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{{Short description|German mathematician and astronomer (1436–1476)}}
{{For|the lunar crater|Regiomontanus (crater)}}
{{Use dmy dates|date=June 2023}}
{{Infobox scientist
| name = Regiomontanus
| image = Johannes Regiomontanus.jpg
| caption = 18th-century portrait ({{lang|la|Iohannes de Regio Monte dictus alias Müllerus}})
| birth_date = 6 June 1436
| birth_place = [[Königsberg, Bavaria|Königsberg]], [[Electorate of Saxony]], Holy Roman Empire
| death_date = {{death date and age|1476|7|6|1436|6|6|df=yes}}
| death_place = [[Rome]], [[Papal States]]
| nationality = German
| field = Mathematics ([[trigonometry]]), [[astronomy]], [[astrology]]
| work_institutions = [[Universitas Istropolitana]]
| education = {{ubli|[[University of Leipzig]] {{nowr|(no degree)}}|[[University of Vienna]] (B.A., 1452; M.A., 1457)}}
| academic_advisors = {{ubl|[[Georg von Peuerbach]]|[[Basilios Bessarion]]}}
| notable_students = [[Domenico Novara da Ferrara]]
| known_for = {{ubli|Founding the world's first scientific printing press|Publishing the first printed astronomical textbook (1472) and the first [[trigonometric tables]] ([[Posthumous publication|posthum.]], 1490)|[[Tangent table]]s}}
}}

'''Johannes Müller von Königsberg''' (6 June 1436 – 6 July 1476<ref name="MacTutor" />), better known as '''Regiomontanus''' ({{IPAc-en|ˌ|r|iː|dʒ|i|oʊ|m|ɒ|n|ˈ|t|eɪ|n|ə|s}}), was a mathematician, [[astrologer]] and [[astronomer]] of the [[German Renaissance]], active in [[Vienna]], [[Buda]] and [[Nuremberg]]. His contributions were instrumental in the development of [[Copernican heliocentrism]] in the decades following his death.

Regiomontanus wrote under the Latinized name of ''Ioannes de Monteregio'' (or ''Monte Regio''; ''Regio Monte''); the toponym ''Regiomontanus'' was first used by [[Philipp Melanchthon]] in 1534. He is named after [[Königsberg, Bavaria|Königsberg]] in [[Lower Franconia]], not the larger [[Königsberg]] (modern [[Kaliningrad]]) in Prussia.

==Life==
[[File:Regiomontanus-Koenigsberg.JPG|thumb|left|Plaque at Regiomontanus' birthplace]]
{{Multiple image
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 | image1 = Nuremberg chronicles f 255r 1 (Johannes de Monteregio).jpg
 | width1 = 224 | height1 = 272
 | caption1 = Regiomontanus
 | image2 = Nuremberg Chronicle f 229r 3.jpg
 | width2 = 199 | height2 = 250
 | caption2 = Comet of 1472
 | footer = Woodcuts from the 1493 ''[[Nuremberg Chronicle]]''
}}

Although little is known of Regiomontanus' early life, it is believed that at eleven years of age, he became a student at the [[University of Leipzig]], [[Electorate of Saxony|Saxony]]. In 1451 he continued his studies at [[University of Vienna|Alma Mater Rudolfina]], the university in [[Vienna]], in the Duchy of Austria, where he became a pupil and friend of [[Georg von Peuerbach]]. In 1452 he was awarded his [[bachelor's degree]] (''baccalaureus''), and he was awarded his [[master's degree]] (''magister artium'') at the age of 21 in 1457.<ref name="NDB">{{NDB|21|270|271|Regiomontan(us) (eigentlich Müller, auch Francus, Germanus), Johannes |Folkerts, Menso; Kühne, Andreas |118641913}}</ref> He lectured in [[optics]] and ancient literature.<ref name="Catholic">{{Catholic |inline=1 |prescript= |wstitle=Johann Müller (Regiomontanus) |volume=10 |first=Johann Georg |last=Hagen }}</ref>

