6 - The curriculum of astronomical studies in the Statute of 1405.

The oldest Statutes of the Università degli Artisti that have come down to us date from 1405. They contain a detailed programme for the teaching of Astronomy which reads as follows:

"During the first year of the astronomy course the Algorismi de minutis et integris (Algorithms) are read, after which the first book of Euclid’s geometry is read, with the commentary of Campanus. When this latter is read the Tabulae Alphonsinae with the Canons is read. After which the Theorica Planetarum (Planetary Theory) is read. During the second year the Tractatus de Sphera is read for first, after which the Canons for the use of the geometric tables are read. Once these are read the treatise on the astrolabe of Messehallah is read. During the third year Alcabitius is read for first, after which the Centiloquium of Ptolemy with the commentary by Haly is read. After which the third book of Geometry is read, after which the Tractatus Quadrantis (Treatise on the Quadrant) is read. During the fourth year all the Quadripartitus is read for first, after which the book De urina non visa (On urines unseen) is read. After which the third edition of the Almagest is read." (28)

The first thing to note about this programme, clearly addressed to the students of Medicine, is the coordination between the mathematics, astronomy-mathematics and astrology parts.

The mathematics part begins with the Algorismi de minutis et integris of Sacrobosco, a treatise on calculation techniques which must have been in use for a long time judging from the fact that there is a late XIIIth-century commentary on it written for the students of Bologna (29). There then follows Euclid’s geometry, with the comment written in the XIIIth century by Johannes Campanus of Novara (XII cen.), which was read in the first, second and third years. This completes the mathematics part.

The teaching of Astronomy began in the first year with an explanation of the use of the Tabulae Alphonsinae codified in the Canons drawn up by John of Saxony in 1370 (30). There then followed a Theorica Planetarum, possibly the one ascribed to Campanus of Novara (31).

Sacrobosco’s Sphera was read in the second year along with the Canons for the use of the astronomical tables drawn up by Jean de Lignières (Johannes de Lineriis) in Paris in 1321 and known in Bologna from 1344 (32). Finally the treatise on the astrolabe of Messehallah (Mâshâ’ allâh ibn Atari) (770-815) was read, translated from the Arabic in 1153 by Johannes de Luna.

In the third year a Tractatus Quadrantis was read, most probably the treatise written at Montpellier in 1274 by Robertus Anglicus and commonly known as Tractatus Quadrantis Vetus. This treatise was published by P. Tannery (33) and can be found with its original title of Tractatus Quadrantis Modernus in the BUB codex 132. Since the treatise took the name "vetus" with the spread of the work Quadranti Novi written in 1288 by Profatius Judaus, this title proves the treatise of Robertus Anglicus was known in Bologna almost from the beginning.

In the fourth year the third section of the Almagest was read. This dealt with the motion of the Sun along the ecliptic, the duration of the seasons and seasonal variation in the length of the days and nights.

The other lectures were all of an astrological nature. The Alcabitius was the Liber introductorius ad magisterium iudiciorum astrarum - also known as Introductorium - of the Arab astronomer ‘Abd al-‘Azîz ibn ‘Othmân al-Qabîsî (Alcabitius) (mid-Xth century), translated in the XIIth century by Johannes de Luna Hispalensis and which is normally accompanied, in the codices and printed versions, by a XIVth-century commentary by John of Saxony.

Two other astrological treatises were the well known treatises of Ptolemy entitled Centiloquium (full name Fructus sive centiloquium) and Quadripartitum (which is the famous Tetrabiblos or rather Previsioni astrologiche indirizzate a Siro), for both of which a classical commentary exists by the Arab astronomer ‘Alî ibn Ridwân (c.998-1061).

The astrological part came to a close with the treatise De Urina non Visa written in Marseilles in 1219 by Guilielmus Anglicus (34). This treatise, condemned to being burnt as a work of black magic by the Sorbonne in 1494, explained how the horoscope could be used, strange though it may seem to us today, to enable the physician to assess the quality of a patient’s urine; since the patient was summoned from afar, the physician had no way of examining the urine directly!

