve other than a circle.
Archimedes' study of the spiral, a curve that he ascribed to his friend Conon of Alexandria, was part of the Greek search for the solution of the three famous problems.
Cooke, Roger (1997). "The Mathematics of the Hindus". The History of Mathematics: A Brief Course. Wiley. pp. 213–215. ISBN 0-471-18082-3.
Simmons, George F. (2007). Calculus Gems: Brief Lives and Memorable Mathematics. Mathematical Association of America. p. 98. ISBN 978-0-88385-561-4.
Gregory, James (1668). Geometriae Pars Universalis. Museo Galileo: Patavii: typis heredum Pauli Frambotti.{{cite book}}: CS1 maint: publisher location (link)
The geometrical lectures of Isaac Barrow, translated, with notes and proofs, and a discussion on the advance made therein on the work of his predecessors in the infinitesimal calculus. Chicago: Open Court. 1916. Translator: J. M. Child (1916)
Boyer, Carl (1939). The History of the Calculus and Its Conceptual Development. Courier Corporation. p. 209. ISBN 9780486605098. {{cite book}}: ISBN / Date incompatibility (help)

arxiv.org (Global: 49^th place; English: 31^st place)

Torres, Delfim F. M. (2021-07-29). "On a Non-Newtonian Calculus of Variations". Axioms. 10 (3): 171. arXiv:2107.14152. doi:10.3390/axioms10030171. ISSN 2075-1680.
Ferguson, James (2004), A Brief Survey of the History of the Calculus of Variations and its Applications, arXiv:math/0402357, Bibcode:2004math......2357F

books.google.com (Global: 3^rd place; English: 3^rd place)

Dun, Liu; Fan, Dainian; Cohen, Robert Sonné (1966). A comparison of Archimdes' and Liu Hui's studies of circles. Chinese studies in the history and philosophy of science and technology. Vol. 130. Springer. p. 279. ISBN 978-0-7923-3463-7., Chapter, p. 279
Zill, Dennis G.; Wright, Scott; Wright, Warren S. (2009). Calculus: Early Transcendentals (3 ed.). Jones & Bartlett Learning. p. xxvii. ISBN 978-0-7637-5995-7. Extract of page 27
Boyer, Carl B. (1959). "III. Medieval Contributions". A History of the Calculus and Its Conceptual Development. Dover. pp. 79–89. ISBN 978-0-486-60509-8. {{cite book}}: ISBN / Date incompatibility (help)
Smith, pp. 91–127., p. 91, at Google Books
See, e.g., Marlow Anderson, Victor J. Katz, Robin J. Wilson, Sherlock Holmes in Babylon and Other Tales of Mathematical History, Mathematical Association of America, 2004, p. 114.
Johnston, William; McAllister, Alex (2009). "Chapter 4: Real Analysis". A Transition to Advanced Mathematics: A Survey Course. Oxford University Press US. p. 333. ISBN 978-0-19-531076-4.
Grattan-Guinness, Ivor (1980). From the Calculus to Set Theory 1630-1910: An Introductory History. Princeton University Press. p. 49. ISBN 978-0-691-07082-7.
Guicciardini, Niccolò (2009). Isaac Newton on Mathematical Certainty and Method. MIT Press. p. 331. ISBN 978-0-262-01317-8.
Press, S. James; Tanur, Judith M. (2016). The Subjectivity of Scientists and the Bayesian Approach. Dover Publications, Inc. p. 88. ISBN 978-0-486-80284-8.
Hall, A. Rupert (1980). Philosophers at War: The Quarrel Between Newton and Leibniz. Cambridge University Press. p. 136. ISBN 978-0-521-22732-2.
Hall, A. Rupert (1980). Philosophers at War: The Quarrel Between Newton and Leibniz. Cambridge University Press. p. 30. ISBN 978-0-521-22732-2.
Goldstine, Herman H. (1980). A History of the Calculus of Variations from the 17th Through the 19th Century. Springer New York. pp. 7–21. ISBN 978-1-4613-8106-8.
Rowlands, Peter (2017). Newton and the Great World System. World Scientific Publishing. pp. 36–39. doi:10.1142/q0108. ISBN 978-1-78634-372-7.

britannica.com (Global: 37^th place; English: 64^th place)

Hosch, William L. (27 Dec 2023). "Rolle's theorem". Encyclopedia Britannica. Retrieved 2025-03-02.
"Gottfried Wilhelm Leibniz | Biography & Facts". Encyclopedia Britannica.