In 1460 the papal legate [[Basilios Bessarion]] came to Vienna on a diplomatic mission. Being a humanist scholar with a great interest in the mathematical sciences, Bessarion sought out Peuerbach's company. [[George of Trebizond]] who was Bessarion's philosophical rival had recently produced a new Latin translation of [[Ptolemy]]'s ''[[Almagest]]'' from the Greek, which Bessarion, correctly, regarded as inaccurate and badly translated, so he asked Peuerbach to produce a new one. Peuerbach's Greek was not good enough to do a translation but he knew the ''Almagest'' intimately so instead he started work on a modernised, improved abridgement of the work. Bessarion also invited Peuerbach to become part of his household and to accompany him back to Italy when his work in Vienna was finished. Peuerbach accepted the invitation on the condition that Regiomontanus could also accompany them. However Peuerbach fell ill in 1461 and died having completed only the first six books of his abridgement of the ''Almagest''. On his death bed Peuerbach made Regiomontanus promise to finish the book and publish it.<ref name="MacTutor">{{MacTutor Biography|id=Regiomontanus}}</ref><ref name="Catholic"/>

In 1461 Regiomontanus left Vienna with Bessarion and spent the next four years travelling around Northern Italy as a member of Bessarion's household, looking for and copying mathematical and astronomical manuscripts for Bessarion, who possessed the largest private library in Europe at the time. Regiomontanus also made the acquaintance of the leading Italian mathematicians of the age such as [[Giovanni Bianchini]] and [[Paolo dal Pozzo Toscanelli]] who had also been friends of Peuerbach during his prolonged stay in Italy more than twenty years earlier.<ref name="MacTutor"/>

In 1467, he went to work for [[János Vitéz (bishop)|János Vitéz]], archbishop of [[Esztergom]]. There he calculated extensive astronomical tables and built astronomical instruments.<ref name="NDB" /> Next he went to [[Buda]], and the court of [[Matthias Corvinus]] of Hungary, for whom he built an astrolabe, and where he collated Greek manuscripts for a handsome salary.<ref name=eb>{{Cite EB1911 |last=Clerke |first=Agnes Mary |author-link=Agnes Mary Clerke |wstitle=Regiomontanus}}</ref> The [[trigonometric tables]] that he created while living in Hungary, his ''Tabulae directionum profectionumque'' (printed [[Posthumous publication|posthum.]], 1490), were designed for astrology, including finding astrological houses.<ref>{{cite web |last=Mosley |first=Adam | url=http://www.hps.cam.ac.uk/starry/regioastrol.html | title=Regiomontanus and Astrology | publisher=Cambridge University: History and Philosophy of Science Department | date=1999 | access-date=12 June 2013 }}</ref> The ''Tabulae'' also contained several [[tangent tables]].<ref>Denis Roegel, [https://hal.inria.fr/inria-00543931/PDF/rheticus1551doc.pdf "A reconstruction of the tables of Rheticus' ''Canon doctrinæ triangulorum'' (1551)"], 2010.</ref>

In 1471 Regiomontanus moved to the Free City of [[Nuremberg]], in [[Franconia]], then one of the Empire's important seats of learning, publication, commerce and art, where he worked with the humanist and merchant [[Bernhard Walther]].<ref name="eb" /> Here he founded the world's first scientific printing press, and in 1472 he published the first printed astronomical textbook, the ''Theoricae novae Planetarum'' of his teacher Georg von Peurbach.<ref name="MacTutor" />

Regiomontanus and Bernhard Walther observed the [[comet of 1472]]. Regiomontanus tried to estimate its distance from Earth, using the angle of parallax.{{efn|See [http://www2.jpl.nasa.gov/teachers/attachments/parallax.html NASA: parallax].}} According to David A. Seargeant:<ref>David A. Seargeant. ''The Greatest Comets in History'', 2009, p. 104</ref>

{{Blockquote|In agreement with the prevailing Aristotelian theory on comets as atmospheric phenomena, he estimated its distance to be at least 8,200 miles (13,120 km) and, from this, estimated the central condensation as 26, and the entire coma as 81 miles (41.6 and 129.6 km respectively) in diameter. These values, of course, fail by orders of magnitude, but he is to be commended for this attempt at determining the physical dimensions of the comet.}}
The 1472 comet was visible from Christmas Day 1471 to 1 March 1472 (Julian Calendar), a total of 59 days.<ref>Donald K. Yeomans, ''[http://ssd.jpl.nasa.gov/?great_comets Jet Propulsion Laboratory: Great Comets in History]'', 2007.</ref>

