Viri Mathematici

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Beginning of the Viri Mathematici (upper half of the first page)

Viri Mathematici quos inclytum Viennense high school ordine celebres habuit ( German  mathematician who had the glorious Vienna University as famous representatives of their class ) is the title of George Tannstetters Latin representation of of 1384 in up to pressure 1514 Vienna active astronomer and mathematician .

This historical review, an early approach to a history of science , appeared as the introductory chapter of an edition of astronomical tables. It contains valuable biographical information on a total of 32 astronomers and mathematicians. Tannstetter presents extensive lists of her works for five of them, namely Johannes von Gmunden , Georg von Peuerbach , Johannes Regiomontanus , Johannes Stabius and Andreas Stiborius  - the books in his library are also mentioned of the latter. A total of around 170 book titles on predominantly mathematical and astronomical topics appear in these Viri Mathematici .

History presentation as part of an edition

An edition of astronomical tables

The review of the Viri Mathematici did not appear as a separate book, but as a chapter within a larger book, namely an edition of astronomical tables. The astronomer Georg Tannstetter, who teaches at the University of Vienna , had astronomical tables printed by Georg Peuerbach and Johannes Regiomontanus in 1514. These two astronomers were the most important representatives of their subject in Vienna up to then. The title page says:

“Tabulae Eclypsium Magistri Georgii Peurbachii. Tabula Primi mobilis Joannis de Monte regio. ”

"Tables of the eclipses by Magister Georg Peurbach. Table of the "first movable" (i.e. the celestial sphere) by Johannes von Königsberg. "

Then it is continued in smaller font:

“Indices praeterea monumentorum, quae clarissimi viri Studii Viennensi alumni in Astronomia et aliis Mathematicis disciplinis scripta reliquerunt.”

"Also lists the works that famous men trained at the University of Vienna left behind on astronomy and other mathematical disciplines."

Editor of this edition

The book was printed by Joannes Winterburger in Vienna on April 13, 1514. The format corresponds to our A4 (= 2 °), and the book consists of 132 sheets. The fact that Tannstetter was the editor is not stated on the title page, but it arises from several clues: The imprint on the last page says: "Drafted and checked by Tannstetter", the dedication letters have Tannstetter as the author, and a letter contained in the book as well Tannstetter named two poems as the editor of these tables. In the specialist literature, Andreas Stiborius is sometimes mistakenly named as co-editor alongside Tannstetter or even as sole editor.

Catalog-like history presentation

The title page of the edition already refers to this history, which is similar to a catalog, and emphasizes the bibliographical aspect. This presentation of history under the heading Viri Mathematici precedes the astronomical tables by Regiomontanus and Peuerbach (on p. Aa3 v to aa6 v ). In it, Tannstetter presented comprehensive catalog raisonnés of these two astronomers - and also of all other astronomers and mathematicians who had worked in Vienna up to that point and of whom Tannstetter had knowledge. In each case he added a few messages about her life; it is therefore a combination of bibliography and biography. The old tradition visible in works De viris illustribus (“About famous men”) is still having an effect here , for example in the book Catalogus illustrium virorum Germaniae (“Catalog of famous men in Germany”) by Johannes Trithemius (printed in 1495, so about two Decades earlier). However, Tannstetter's account of the Viri Mathematici is not extensive - it only contains about 3000 words.

Meaning of this early account of history

Sky observer, French knitting around 1500

Tannstetter's review is an early approach to the history of science. Ernst Zinner's book on the history of astronomy also includes a chapter on astronomy historiography , starting with the Chinese and Arabs. Then Zinner describes the history of astronomy among the "Teutons" and begins with this work by Tannstetter. Tannstetter's retrospective is also considered in the history of mathematics.

Historians speak of "the well-known Viennese school of mathematicians and astronomers", which reached its climax with Regiomontanus and "has contributed significantly to the renewal of the mathematical sciences". The main source for this school is Tannstetter's review. The University of Vienna had achieved international renown in mathematics and astronomy in the middle of the 15th century, while the universities in Paris , Krakow and Oxford had previously been leading in the natural sciences .

