Exponentiation (English Wikipedia)

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

Last modified: 18:53:42, 19 September 2026 (UTC)

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Olver, Frank W. J.; Lozier, Daniel W.; Boisvert, Ronald F.; Clark, Charles W., eds. (2010). NIST Handbook of Mathematical Functions. National Institute of Standards and Technology (NIST), U.S. Department of Commerce, Cambridge University Press. ISBN 978-0-521-19225-5. MR 2723248.

ams.org

Rotman, Joseph J. (2015). Advanced Modern Algebra, Part 1. Graduate Studies in Mathematics. Vol. 165 (3rd ed.). Providence, RI: American Mathematical Society. p. 130, fn. 4. ISBN 978-1-4704-1554-9.

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

Anton, Howard; Bivens, Irl; Davis, Stephen (2012). Calculus: Early Transcendentals (9th ed.). John Wiley & Sons. p. 28. ISBN 9780470647691.
Bloom, David M. (1979). Linear Algebra and Geometry. Cambridge University Press. p. 45. ISBN 978-0-521-29324-2.
Herschel, John Frederick William (1820). "Part III. Section I. Examples of the Direct Method of Differences". A Collection of Examples of the Applications of the Calculus of Finite Differences. Cambridge, UK: Printed by J. Smith, sold by J. Deighton & sons. pp. 1–13 [5–6]. Archived from the original on 2020-08-04. Retrieved 2020-08-04. (NB. Inhere, Herschel refers to his 1813 work and mentions Hans Heinrich Bürmann's older work.)
"80 Contents". 80 Micro (45). 1001001, Inc.: 5. October 1983. ISSN 0744-7868. Retrieved 2020-02-06.
Szabó, Árpád (1978). The Beginnings of Greek Mathematics. Synthese Historical Library. Vol. 17. Translated by A.M. Ungar. Dordrecht: D. Reidel. p. 37. ISBN 90-277-0819-3.
Ball, W. W. Rouse (1915). A Short Account of the History of Mathematics (6th ed.). London: Macmillan. p. 38.
Cajori, Florian (1928). A History of Mathematical Notations. Vol. 1. The Open Court Company. p. 102.
Cajori, Florian (1928). A History of Mathematical Notations. Vol. 1. London: Open Court Publishing Company. p. 344.
Stifel, Michael (1544). Arithmetica integra. Nuremberg: Johannes Petreius. p. 235v.
Cajori, Florian (1928). A History of Mathematical Notations. Vol. 1. The Open Court Company. p. 204.

bbc.co.uk (Global: 11^th place; English: 10^th place)

"Laws of indices". GCSE Maths Revision. BBC Bitesize. Retrieved 2026-08-29.

bnf.fr (Global: 61^st place; English: 357^th place)

gallica.bnf.fr

Descartes, René (1637). "La Géométrie". Discourse de la méthode [...]. Leiden: Jan Maire. p. 299. Et aa, ou $a 2$ , pour multiplier $a$ par soy mesme; Et $a 3$ , pour le multiplier encore une fois par $a$ , & ainsi a l'infini (And $aa$ , or $a 2$ , in order to multiply $a$ by itself; and $a 3$ , in order to multiply it once more by $a$ , and thus to infinity).
Euler, Leonhard (1748). Introductio in analysin infinitorum (in Latin). Vol. I. Lausanne: Marc-Michel Bousquet. pp. 69, 98–99. Primum ergo considerandæ sunt quantitates exponentiales, seu Potestates, quarum Exponens ipse est quantitas variabilis. Perspicuum enim est hujusmodi quantitates ad Functiones algebraicas referri non posse, cum in his Exponentes non nisi constantes locum habeant.

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

Hodge, Jonathan K.; Schlicker, Steven; Sundstorm, Ted (2014). Abstract Algebra: an inquiry based approach. CRC Press. p. 94. ISBN 978-1-4665-6706-1.
Achatz, Thomas (2005). Technical Shop Mathematics (3rd ed.). Industrial Press. p. 101. ISBN 978-0-8311-3086-2.
Tao, Terence (2016). "Limits of sequences". Analysis I. Texts and Readings in Mathematics. Vol. 37. pp. 126–154. doi:10.1007/978-981-10-1789-6_6. ISBN 978-981-10-1789-6.
Herschel, John Frederick William (1820). "Part III. Section I. Examples of the Direct Method of Differences". A Collection of Examples of the Applications of the Calculus of Finite Differences. Cambridge, UK: Printed by J. Smith, sold by J. Deighton & sons. pp. 1–13 [5–6]. Archived from the original on 2020-08-04. Retrieved 2020-08-04. (NB. Inhere, Herschel refers to his 1813 work and mentions Hans Heinrich Bürmann's older work.)
Cajori, Florian (1952) [March 1929]. A History of Mathematical Notations. Vol. 2 (3rd ed.). Chicago, USA: Open court publishing company. pp. 108, 176–179, 336, 346. ISBN 978-1-60206-714-1. Retrieved 2016-01-18. {{cite book}}: ISBN / Date incompatibility (help)
Daneliuk, Timothy "Tim" A. (1982-08-09). "BASCOM - A BASIC compiler for TRS-80 I and II". InfoWorld. Software Reviews. Vol. 4, no. 31. Popular Computing, Inc. pp. 41–42. Archived from the original on 2020-02-07. Retrieved 2020-02-06.