In 1475, Regiomontanus was called to Rome by [[Pope Sixtus IV]] on to work on the planned [[Gregorian calendar#Background|calendar reform]]. Sixtus promised substantial rewards, including the title of [[bishop of Regensburg]],<ref>{{Cite book |url=https://books.google.com/books?id=antLAAAAcAAJ&pg=PA351 |title=Versuch einer allgemeinen Geschichte der Mathematik |last=Boffut |first=Carl |publisher=L. G. Hoffmann |year=1804 |pages=351 |language=de}}</ref><ref>Rudolf Schmidt,  [http://www.zeno.org/Schmidt-1902/A/Regiomontanus,+Johann Regiomontanus, Johann] in: ''Deutsche Buchhändler. Deutsche Buchdrucker'' vol. 5 (1908), 797f.</ref> but it is unlikely that he was actually appointed to the role.<ref name="Catholic" />

On his way to Rome, stopping in Venice, he commissioned the publication of his ''Calendarium'' with [[Erhard Ratdolt]] (printed in 1476).<ref>{{Cite web |url=https://openbook.lib.utah.edu/tag/erhard-ratdolt/ |title=Erhard Ratdolt |date=17 March 2014 |website=Open Book |publisher=[[University of Utah]]  |access-date=21 May 2019}}</ref> Regiomontanus reached Rome, but he died there after only a few months, in his 41st year, on 6 July 1476. According to a rumor repeated by [[Pierre Gassendi|Gassendi]] in his Regiomontanus biography, he was poisoned by relatives of [[George of Trebizond]] whom he had criticized in his writing; it is however considered more likely that he died from the plague.<ref name="MacTutor" />

==Work==
[[File:Regiomontanus - De triangulis planis et sphaericis libri, per Henrichum Petri et Petrum Pernam - 4683051.tif|thumb|upright|''De triangulis planis et sphaericis libri'']]
[[File:Houghton Typ Inc 4366 - Regiomontanus 1.jpg|thumb|upright|Title page for ''Qvesta opra da ogni parte e un libro doro'', 1476]]

During his time in Italy he completed Peuerbach's abridgement of ''[[Almagest]]'', ''Epytoma in almagesti Ptolemei''. In 1464, he completed ''De triangulis omnimodis'' ("On Triangles of All Kinds"). ''De triangulis omnimodis'' was one of the first textbooks presenting the current state of [[trigonometry]] and included lists of questions for review of individual chapters. In it he wrote:

{{quote|You who wish to study great and wonderful things, who wonder about the movement of the stars, must read these theorems about triangles. Knowing these ideas will open the door to all of astronomy and to certain geometric problems.}}

In 1465, he built a portable [[sundial]] for [[Pope Paul II]].

In ''Epytoma in almagesti Ptolemei'', he critiqued the translation of ''Almagest'' by [[George of Trebizond]], pointing out inaccuracies. Later [[Nicolaus Copernicus]] would refer to this book as an influence on his own work.

A prolific author, Regiomontanus was internationally famous in his lifetime. Despite having completed only a quarter of what he had intended to write, he left a substantial body of work. [[Nicolaus Copernicus]]' teacher, [[Domenico Maria Novara da Ferrara]], referred to Regiomontanus as having been his own teacher. There is speculation that Regiomontanus had arrived at a theory of heliocentrism before he died; a manuscript shows particular attention to the [[heliocentric]] theory of the [[Pythagoreanism|Pythagorean]] [[Aristarchus of Samos|Aristarchus]], mention was also given to the motion of the earth in a letter to a friend.<ref>[[Arthur Koestler]], ''The Sleepwalkers'', Penguin Books, 1959, p. 212.</ref>

Much of the material on [[spherical trigonometry]] in Regiomontanus' ''On Triangles'' was taken directly{{dubious|date=March 2017}} from the twelfth-century work of [[Jabir ibn Aflah]] otherwise known as Geber, as noted in the sixteenth century by [[Gerolamo Cardano]].<ref>{{Cite book
  | editor = Victor J. Katz
  | title = The mathematics of Egypt, Mesopotamia, China, India, and Islam: a sourcebook
  | publisher = [[Princeton University Press]]
  | date = 2007
  | url = http://press.princeton.edu/chapters/i8583.html
  | isbn = 978-0-691-11485-9
  | access-date = 16 March 2008
  | archive-date = 1 October 2016
  | archive-url = https://web.archive.org/web/20161001214903/http://press.princeton.edu/chapters/i8583.html
  | url-status = dead
  }}, p.4</ref>