List of the 21 scholars named in the headings

The names of the 21 astronomers and mathematicians presented in the 19 subheadings of the text Viri Mathematici are in the original wording as follows (including the indications of origin, insofar as these are mentioned in the headings themselves):

  • Henricus de Hassia Germanus
  • Joannes de Gmunden
  • Georgius ex Peurbach
  • Joannes de Monteregio Francus
  • Christiannus Molitoris ex Clagenfurt
  • Joannes Muntz ex Plabeirn
  • Joannes Stabius Austriacus
  • Andreas Stiborius Boius
  • Stephanus Rosinus
  • Joannes Angelus
  • Georgius Ratzenperger
  • Dominus Paul
  • Joannes Epperies
  • Erasmus Ericius
  • Jacobus Lateranus
  • Joannes Fabricius ex Reyffling
  • Joannes Tzerte
  • Andreas Kuenhofer
  • Georgius Strolin
  • Joannes Kolpeck ex Ratisbona
  • Et ego (German: "And I", namely Georgius Tannstetter Collimitius)

Presentation of the content: mathematicians and astronomers in Vienna until 1514

When describing some of the 21 Viennese astronomers and mathematicians listed in the headings, Tannstetter also mentions - a total of 11 - names of advanced students and other colleagues. So there are a total of 32 astronomers and mathematicians working in Vienna, which is a very large number for the period from 1384 (when Heinrich von Langenstein came to Vienna) to 1514. Tannstetter's directory could be expanded, for example by Conrad Celtis , the had included the natural sciences in his university teaching.

Several of the scholars mentioned received the academic degree of a Magister, called " Magister artium " or "Magister artium et philosophiae". This degree was acquired at the basic, the " Artes Liberales " teaching artist faculty . This “facultas artium” conveyed several qualifications (“artes”), namely three linguistic (in the trivium , such as Latin grammar) and four mathematical-scientific (in the quadrivium , such as arithmetic and astronomy).

Heinrich von Langenstein as the founder of astronomy in Vienna

Illumination around 1400: The Duke's College with a tower

Heinrich von Langenstein in Hessen , "a German" (Germanus) , "came from the venerable University of Paris and soon after the founding of our Vienna University (studium Viennensis) introduced theology and astronomy"; "He taught theology with Heinrich von Oyta "; Both were called at the same time from Paris to Vienna to build up the theological faculty founded in 1384 - only now the university, founded in 1365, was considered complete.

His thorough knowledge "of astronomy is evident in the first book of his Commentaries on Genesis ". "He wrote about planetary theories" and others; "His works are kept in the library of the Herzogskolleg". This ducal college formed the center of the artist faculty; the tower was used to observe the sky. Langenstein "died on February 11, 1397."

Johannes von Gmunden and his specialization in astronomy

Johannes von Gmunden “received his master's degree in artes liberales in Vienna in 1406 , then taught astronomy and also devoted himself to sacred theology. He received ... a position as a canon at the church of St. Stephan in Vienna and became vice-chancellor at the university ... He died in 1442. "Of the 24 canons (canons), 8 should be reserved for masters of the university, namely for those who had previously belonged to the Herzogskolleg. In his classes at the university, Johannes was able to specialize in astronomy, while the other masters took turns taking turns in the subjects.

Tannstetter then lists eight writings by Johannes that were "available in the library of the artist faculty" at the time. It is about astronomical writings like

Tabulae de planetarum motibus: et luminarium eclypsibus verissimas ad meridianum Viennensem (tables of planetary movements as well as solar and lunar eclipses, related to the Vienna meridian) ,

and about math, like

Tractatus sinuum (Treatise on Sinus Functions ) .

Johannes had important students, u. a.

  • “Georg Pruner from Ruspach, who eagerly observed the stars and left behind wonderful instruments and some books”, including copies of works by his teacher.

Tannstetter then mentions three other Masters who were working in Vienna at the time, without giving any further details and without claiming a closer connection to Johannes von Gmunden:

  • Georg, the provost of Neuburg (Latin: "dominus Georgius praepositus Neoburgensis") - probably Georg Müstinger of Klosterneuburg († 1442).
  • "Joannes Schinttel", in the more recent specialist literature also Johann (es) Schintel or Schindel, from Bohemia, taught in Vienna 1407–1409, was city doctor in Nuremberg around 1430, later went back to Prague, where he died after 1440.
  • "Joannes Feldner".