cambridge.org (Global: 209^th place; English: 151^st place)

Olver, Frank W. J.; Lozier, Daniel W.; Boisvert, Ronald F.; Clark, Charles W., eds. (2010). NIST Handbook of Mathematical Functions. National Institute of Standards and Technology (NIST), U.S. Department of Commerce, Cambridge University Press. ISBN 978-0-521-19225-5. MR 2723248.

ccrwest.org (Global: low place; English: low place)

Gordon, D. M. (1998). "A Survey of Fast Exponentiation Methods" (PDF). Journal of Algorithms. 27: 129–146. doi:10.1006/jagm.1997.0913. Archived from the original (PDF) on 2018-07-23. Retrieved 2024-01-11.

computerhistory.org (Global: 2,702^nd place; English: 1,789^th place)

archive.computerhistory.org

Backus, John Warner; Beeber, R. J.; Best, Sheldon F.; Goldberg, Richard; Herrick, Harlan L.; Hughes, R. A.; Mitchell, L. B.; Nelson, Robert A.; Nutt, Roy; Sayre, David; Sheridan, Peter B.; Stern, Harold; Ziller, Irving (1956-10-15). Sayre, David (ed.). The FORTRAN Automatic Coding System for the IBM 704 EDPM: Programmer's Reference Manual (PDF). New York, USA: Applied Science Division and Programming Research Department, International Business Machines Corporation. p. 15. Archived (PDF) from the original on 2022-07-04. Retrieved 2022-07-04. (2+51+1 pages)
Backus, John Warner; Herrick, Harlan L.; Nelson, Robert A.; Ziller, Irving (1954-11-10). Backus, John Warner (ed.). Specifications for: The IBM Mathematical FORmula TRANSlating System, FORTRAN (PDF) (Preliminary report). New York, USA: Programming Research Group, Applied Science Division, International Business Machines Corporation. pp. 4, 6. Archived (PDF) from the original on 2022-03-29. Retrieved 2022-07-04. (29 pages)

digizeitschriften.de (Global: low place; English: low place)

Steiner, J.; Clausen, T.; Abel, Niels Henrik (1827). "Aufgaben und Lehrsätze, erstere aufzulösen, letztere zu beweisen" [Problems and propositions, the former to solve, the later to prove]. Journal für die reine und angewandte Mathematik. 2: 286–287.

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

Knobloch, Eberhard (1994). "The infinite in Leibniz's mathematics – The historiographical method of comprehension in context". In Kostas Gavroglu; Jean Christianidis; Efthymios Nicolaidis (eds.). Trends in the Historiography of Science. Boston Studies in the Philosophy of Science. Vol. 151. Springer Netherlands. p. 276. doi:10.1007/978-94-017-3596-4_20. ISBN 9789401735964. A positive power of zero is infinitely small, a negative power of zero is infinite.
Tao, Terence (2016). "Limits of sequences". Analysis I. Texts and Readings in Mathematics. Vol. 37. pp. 126–154. doi:10.1007/978-981-10-1789-6_6. ISBN 978-981-10-1789-6.
Gordon, D. M. (1998). "A Survey of Fast Exponentiation Methods" (PDF). Journal of Algorithms. 27: 129–146. doi:10.1006/jagm.1997.0913. Archived from the original (PDF) on 2018-07-23. Retrieved 2024-01-11.
Herschel, John Frederick William (1813) [1812-11-12]. "On a Remarkable Application of Cotes's Theorem". Philosophical Transactions of the Royal Society of London. 103 (Part 1). London: Royal Society of London, printed by W. Bulmer and Co., Cleveland-Row, St. James's, sold by G. and W. Nicol, Pall-Mall: 8–26 [10]. doi:10.1098/rstl.1813.0005. JSTOR 107384. S2CID 118124706.
Archimedes. (2009). THE SAND-RECKONER. In T. Heath (Ed.), The Works of Archimedes: Edited in Modern Notation with Introductory Chapters (Cambridge Library Collection - Mathematics, pp. 229-232). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511695124.017.
Kneusel, Ronald T (2025). Numbers and Computers. Texts in Computer Science. pp. 84–85. doi:10.1007/978-3-031-67482-2. ISBN 978-3-031-67481-5.

etymonline.com (Global: 669^th place; English: 670^th place)

"Exponent | Etymology of exponent by etymonline".