cam.ac.uk (Global: 569^th place; English: 354^th place)

cudl.lib.cam.ac.uk

Newton, Isaac. "Waste Book". Retrieved 10 January 2012.

doi.org (Global: 2^nd place; English: 2^nd place)

Ossendrijver, Mathieu (29 January 2016). "Ancient Babylonian astronomers calculated Jupiter's position from the area under a time-velocity graph". Science. 351 (6272): 482–484. Bibcode:2016Sci...351..482O. doi:10.1126/science.aad8085. PMID 26823423. S2CID 206644971.
Katz, Victor J. (June 1995). "Ideas of Calculus in Islam and India". Mathematics Magazine. 68 (3): 163–174. doi:10.1080/0025570X.1995.11996307. ISSN 0025-570X. JSTOR 2691411.
Berggren, J. L.; Al-Tūsī, Sharaf Al-Dīn; Rashed, Roshdi; Al-Tusi, Sharaf Al-Din (April 1990). "Innovation and Tradition in Sharaf al-Dīn al-Ṭūsī's Muʿādalāt". Journal of the American Oriental Society. 110 (2): 304–309. doi:10.2307/604533. JSTOR 604533.
Stillwell, John (2010). "Mathematics and Its History". Undergraduate Texts in Mathematics. doi:10.1007/978-1-4419-6053-5. ISSN 0172-6056.
Hollingdale, Stuart (1991). "Review of Before Newton: The Life and Times of Isaac Barrow". Notes and Records of the Royal Society of London. 45 (2): 277–279. doi:10.1098/rsnr.1991.0027. ISSN 0035-9149. JSTOR 531707. S2CID 165043307. The most interesting to us are Lectures X-XII, in which Barrow comes close to providing a geometrical demonstration of the fundamental theorem of the calculus ... He did not realize, however, the full significance of his results, and his rejection of algebra means that his work must remain a piece of mid-17th century geometrical analysis of mainly historic interest.
Bressoud, David M. (2011). "Historical Reflections on Teaching the Fundamental Theorem of Integral Calculus". The American Mathematical Monthly. 118 (2): 99–115. doi:10.4169/amer.math.monthly.118.02.099. S2CID 21473035.
Cajori, Florian (1919). "Who Was the First Inventor of the Calculus?". The American Mathematical Monthly. 26 (1): 15–20. doi:10.2307/2974042. JSTOR 2974042.
Reyes 2004, p. 160 Reyes, Mitchell (2004). "The Rhetoric in Mathematics: Newton, Leibniz, the Calculus, and the Rhetorical Force of the Infinitesimal". Quarterly Journal of Speech. 90 (2): 159–184. doi:10.1080/0033563042000227427. S2CID 145802382.
Boyer, Carl B. (1970). "The History of the Calculus". The Two-Year College Mathematics Journal. 1 (1): 60–86. doi:10.2307/3027118. ISSN 0049-4925. JSTOR 3027118.
Torres, Delfim F. M. (2021-07-29). "On a Non-Newtonian Calculus of Variations". Axioms. 10 (3): 171. arXiv:2107.14152. doi:10.3390/axioms10030171. ISSN 2075-1680.
Rowlands, Peter (2017). Newton and the Great World System. World Scientific Publishing. pp. 36–39. doi:10.1142/q0108. ISBN 978-1-78634-372-7.

en.wikisource.org (Global: 82^nd place; English: 41^st place)

Chisholm, Hugh, ed. (1911). "Infinitesimal Calculus § History" . Encyclopædia Britannica. Vol. 14 (11th ed.). Cambridge University Press. p. 537.

jstor.org (Global: 23^rd place; English: 15^th place)

Katz, Victor J. (June 1995). "Ideas of Calculus in Islam and India". Mathematics Magazine. 68 (3): 163–174. doi:10.1080/0025570X.1995.11996307. ISSN 0025-570X. JSTOR 2691411.
Berggren, J. L.; Al-Tūsī, Sharaf Al-Dīn; Rashed, Roshdi; Al-Tusi, Sharaf Al-Din (April 1990). "Innovation and Tradition in Sharaf al-Dīn al-Ṭūsī's Muʿādalāt". Journal of the American Oriental Society. 110 (2): 304–309. doi:10.2307/604533. JSTOR 604533.
Hollingdale, Stuart (1991). "Review of Before Newton: The Life and Times of Isaac Barrow". Notes and Records of the Royal Society of London. 45 (2): 277–279. doi:10.1098/rsnr.1991.0027. ISSN 0035-9149. JSTOR 531707. S2CID 165043307. The most interesting to us are Lectures X-XII, in which Barrow comes close to providing a geometrical demonstration of the fundamental theorem of the calculus ... He did not realize, however, the full significance of his results, and his rejection of algebra means that his work must remain a piece of mid-17th century geometrical analysis of mainly historic interest.
Cajori, Florian (1919). "Who Was the First Inventor of the Calculus?". The American Mathematical Monthly. 26 (1): 15–20. doi:10.2307/2974042. JSTOR 2974042.
Boyer, Carl B. (1970). "The History of the Calculus". The Two-Year College Mathematics Journal. 1 (1): 60–86. doi:10.2307/3027118. ISSN 0049-4925. JSTOR 3027118.