Georg von Peuerbach and Johannes von Monteregio

Georg von Peuerbach (or Peurbach) "was born on the border between Bavaria and Austria, was at the Vienna University Master", "taught at the public school (collegium civium) of St. Stephen , and was a teacher of John de Monte Regio." Peuerbach was therefore one of those masters at the university who also belonged to the teaching staff of this middle school.

Tannstetter calls him the "new founder (novus instaurator) of astronomy in Vienna" and then emphasizes his relationship with several high-ranking people, by whom he was very much appreciated; he names Kaiser Friedrich III. , Archduke Sigismund and Cardinal Bessarion . In Tannstetter's statement that Peuerbach “died not yet 40 years old on April 8, 1462”, historians consider the year of death to be an error - 1461 is correct.

Tannstetter lists around 20 works by Peuerbach, based on a list already compiled by Stiborius. It mainly mentions astronomical works, such as his well-known planetary theories (Theoricae planetarum) , but also mathematical works, such as an introduction to arithmetic (Introductorium in Arithmeticam) .

Johannes de Monteregio, "a Franconian" (Francus) , today mostly called Regiomontanus or Regiomontan, came, as his name suggests, from Königsberg . "Magister and an ornament of Germany" (Germaniae decus) . "He was so distinguished in astronomy and every mathematical art that he was seen as the new founder of art (princeps artis) ."

Tannstetter then emphasizes Regiomontan's contacts to the Hungarian King Matthias Corvinus and the local bishops. "Then he moved to Nuremberg ... Finally, to improve our calendar, Pope Sixtus IV called him to the city (Rome), where he died - either of the plague or ... because he was poisoned by the sons of Georgios Trapezuntios ."

Tannstetter lists around 30 works by other authors that Regiomontan had printed - as the editor, so to speak - including Ptolemy's basic astrological work , called Quadripartitum ( the four-part or four books , i.e. the content is divided into four volumes). The following is a list of about 30 books by Regiomontan himself, u. a. his ephemeris , also called almanac .

Regiomontan quickly made use of the new possibilities that had arisen from the printing press developed by his contemporary Johannes Gutenberg . The focus of his " publishing program " was on astronomy and mathematics, but also included astrology, physics and music.

Tannstetter finally judges that Georg von Peuerbach and Regiomontanus through their work restored astronomy "in full splendor" (magnifice restituerunt) . As successors, not necessarily personal students, Tannstetter names five "outstanding astronomers":

  • Mag. Heinrich Seldner,
  • Mag. Eberhard Schleisinger,
  • Mag. Johannes von Pforzheim (Phortzen) , "philosopher, astronomer and theologian"
  • Mag. Johannes von Kupfersberg
  • Johannes Dorn (Doren) , “who made their (i.e. Peuerbach and Regiomontans) instruments with great skill. He later entered the Dominican order ... died in 1509. "

The lifetime of these students already protruded into Tannstetter's own lifetime. The scholars described by Tannstetter are distributed unevenly over the period 1384–1514; the majority of them worked during the last decades of this period.

The astrologers Christian Molitoris and Johannes Muntz

Christian Molitoris “from Klagenfurt”, “Magister of our university”, gained great recognition through his (astrological) prognoses , “died 1495 of the plague”. Tannstetter names one of his students

  • Mag. Johannes Fabri from Weyssenburg , who then went to his relatives
  • Mag. Christoph Fabri taught astronomy.

Johannes Muntz "from Blaubeuren " (Plabeirn) in Württemberg, "Magister of the Arts, Bachelor of Holy Theology and Canon of the Viennese Episcopal Church (ecclesiae cathedralis Viennensis canonicus) ". "He wrote forecasts based on star constellations ... died in Vienna on December 3, 1503."