== Publications ==
* {{Cite book|title=Ephemerides|volume=|publisher=Peter Liechtenstein|location=Venezia|year=1498|language=la|url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=4667641}}
* {{Cite book|title=De triangulis planis et sphaericis libri|volume=|publisher=Heinrich Petri & Peter Perna|location=Bern|year=1561|language=la|url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=4683051}}

==Legacy==
[[Simon Stevin]], in his book describing [[decimal representation]] of [[fraction (mathematics)|fraction]]s ([[De Thiende]]), cites the trigonometric tables of Regiomontanus as suggestive of [[positional notation]].<ref>[[E. J. Dijksterhuis]] (1970) ''Simon Stevin: Science in the Netherlands around 1600'', pages 17–19, [[Martinus Nijhoff Publishers]], Dutch original 1943</ref>

Regiomontanus designed his own [[Astrological houses#Regiomontanus|astrological house system]], which became one of the most popular systems in Europe.<ref name="Lewis2003">{{cite book |last=Lewis |first=James R. |title=The Astrology Book: The Encyclopedia of Heavenly Influences|url=https://books.google.com/books?id=lmv4930JbY0C&pg=PA574|access-date=4 August 2012|date=1 March 2003|publisher=[[Visible Ink Press]]|isbn=978-1-57859-144-2|pages=574}}</ref>

In 1561, [[Daniel Santbech]] compiled a collected edition of the works of Regiomontanus, ''De triangulis planis et sphaericis libri quinque'' (first published in 1533) and ''Compositio tabularum sinum recto'', as well as Santbech's own ''Problematum astronomicorum et geometricorum sectiones septem''. It was published in [[Basel]] by [[Henrich Petri]] and [[Petrus Perna]].

There is an image of him in Hartmann Schedel's 1493 ''[[Nuremberg Chronicle]]''. He is holding an [[astrolabe]]. Yet, although there are thirteen illustrations of comets in the ''Chronicle'' (from 471 to 1472), they are stylized, rather than representing the actual objects.{{efn|See [http://www.icq.eps.harvard.edu/DanComet2.gif image].}}

The crater [[Regiomontanus (crater)|Regiomontanus]] on the Moon is named after him.

==See also==
* [[List of unsolved deaths]]
* [[Regiomontanus' angle maximization problem]]

==Notes==
{{Notelist}}

==References==
{{Reflist}}

==Further reading==
* Irmela Bues, ''Johannes Regiomontanus (1436–1476)''. In: ''Fränkische Lebensbilder'' 11. Neustadt/Aisch 1984, pp.&nbsp;28–43
* Rudolf Mett: ''Regiomontanus. Wegbereiter des neuen Weltbildes''. Teubner / Vieweg, Stuttgart / Leipzig 1996, {{isbn|3-8154-2510-7}}
* Helmuth Gericke: ''Mathematik im Abendland: Von den römischen Feldmessern bis zu Descartes''.  Springer-Verlag, Berlin 1990, {{isbn|3-540-51206-3}}
* Günther Harmann (Hrsg.): ''Regiomontanus-Studien''. (= Österreichische Akademie der Wissenschaften, Philosophisch-historische Klasse, Sitzungsberichte, Bd. 364; Veröffentlichungen der Kommission für Geschichte der Mathematik, Naturwissenschaften und Medizin, volumes 28–30), Vienna 1980. {{isbn|3-7001-0339-5}}
* [[Samuel Eliot Morison]], ''Christopher Columbus, Mariner'', Boston, Little, Brown and Company, 1955.
* Ralf Kern: Wissenschaftliche Instrumente in ihrer Zeit/Band 1. Vom Astrolab zum mathematischen Besteck. Köln, 2010. {{isbn|978-3-86560-865-9}}
* [[Michela Malpangotto]], ''Regiomontano e il rinnovamento del sapere matematico e astronomico nel Quattrocento'', Cacucci, 2008 (with the critical edition of ''Oratio in praelectione Alfragani'', ''Editorial Programm'', Preface to the ''Dialogus inter Viennensem et Cracoviensem adversus Gerardi Cremonensis in planetarum theoricas deliramenta'')
* [[Ernst Zinner]]: ''Leben und Wirken des Joh. Müller von Königsberg, genannt Regiomontanus''; Translated into English by [[Ezra A. Brown]] as ''Regiomontanus: His Life and Work''