kyoto-u.ac.jp (Global: 2,808^th place; English: 4,826^th place)

kurims.kyoto-u.ac.jp

Osada, Naoki (Aug 26, 2011). "収束の加速法の歴史 : 17世紀ヨーロッパと日本の加速法 (数学史の研究)" (PDF). Study of the History of Mathematics RIMS Kôkyûroku (in Japanese). 1787: 100–102 – via Kyoto University.

mathpages.com (Global: low place; English: low place)

MathPages — Archimedes on Spheres & Cylinders Archived 2010-01-03 at the Wayback Machine

nasa.gov (Global: 12^th place; English: 73^rd place)

"Johannes Kepler: His Life, His Laws and Times". NASA. 24 September 2016. Archived from the original on 2021-06-24. Retrieved 2021-06-10.

nih.gov (Global: 5^th place; English: 5^th place)

pubmed.ncbi.nlm.nih.gov

Ossendrijver, Mathieu (29 January 2016). "Ancient Babylonian astronomers calculated Jupiter's position from the area under a time-velocity graph". Science. 351 (6272): 482–484. Bibcode:2016Sci...351..482O. doi:10.1126/science.aad8085. PMID 26823423. S2CID 206644971.

nytimes.com (Global: 7^th place; English: 7^th place)

Chang, Kenneth (2016). "Signs of Modern Astronomy Seen in Ancient Babylon". New York Times.

oed.com (Global: 743^rd place; English: 419^th place)

"calculus". Oxford English Dictionary (online ed.). Oxford University Press. (Subscription or participating institution membership required.)

rutgers.edu (Global: 2,011^th place; English: 1,139^th place)

math.rutgers.edu

Pellegrino, Dana. "Pierre de Fermat". Retrieved 2008-02-24.

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

Ossendrijver, Mathieu (29 January 2016). "Ancient Babylonian astronomers calculated Jupiter's position from the area under a time-velocity graph". Science. 351 (6272): 482–484. Bibcode:2016Sci...351..482O. doi:10.1126/science.aad8085. PMID 26823423. S2CID 206644971.
Hollingdale, Stuart (1991). "Review of Before Newton: The Life and Times of Isaac Barrow". Notes and Records of the Royal Society of London. 45 (2): 277–279. doi:10.1098/rsnr.1991.0027. ISSN 0035-9149. JSTOR 531707. S2CID 165043307. The most interesting to us are Lectures X-XII, in which Barrow comes close to providing a geometrical demonstration of the fundamental theorem of the calculus ... He did not realize, however, the full significance of his results, and his rejection of algebra means that his work must remain a piece of mid-17th century geometrical analysis of mainly historic interest.
Bressoud, David M. (2011). "Historical Reflections on Teaching the Fundamental Theorem of Integral Calculus". The American Mathematical Monthly. 118 (2): 99–115. doi:10.4169/amer.math.monthly.118.02.099. S2CID 21473035.
Reyes 2004, p. 160 Reyes, Mitchell (2004). "The Rhetoric in Mathematics: Newton, Leibniz, the Calculus, and the Rhetorical Force of the Infinitesimal". Quarterly Journal of Speech. 90 (2): 159–184. doi:10.1080/0033563042000227427. S2CID 145802382.

sjsu.edu (Global: 7,460^th place; English: 4,844^th place)

"The Calculus of Infinitesimals".

springer.com (Global: 182^nd place; English: 172^nd place)

link.springer.com

Stillwell, John (2010). "Mathematics and Its History". Undergraduate Texts in Mathematics. doi:10.1007/978-1-4419-6053-5. ISSN 0172-6056.