Johannes Stabius and Andreas Stiborius, Tannstetters teachers

Johannes Stabius , "an Austrian". Such an origin was rather rare among the Viennese university professors; these came mainly from southern Germany. According to Tannstetter, Stabius was a “seer (vates) and poet, imperial geographer (cosmographus) and historian” as well as a gifted inventor: “Emperor Maximilian I enjoys his extraordinary inventions every day ” - so something that is present is being described here; "As he admired the genius of Stabius and Stiborius ..., he donated lectures in astronomy and mathematics in Vienna". This is an indication of two newly established chairs for these subjects, namely at the University of Vienna. Whether these should belong to the artist faculty or to the Poet College of Conrad Celtis is controversial among historians.

Tannstetter as - as he describes himself here - "his pupil" lists more than ten astrological and geographical works by Stabius, including tools for calculating a horoscope or for creating maps.

Andreas Stiborius , "a Bavarian" (Boius) , "philosopher, mathematician and theologian, canon of the Vienna Episcopal Church, was a public professor of mathematics for many years". He belonged to the ducal college.

With regard to his works, Tannstetter is also thinking of those that Stiborius will write in the future - “God willing” -. This reservation is perhaps an expression of Tannstetter's premonition, because Stiborius died the following year, around 50 years old. Tannstetter then lists more than ten works by - as he calls him here - "Magister Andreas Stiborius Boius, my teacher", u. a. a Libellus de variis quadrantibus ( booklet on different quadrants ).

Only here, with Stiborius, does Tannstetter also list the books in his possession - printed or handwritten - and thus give an impression of the library of a humanistic naturalist at the time. In this index vetustissimorum exemplarium ( list of very old editions ) he lists the 60 or so books thematically: more than 20 books on astronomy, about ten each on perspective , geometry and arithmetic , and about five each on metaphysics and magic .

Stephanus Rosinus and Johannes Angelus

After specifying the origin of Rosinus (also called Rösslein or Rösel in German texts ) "from Augsburg", Tannstetter names his three academic degrees: Magister, Bachelor of Holy Scripture and Licentiate of Decrees . He was “canon of the Viennese bishop's church, taught astronomy for a long time”, “calculated a table of the declinations of the fixed stars and prognostics .” He belonged to the ducal college. He later taught astronomy in Wittenberg .

Johannes Angelus (or Engel ), "a Bavarian from Aichen , doctor of the arts (artes) and medicine ". This imprecise term "artium et medicinae doctor" was common at the time. But the degree in the “arts” was the degree of a master’s degree, while the degree of doctor was only obtained afterwards at one of the three higher faculties, theology, law or medicine. Correctly speaking, Angelus was therefore a Master of Arts and a Doctor of Medicine.

In his works, Tannstetter mentions a little book (libellus) for calendar correction and the calculation of ephemeris and prognoses . "He died in Vienna on September 29, 1512." The indication of this date shows that Tannstetter brought his historical report close to the year of publication 1514, that is, that there is no period of years between the completion of his manuscript and the printing.

Tannstetter and his colleagues

Tannstetter only gives brief information about some astronomers: Georg Ratzenperger, “Magister”, “a Bavarian from Reb”, “outstanding in astronomy”. And the Dominican "Dominus Paulus in Melk Monastery , astronomer and geographer".

Johannes Epperies (from Eperies in Slovakia) and Erasmus Ericius (from Horitz in South Bohemia) “taught mathematics”.

Tannstetter also describes the following two astronomers as philosophers: Jakob Ziegler (Lateranus) was a “philosopher, astronomer and poet”. Johannes Fabricius from Reifling (in Styria), “philosopher and astronomer”, was the colleague of Tannstetter who wrote: “This Fabriciius was my brother (confrater) and due to his services to the other astronomical lecture (alterius lectionis astronomicae) more neat Professor (professor ordinarius) of his subject. ”This statement reminds us that Emperor Maximilian had donated two professorships. The past tense used here by Tannstetter indicates that Fabricius was no longer the holder of his professorship in 1514 (while Tannstetter still was).

Johannes Tzerte, "Councilor of the City of Vienna", deals with mathematics with regard to the "calculation of plans and buildings", ie especially with architecture .

Bookplate from Tannstetter, the author of Viri Mathematici

Andreas Kuenhofer came "from Nuremberg, made so great progress under our teachers Stabius and Stiborius in Vienna in geography and all mathematics that he is highly respected in Italy and especially in the city (Rome) itself." So he was probably a fellow student of Tannstetter, already in Ingolstadt, where he had been studying since 1496. He described the manufacture of sundials.