==External links==
{{Commons category|Johannes Regiomontanus}}
*{{BBKL|r/regiomontanus}}
*{{de-ADB|22|564|581|Johannes Müller Regiomontanus|Günther}}
*Adam Mosley, [http://www.hps.cam.ac.uk/starry/regiomontanus.html Regiomontanus Biography], web site at the Department of History and Philosophy of Science of the University of Cambridge (1999).
*[http://www.univie.ac.at/hwastro Electronic facsimile-editions of the rare book collection at the Vienna Institute of Astronomy]
*[http://www.hps.cam.ac.uk/starry/regiocalen.html Regiomontanus and Calendar Reform]
*[https://web.archive.org/web/20071019135140/http://www.polybiblio.com/marta/165.html Polybiblio: Regiomontanus, Johannes/Santbech, Daniel, ed. ''De triangulis planis et sphaericis libri''. Basel Henrich Petri & Petrus Perna 1561]
*[https://web.archive.org/web/20080507135500/http://www.jnul.huji.ac.il/dl/books/html/bk1262728.htm Joannes Regiomontanus: ''Calendarium''], Venedig 1485, Digitalisat
*[http://naa.net/ain/personen/regiomontanus.asp Beitrag bei „Astronomie in Nürnberg“] "{{Webarchive|url=https://web.archive.org/web/20080724043215/http://www.naa.net/ain/personen/regiomontanus.asp |date=24 July 2008 }}"
*[https://web.archive.org/web/20120209054806/http://num-scd-ulp.u-strasbg.fr:8080/view/authors/Regiomontanus,_Johannes.html Digitalisierte Werke von Regiomontanus]—SICD der Universitäten von Strasbourg
*{{Cite AmCyc|wstitle=Regiomontanus |short=x}}
*{{Cite EB9|wstitle=Regiomontanus |volume=20 |short=x}}
*{{MathGenealogy|id=126109}}
*[http://hos.ou.edu/galleries//15thCentury/Regiomontanus/ Online Galleries, History of Science Collections, University of Oklahoma Libraries] ({{Webarchive|url=https://web.archive.org/web/20211008004233/https://hos.ou.edu/galleries//15thCentury/Regiomontanus/ |date=8 October 2021 }}). High resolution images of works by and/or portraits of Regiomontanus in JPEG and TIFF formats.
*[https://hdl.loc.gov/loc.rbc/rosenwald.0025.1 Regiomontanus, Joannes, 1436–1476. Calendarium.] Venice, Bernhard Maler Pictor, Erhard Ratdolt, Peter Löslein, 1476. [32] leaves. woodcuts: border, diagrs. (1 movable, 1 with brass pointer) 29.6&nbsp;cm. (4to). From the [https://www.loc.gov/rr/rarebook/coll/211.html Lessing J. Rosenwald Collection] in the Rare Book and Special Collections Division at the [[Library of Congress]]
*[https://hdl.loc.gov/loc.rbc/General.36265 Doctissimi viri et mathematicarum disciplinarum eximii professoris Ioannis de Regio Monte De triangvlis omnímodis libri qvinqve] From the Rare Book and Special Collection Division at the [[Library of Congress]]
*[https://regio.dartmouth.edu/ Regiomontanus' ''Defensio Theonis'' digital edition (scans and transcription)]

{{Authority control}}

{{DEFAULTSORT:Regiomontanus}}
[[Category:1436 births]]
[[Category:1476 deaths]]
[[Category:15th-century apocalypticists]]
[[Category:15th-century astrologers]]
[[Category:15th-century German astronomers]]
[[Category:15th-century German mathematicians]]
[[Category:15th-century German writers]]
[[Category:15th-century writers in Latin]]
[[Category:Catholic clergy scientists]]
[[Category:Christian astrologers]]
[[Category:German astrological writers]]
[[Category:German male writers]]
[[Category:German Roman Catholics]]
[[Category:Medieval German astrologers]]
[[Category:People from Königsberg, Bavaria]]
[[Category:German scientific instrument makers]]
[[Category:Unsolved deaths]]
[[Category:Astronomical instrument makers]]