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

Herschel, John Frederick William (1813) [1812-11-12]. "On a Remarkable Application of Cotes's Theorem". Philosophical Transactions of the Royal Society of London. 103 (Part 1). London: Royal Society of London, printed by W. Bulmer and Co., Cleveland-Row, St. James's, sold by G. and W. Nicol, Pall-Mall: 8–26 [10]. doi:10.1098/rstl.1813.0005. JSTOR 107384. S2CID 118124706.
Callanan, Cecelia (March 1967). "Scientific Notation". The Mathematics Teacher. 60 (3): 252–56 – via JSTOR.

loc.gov (Global: 63^rd place; English: 47^th place)

lccn.loc.gov

Knebelman, Morris S.; Thomas, Tracy Y. (1942). Principles of College Algebra. New York: Prentice-Hall, Inc. p. 118. LCCN 42023721. OCLC 795498.
Lick, Dale W. (1970). Fundamentals of Algebra. Eaglewood Cliffs, New Jersey: Prentice-Hall, Inc. p. 77. ISBN 0-13-334235-2. LCCN 75-101204. OCLC 74002.
Beckenbach, Edwin F.; Drooyan, Irving (1968). Modern College Algebra and Trigonometry. Belmont, California: Wadsworth Publishing Company, Inc. p. 27. LCCN 67-25821. OCLC 2656112.

loc.gov

Euler, Leonard (1840). Elements of Algebra [Vollständige Anleitung zur Algebra]. Translated by Hewlett, John (5th ed.). London: Longman, Orme, and Co. p. 48. (In chapter XVI, "Of Powers in general.") Reprinted by Springer-Verlag, 1984; LCCN 84-13898; ISBN 0-387-96014-7, 3-540-96014-7; OCLC 10948598.

mcgraw-hill.com (Global: low place; English: low place)

highered.mcgraw-hill.com

Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2001). Introduction to Algorithms (second ed.). MIT Press. ISBN 978-0-262-03293-3. Online resource Archived 2007-09-30 at the Wayback Machine.

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

The most recent usage in this sense cited by the OED is from 1806 ("involution". Oxford English Dictionary (online ed.). Oxford University Press. (Subscription or participating institution membership required.)).

quickclick.es (Global: low place; English: low place)

Torres Quevedo, Leonardo (1914-11-19). "Automática: Complemento de la Teoría de las Máquinas" (PDF). Revista de Obras Públicas. LXII (2043): 575–583. Archived (PDF) from the original on 2023-08-10. Retrieved 2026-06-18.

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

api.semanticscholar.org

Herschel, John Frederick William (1813) [1812-11-12]. "On a Remarkable Application of Cotes's Theorem". Philosophical Transactions of the Royal Society of London. 103 (Part 1). London: Royal Society of London, printed by W. Bulmer and Co., Cleveland-Row, St. James's, sold by G. and W. Nicol, Pall-Mall: 8–26 [10]. doi:10.1098/rstl.1813.0005. JSTOR 107384. S2CID 118124706.

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

mathshistory.st-andrews.ac.uk

O'Connor, John J.; Robertson, Edmund F. "Etymology of some common mathematical terms". MacTutor History of Mathematics Archive. University of St Andrews.
O'Connor, John J.; Robertson, Edmund F. "Abu'l Hasan ibn Ali al Qalasadi". MacTutor History of Mathematics Archive. University of St Andrews.

tripod.com (Global: 666^th place; English: 543^rd place)

jeff560.tripod.com

"Earliest Known Uses of Some of the Words of Mathematics (E)". 2017-06-23. Archived from the original on 2024-09-15.

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

Shiver, Janet; Wiilard, Terri. "Scientific notation: working with orders of magnitude". Visionlearning. Archived from the original on 2026-03-06. Retrieved 2026-06-18.