The following two astronomers were - like Tannstetter - also physicians. Georg Strolin, "Patrician from Ulm". Tannstetter mentions his help in the preparation of the 1514 edition of the astronomical tables and emphasizes a "close bond", a kind of friendly relationship. Strolin studied in Vienna from 1511, later in Bologna and finally in Tübingen, where he became a doctor of medicine. Johannes Kolpeck "from Regensburg, student of medicine and astronomy, manufactures astronomical instruments ...".

Tannstetter's name is not mentioned within the Viri Mathematici , but the last section, headed with an anonymous “Also I” (Et ego) , refers to Tannstetter. The fact that Stiborius - who is sometimes erroneously referred to as the editor of this book in the specialist literature - cannot be meant is due to the fact that Stiborius has already been dealt with, where the author (this "I") describes himself as a student of Stiborius.

Tannstetter writes here: "... according to the will of Emperor Maximilian I (teneo) hold the chair for the mathematical subjects (cathedram in mathematic (is) disciplinis) ", so he is the chair holder at that time (1514).

Editions

Latin edition

Edition with translation (Latin / German)

  • Franz Graf-Stuhlhofer: Humanism between Court and University (see below literature), 1996, pp. 156–171 (translated with the significant assistance of Hubert Reitterer).

Literature about astronomers in Vienna

  • Joseph Aschbach : History of the University of Vienna , Vol. 1 and 2, Vienna 1865 and 1877.
  • Franz Graf-Stuhlhofer : Humanism between court and university. Georg Tannstetter (Collimitius) and his scientific environment in Vienna in the early 16th century . Vienna 1996 (revision of the dissertation).
  • Helmuth Grössing : Humanistic natural science. On the history of the Viennese mathematical schools of the 15th and 16th centuries (=  Saecula Spiritalia ; 8). Baden-Baden 1983 (printed version of the habilitation thesis).
  • Günther Hamann (Ed.): Regiomontanus Studies (=  Austrian Academy of Sciences , Philosophical-Historical Class, Meeting Reports ; 364). Vienna 1980 (printed version of the 25 lectures at a symposium in Vienna in 1976).
  • Abraham Gotthelf Kästner : History of Mathematics from the Restoration of Science to the End of the Eighteenth Century , Vol. 2. Johann Georg Rosenbusch, Göttingen 1797 (description of the table edition p. 526-535, especially the “Viri Mathematici” on p 529-532). Digitized
  • Paul Uiblein: The Vienna University, its Masters and students at the time of Regiomontan . In: Hamann: Regiomontanus Studies , 1980, pp. 393-432.

