Regiomontanus: Tabulae directionum et profectionum

The German Johannes Müller (1436–1476), known as Regiomontanus after his native Königsberg in Franconia, was the most important mathematician and astronomer of the age.[1] In 1464, he met the Polish Marcin Bylica (1435–1493/1494), later court astrologer to Matthias Corvinus (King of Hungary 1458–1490, King of the Bohemia 1469–1490), in Rome. In 1465, they met Janus Pannonius (1434–1472), who invited the two astronomers to teach at the newly founded University of Bratislava on behalf of his uncle, Johannes de Zredna (1408?–1472), Archbishop of Esztergom.[2] Regiomontanus and Bylica arrived in Hungary sometime between 1465 and 1467 (the exact date is not known).[3] Together, in 1467, they completed Regiomontanus’ Tabulae directionum et profectionum, which is included in the present corvina,[4] on which the astronomer had been working since 1464.[5] Regiomontanus dedicated the finished work to his patron, the Archbishop[6] (the present copy is probably not a presentation manuscript for the Archbishop, at least there is no indication to that effect[7]). The work first appeared in print in 1490,[8] no modern edition or translation exists. Whether the two astronomers actually taught at the University of Bratislava is not known for sure, and no sources have survived to confirm this. Bylica very quickly became the de facto court astrologer of Matthias. According to the small number of surviving sources, Regiomontanus preferred to work on his own scientific ‘projects’. Regiomontanus left the country in the spring of 1471 and settled in Nuremberg, but the manuscript did not reach Nuremberg by this route.

Directions and profections (from the Latin proficiscor, ‘to set off’) are both methods of prognostication in astrology. The directions involve projecting the elements of the horoscope you want to move from the ecliptic to the celestial equator and back again, which requires some serious mathematical calculations (spherical trigonometry). These calculations were made easier by Regiomontanus’ tables. The Tabulae directionum contained, among other things, the first modern tangent tables.[9] The work of Regiomontanus, and in particular the Tabulae directionum, is clear evidence that the development of mathematics and mathematical astronomy has been stimulated by its use for astrological purposes.

The work is also significant in the history of astrology because in it Regiomontanus described and criticized the Campanus house system used by the Albanian-born Gjon Gazulli of Ragusa (c. 1400–1465, Ivan Gazulič, Giovanni Gazulo in Italian) and proposed instead the method that he called ‘rational’, which now bears his name. Thanks to the astronomical authority of Regiomontanus, his house system has widely replaced the the previously used Alcabitius house system and enjoyed universal popularity until the eighteenth century.[10]

The hand-written entry on fol. I* r., ‘maior mora 288 dies | media mora 273 dies | minor mora 258 dies’ are the ancient values of the length of pregnancy used in astrology to rectify the birth chart (the method known as trutina Hermetis, ‘Hermes’ scales’).[11]

The coat of arms of Matthias Corvinus in the volume is not original, but a sixteenth-century addition, which was added at the request of the owner of the manuscript, Wilhelm IV Haller (1478–1534), a patrician of Nuremberg who was interested in astronomy. Haller’s father, Wilhelm III Haller (c. 1444–1504), went on several diplomatic missions to Hungary and entered the service of Matthias around 1480. It is also possible that Wilhelm IV Haller owned another corvina (ÖNB Cod. 2271). On the basis of all this, research suggests that the later addition of the coat of arms is not an attempt at forgery, but a record of information that was still in the possession of contemporaries, i.e. the volume really comes from the library of Matthias Corvinus.[12] Whether the volume was originally copied for Johannes de Zredna or Matthias is not clear. According to Edina Zsupán, the manuscript is the work of the same scribe as the Trapezuntius-corvina of Budapest (OSZK Cod. lat. 281.).[13] (Márton Veszprémy)

The source of the data sheet below is the detailed description of the manuscript: CERMANN, Regina, “Beschreibung einer problematischen Corvine: Cod. Guelf. 69.9 Aug. 2°”, in ZSUPÁN, Edina, Hrsg., unter Mitarbeit von HEITZMANN, Christian, Corvina Augusta. Die Handschriften des Königs Matthias Corvinus in der Herzog August Bibliothek Wolfenbüttel. Ex Bibliotheca Corviniana. Supplementum Corvinianum 3. (Budapest: Bibliotheca Nationalis Hungariae, 2004.), 122–151.