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

Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2001). Introduction to Algorithms (second ed.). MIT Press. ISBN 978-0-262-03293-3. Online resource Archived 2007-09-30 at the Wayback Machine.
Gordon, D. M. (1998). "A Survey of Fast Exponentiation Methods" (PDF). Journal of Algorithms. 27: 129–146. doi:10.1006/jagm.1997.0913. Archived from the original (PDF) on 2018-07-23. Retrieved 2024-01-11.
Herschel, John Frederick William (1820). "Part III. Section I. Examples of the Direct Method of Differences". A Collection of Examples of the Applications of the Calculus of Finite Differences. Cambridge, UK: Printed by J. Smith, sold by J. Deighton & sons. pp. 1–13 [5–6]. Archived from the original on 2020-08-04. Retrieved 2020-08-04. (NB. Inhere, Herschel refers to his 1813 work and mentions Hans Heinrich Bürmann's older work.)
Backus, John Warner; Beeber, R. J.; Best, Sheldon F.; Goldberg, Richard; Herrick, Harlan L.; Hughes, R. A.; Mitchell, L. B.; Nelson, Robert A.; Nutt, Roy; Sayre, David; Sheridan, Peter B.; Stern, Harold; Ziller, Irving (1956-10-15). Sayre, David (ed.). The FORTRAN Automatic Coding System for the IBM 704 EDPM: Programmer's Reference Manual (PDF). New York, USA: Applied Science Division and Programming Research Department, International Business Machines Corporation. p. 15. Archived (PDF) from the original on 2022-07-04. Retrieved 2022-07-04. (2+51+1 pages)
Backus, John Warner; Herrick, Harlan L.; Nelson, Robert A.; Ziller, Irving (1954-11-10). Backus, John Warner (ed.). Specifications for: The IBM Mathematical FORmula TRANSlating System, FORTRAN (PDF) (Preliminary report). New York, USA: Programming Research Group, Applied Science Division, International Business Machines Corporation. pp. 4, 6. Archived (PDF) from the original on 2022-03-29. Retrieved 2022-07-04. (29 pages)
Daneliuk, Timothy "Tim" A. (1982-08-09). "BASCOM - A BASIC compiler for TRS-80 I and II". InfoWorld. Software Reviews. Vol. 4, no. 31. Popular Computing, Inc. pp. 41–42. Archived from the original on 2020-02-07. Retrieved 2020-02-06.
"Earliest Known Uses of Some of the Words of Mathematics (E)". 2017-06-23. Archived from the original on 2024-09-15.
Torres Quevedo, Leonardo (1914-11-19). "Automática: Complemento de la Teoría de las Máquinas" (PDF). Revista de Obras Públicas. LXII (2043): 575–583. Archived (PDF) from the original on 2023-08-10. Retrieved 2026-06-18.
Shiver, Janet; Wiilard, Terri. "Scientific notation: working with orders of magnitude". Visionlearning. Archived from the original on 2026-03-06. Retrieved 2026-06-18.

wolfram.com (Global: 1,091^st place; English: 1,169^th place)

mathworld.wolfram.com

Weisstein, Eric W. "Power". MathWorld. Retrieved 2020-08-27.
Weisstein, Eric W. "Principal root of unity". MathWorld.

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

search.worldcat.org

Knebelman, Morris S.; Thomas, Tracy Y. (1942). Principles of College Algebra. New York: Prentice-Hall, Inc. p. 118. LCCN 42023721. OCLC 795498.
Lick, Dale W. (1970). Fundamentals of Algebra. Eaglewood Cliffs, New Jersey: Prentice-Hall, Inc. p. 77. ISBN 0-13-334235-2. LCCN 75-101204. OCLC 74002.
Beckenbach, Edwin F.; Drooyan, Irving (1968). Modern College Algebra and Trigonometry. Belmont, California: Wadsworth Publishing Company, Inc. p. 27. LCCN 67-25821. OCLC 2656112.
Rich, Barnett (1960). (Schaum's Principles And Problems Of) Elementary Algebra. New York: Schaum Publishing Company. p. 9. OCLC 29567756.
"80 Contents". 80 Micro (45). 1001001, Inc.: 5. October 1983. ISSN 0744-7868. Retrieved 2020-02-06.

worldcat.org

Euler, Leonard (1840). Elements of Algebra [Vollständige Anleitung zur Algebra]. Translated by Hewlett, John (5th ed.). London: Longman, Orme, and Co. p. 48. (In chapter XVI, "Of Powers in general.") Reprinted by Springer-Verlag, 1984; LCCN 84-13898; ISBN 0-387-96014-7, 3-540-96014-7; OCLC 10948598.

worldwidewords.org (Global: 8,811^th place; English: 5,849^th place)

Quinion, Michael. "Zenzizenzizenzic". World Wide Words. Retrieved 2020-04-16.

Exponentiation (English Wikipedia)

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