Web links

Individual evidence

  1. ↑ These arguments in Graf-Stuhlhofer: Humanismus , 1996, pp. 91–94.
  2. ↑ Examples are given by Graf-Stuhlhofer: Humanismus , 1996, p. 92, note 336, namely publications by Dieter Wuttke , Helmuth Grössing and Christoph Schöner ( Mathematics and Astronomy at the University of Ingolstadt in the 15th and 16th centuries . Berlin 1994).
  3. ^ So Graf-Stuhlhofer: Humanismus , 1996, p. 156.
  4. ↑ Ernst Zinner: The history of astronomy from the first beginnings to the present . Berlin 1931, p. 613 f.
  5. ↑ For example with Christa Binder : Austria . In: Joseph W. Dauben , Christoph J. Scriba (Ed.): Writing the History of Mathematics. Its Historical Development . Basel 2002, pp. 213-219, there pp. 215 f.
  6. ^ As formulated by Fritz Krafft (Ed.): Große Naturwissenschaftler. Biographical Lexicon . Düsseldorf 1986, p. 290.
  7. ^ Moritz Cantor : Lectures on the History of Mathematics , Vol. 2. Leipzig 1892, p. 361, 2nd edition 1900, p. 393.
  8. ^ So Menso Folkerts : Science at the Universities of the Middle Ages . In: Erwin Neuenschwander : Science, Society and Political Power . Basel u. a. 1993, pp. 17-38, there 34 f.
  9. ↑ Two headings each contain two names: one heading contains the two names Epperies and Ericius , another contains the names Lateranus and Fabricius .
  10. ↑ Grössing: Humanistische Naturwissenschaft , 1983, p. 147, Celtis even calls the "head of the second Viennese mathematical school".
  11. ^ Kurt Mühlberger : The University of Vienna. Brief glimpses of a long story. Vienna 1996, p. 14.
  12. ^ Aschbach: History of the University of Vienna , Vol. 1, 1865, p. 40.
  13. ↑ According to Grössing: Humanistische Naturwissenschaft , 1983, pp. 254 f, 71, 78, 98, Pruner matriculated in Vienna in 1410, became a priest and probably died in 1469.
  14. ↑ This equation represents Menso Folkerts: The mathematical studies of Regiomontans in his time in Vienna. In: Hamann: Regiomontanus Studies , 1980, pp. 175–209, there 192. Grössing: Humanistische Naturwissenschaft , 1983, pp. 76–79, 264, gives life data on "Georg I. Muestinger", provost of Klosterneuburg since 1418.
  15. ^ After Grössing: Humanistische Naturwissenschaft , 1983, p. 70 (lit. about him, p. 251). See also Hamann: Regiomontanus-Studien , 1980, especially p. 192, 280.
  16. ^ According to Aschbach: History of the University of Vienna , Vol. 1, 1865, p. 40, these were - since the re-establishment by Duke Albrecht III. - 4 Masters each.
  17. ↑ See e.g. B. Grössing: Humanistische Naturwissenschaft , 1983, p. 83.
  18. ↑ A “Magister Johann Rout (also Veyhinger) from Pforzheim” is mentioned by Uiblein: Wiener Universität , 1980, p. 399. He gave lectures on astronomical topics from 1454 to 1475 in Vienna.
  19. ↑ Uiblein mentions a “Johann Reybel from Kupferberg”: Wiener Universität , 1980, p. 399 f. He read in Vienna on astronomical topics from 1456-77 and is said to have died in 1509 as pastor of Kremnitz (Upper Hungary). Grössing: Humanistische Naturwissenschaft , 1983, p. 145: “Johann Reibel from Kupferberg in Franconia”, came to Vienna in 1460 as a master’s degree.
  20. ↑ Grössing: Humanistische Naturwissenschaft , 1983, pp. 145, 278: "Hans Dorn".
  21. ↑ On his prediction for the year 1495 see Grössing: Humanistische Naturwissenschaft , 1983, p. 146; also p. 278 about the possible identity with Johannes Münz, personal physician of Matthias Corvinus.
  22. ↑ In the 15th century Bavaria, Swabia and Franconia (which belonged to the "Rhenish university nation") usually made up more than half of the students in Vienna. See Uiblein: Wiener Universität , 1980, p. 397.
  23. ↑ Hermann Göhler: The Viennese collegiate, later cathedral chapter on St. Stephen in its personal composition in the first two centuries of its existence. 1365-1665. Dissertation Vienna 1932, p. 456.
  24. ↑ Instead of very old , literally oldest could also be translated; therefore it is conceivable that Tannstetter only gives a selection here, that is, names the particularly old / valuable books. So Grössing: Humanistische Naturwissenschaft , 1983, p. 174, in his characterization of this inventory of Stiborius' books, "as they probably belonged to the repertory of a humanistic scientist of the early 16th century".
  25. ↑ According to Grössing: Humanistische Naturwissenschaft , 1983, pp. 147, 190 f he obtained his master's degree in 1496 in Cracow and in 1503 took up a permanent professorship in Vienna.
  26. ↑ Hermann Göhler: The Viennese collegiate, later cathedral chapter on St. Stephen in its personal composition in the first two centuries of its existence. 1365-1665. Dissertation Vienna 1932, p. 475.
  27. ^ Józef Babicz: The exact sciences at the University of Cracow and the influence of Regiomontans on their development . In: Hamann: Regiomontanus-Studien , 1980, pp. 301-314, there 309.
  28. ↑ Grössing: Humanistische Naturwissenschaft , 1983, p. 190.
  29. ↑ Grössing: Humanistische Naturwissenschaft , 1983, pp. 190, 295.
This version was added to the list of articles worth reading on June 28, 2013 .