st-andrews.ac.uk (Global: 1,053^rd place; English: 1,274^th place)

mathshistory.st-andrews.ac.uk

"Indian mathematics". Maths History. Retrieved 2026-03-26.
O'Connor, John J.; Robertson, Edmund F. (November 2000). "Paramesvara". MacTutor History of Mathematics Archive. University of St Andrews.
"Gottfried Leibniz - Biography".

stackexchange.com (Global: 4,114^th place; English: 3,027^th place)

skeptics.stackexchange.com

See, for example:
- "history - Were metered taxis busy roaming Imperial Rome?". Skeptics Stack Exchange. 2020-06-17. Retrieved 2022-02-13.

stanford.edu (Global: 194^th place; English: 182^nd place)

plato.stanford.edu

"Gottfried Wilhelm Leibniz". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. 2020.

tandfonline.com (Global: 286^th place; English: 209^th place)

Katz, Victor J. (June 1995). "Ideas of Calculus in Islam and India". Mathematics Magazine. 68 (3): 163–174. doi:10.1080/0025570X.1995.11996307. ISSN 0025-570X. JSTOR 2691411.
Bressoud, David M. (2011). "Historical Reflections on Teaching the Fundamental Theorem of Integral Calculus". The American Mathematical Monthly. 118 (2): 99–115. doi:10.4169/amer.math.monthly.118.02.099. S2CID 21473035.

upf.edu (Global: low place; English: low place)

econ.upf.edu

Paradís, Jaume; Pla, Josep; Viader, Pelagrí. "Fermat's Treatise On Quadrature: A New Reading" (PDF). Archived from the original (PDF) on 2007-01-07. Retrieved 2008-02-24.

web.archive.org (Global: 1^st place; English: 1^st place)

MathPages — Archimedes on Spheres & Cylinders Archived 2010-01-03 at the Wayback Machine
"Johannes Kepler: His Life, His Laws and Times". NASA. 24 September 2016. Archived from the original on 2021-06-24. Retrieved 2021-06-10.
Paradís, Jaume; Pla, Josep; Viader, Pelagrí. "Fermat's Treatise On Quadrature: A New Reading" (PDF). Archived from the original (PDF) on 2007-01-07. Retrieved 2008-02-24.
Deleuze, Gilles. "DELEUZE / LEIBNIZ Cours Vincennes - 22/04/1980". Archived from the original on 11 September 2012. Retrieved 30 April 2013.

webdeleuze.com (Global: low place; English: low place)

Deleuze, Gilles. "DELEUZE / LEIBNIZ Cours Vincennes - 22/04/1980". Archived from the original on 11 September 2012. Retrieved 30 April 2013.

worldcat.org (Global: 4^th place; English: 4^th place)

search.worldcat.org

Katz, Victor J. (June 1995). "Ideas of Calculus in Islam and India". Mathematics Magazine. 68 (3): 163–174. doi:10.1080/0025570X.1995.11996307. ISSN 0025-570X. JSTOR 2691411.
Stillwell, John (2010). "Mathematics and Its History". Undergraduate Texts in Mathematics. doi:10.1007/978-1-4419-6053-5. ISSN 0172-6056.
Hollingdale, Stuart (1991). "Review of Before Newton: The Life and Times of Isaac Barrow". Notes and Records of the Royal Society of London. 45 (2): 277–279. doi:10.1098/rsnr.1991.0027. ISSN 0035-9149. JSTOR 531707. S2CID 165043307. The most interesting to us are Lectures X-XII, in which Barrow comes close to providing a geometrical demonstration of the fundamental theorem of the calculus ... He did not realize, however, the full significance of his results, and his rejection of algebra means that his work must remain a piece of mid-17th century geometrical analysis of mainly historic interest.
Such as Kepler, Descartes, Fermat, Pascal and Wallis. Calinger 1999, p. 556 Calinger, Ronald (1999). A Contextual History of Mathematics. Prentice-Hall. ISBN 978-0-02-318285-3. OCLC 40479696.
Calinger 1999, p. 610 Calinger, Ronald (1999). A Contextual History of Mathematics. Prentice-Hall. ISBN 978-0-02-318285-3. OCLC 40479696.
Boyer, Carl B. (1970). "The History of the Calculus". The Two-Year College Mathematics Journal. 1 (1): 60–86. doi:10.2307/3027118. ISSN 0049-4925. JSTOR 3027118.
Torres, Delfim F. M. (2021-07-29). "On a Non-Newtonian Calculus of Variations". Axioms. 10 (3): 171. arXiv:2107.14152. doi:10.3390/axioms10030171. ISSN 2075-1680.

History of calculus (English Wikipedia)

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