[1] The most detailed biography of Regiomontanus to date is ZINNER, Ernst, Regiomontanus: his Life and Work. Studies in the History and Philiosophy of Mathematics 1., transl. by BROWN, E. (Amsterdam: Elsevier, 1990). Published originally: ZINNER, Ernst, Leben und Wirken des Johannes Müller von Königsberg, genannt Regiomontanus (München: C. H. Beck, 1938).

[2] We know that Regiomontanus came to Hungary for this very reason from his dedication of Tabulae directionum to Johannes de Zredna.

[3] ZINNER, Regiomontanus 89–90.

[4] CSÁSZÁR Mihály, Az Academia Istropolitana, Mátyás király pozsonyi egyeteme. (Pozsony: Eder Ny., 1914.) 18., ZINNER: Regiomontanus 95.

[5] FOLKERTS, Menso, „Regiomontanus als Mathematiker”, in Centaurus 21. (1977) 3–4., 214–245., 235.

[6] The 24 surviving manuscripts of the work are enumerated by CERMANN, Regina, “Beschreibung einer problematischen Corvine: Cod. Guelf. 69.9 Aug. 2°”, in ZSUPÁN, Edina, Hrsg., unter Mitarbeit von HEITZMANN, Christian, Corvina Augusta. Die Handschriften des Königs Matthias Corvinus in der Herzog August Bibliothek Wolfenbüttel. Ex Bibliotheca Corviniana. Supplementum Corvinianum 3. (Budapest: Bibliotheca Nationalis Hungariae, 2004.), 122–151., 126–129.

[7] The widespread opinion that the manuscript contains emendations and marginal notes by Johannes de Zredna is not supported by a thorough examination. CERMANN, „Beschreiburng…” 133.

[8] CERMANN, „Beschreiburng…” 130. Subsequent editions are listed by CERMANN, „Beschreiburng…” 130.

[9] ZINNER, Regiomontanus 93.

[10] For more details see: VESZPRÉMY Márton, „Az asztrológiai házrendszerek történetének magyarországi vonatkozásai”, in KINCSES Katalin Mária szerk., Hadi és más nevezetes történetek. Tanulmányok Veszprémy László tiszteletére ([Budapest]: HM Hadtörténeti Intézet és Múzeum, 2018.) 615–622.

[11] For more details on this question, see: SELA, Shlomo, „Calculating Birth. Abraham Ibn Ezra’s Role in the Creation and Diffusion of the Trutina Hermetis”, in DOPFEL, Constanza Gislon, FOSCATI, Alessandra, BURNETT, Charles, ed., Pregnancy and Childbirth in the Premodern World. European and Middle Eastern Cultures, from Late Antiquity to the Renaissance. (Turnhout: Brepols, cop. 2019.) 79–106., 84.

[12] CERMANN, „Beschreiburng…” 142.

[13] CERMANN, „Beschreiburng…” 132.


Shelfmark: Cod. Guelf. 69.9. Aug 2°
Country: Germany
City: Wolfenbüttel
Keeper location: Herzog August Bibliothek
Digitized corvina: at the keeper location
Author: Johannes Regiomontanus (1436–1476), Marcin Bylica (1435–1493/1494)
Content: Tabulae directionum et profectionum
Writing medium: parchment
Number of sheets: I + 90 + I*
Sheet size: 290 × 216 mm
Place of writing: Hungary, probably the circle of Johannes de Zredna (1408?–1472), Archbishop of Esztergom
Date of writing: c. 1470
Scriptor: scribe of OSZK Cod. Lat. 281.
Illuminator: Jakob Elsner (?–1517)
Place of illumination: Nuremberg
Date of illumination: c. 1507/1510
Crest: coat-of-arms of Matthias Corvinus (King of Hungary 1458–1490, King of Bohemia 1469–1490) as King of Hungary and Bohemia (sixteenth-century addition)
Possessor, provenience: Matthias Corvinus; it was in the possession of Wilhelm IV Haller (1478–1534), patrician of Nuremberg, who let the coat-of-arms of Matthias Corvinus be painted in the volume; it was acquired in or around 1652/1653 by Augustus II, Duke of Brunswick (r. 1635–1666)
Binding: original leather binding (Nuremberg, c. 1510)
Language of corvina: Latin
Condition: the binding is restored (1997)