Since in more than one codex of the XIVth-century Corpus Astronomicum, still extant in Bologna’s libraries (35), we find several of the astronomical and astrological treatises mentioned above, it is probably fair to say that the programme referred to by the Statutes of 1405 was essentially the one already adopted from the mid-XIVth century.

There can be no doubt however that the main points of the programme are based on the teachings of Cecco d’Ascoli. Between Bartholomeus de Parma’s commentary on Sacrobosco and this latter’s there are not only profound differences in attitude towards astrology that have already been mentioned and continuous cross-references to Arabic astrological texts, but also signs of the courses being organized over a period of years, as witness the declared intention of continuing the course, "Si Deo placuerit" (God willing), by commenting Ptolemy’s Centiloquium (36). God was most probably not pleased since poor Cecco d’Ascoli was soon after burnt at the stake in Florence and no trace remains of the commentary promised on the Centiloquium.

By the time the most recent of the above mentioned treatises, the Canons of Jean de Lignières, had reached Bologna in 1344, Tommaso da Pizzano had just begun to read astronomy. Tommaso continued with the subject until 1378 when he left Italy for Paris, summoned there by Charles V. From what we know of him and his medical and astrological interests (37) the 1405 programme could well have been his.

  1. - C. Malagola: 1888, Statuti delle Università e dei Collegi dello Studio Bolognese, p.276, Bologna.
    "Durante il primo anno del corso di astronomia si leggano gli Algorismi de minutis et integris, letti i quali si legga il primo libro della Geometria di Euclide, con il commento del Campano. Letto quest'ultimo si leggano le Tabulae Alphonsinae con i Canoni. Letti i quali si legga la Theorica Planetarum. Durante il secondo anno si legga per prima cosa il Tractatus de sphera, letto il quale si legga il secondo libro della Geometria di Euclide, letto il quale si leggano i Canoni per l'uso delle tavole geometriche. Letti questi, si legga il trattato dell'astrolabio di Messachele. Durante il terzo anno si legga per prima cosa Alcabitius, letto il quale si legga il Centiloquium di Tolomeo con il commento di Haly. Letto il quale si legga il terzo libro della Geometria, letto il quale si legga il Tractatus quadrantis. Durante il quarto anno si legga per prima cosa tutto il Quadripartito, letto il quale si legga il libro De urina non visa. Letto il quale si legga la terza edizione dell'Almagesto."
  2. - F. S. Pedersen: 1983, Petri Philomenae de Dacia et Petri de S. Audomaro: Opera quadrivialia, Pars I, Copenhagen.
  3. - E. Poulle (a cura di): 1984, Les Tables Alphonsines avec les Canons de Jean de Saxe, Paris.
  4. - F. S. Jr. Benjamin and G.J. Toomer (a cura di): 1971, Campanus of Novara and Medieval Planetary Theory: Theorica planetarum. Milwaukee and London.
  5. - L. Thorndike: 1959, Isis, 50, 44.
  6. - Questo trattato è stato pubblicato da P. Tannery (1922, Mem. Scient., V, Paris) e lo si trova con il suo titolo originario di Tractatus Quadrantis Modernus nel codice BUB 132 (L. Thorndike 1959, Isis, 50, p.44). Poiché il trattato prese il nome di "vetus" col diffondersi dell'opera Quadranti Novi scritta nel 1288 da Profazio Giudaico, questo titolo attesta la conoscenza di prima epoca del trattato di Roberto Anglico a Bologna.
  7. - Il trattato fu condannato ad essere bruciato come opera di magia nera dalla Sorbona nel 1494 (L. Thorndike: A history of magic and experimental science op. cit., III, p.214).
  8. - Biblioteca Comunale Archiginnasio Bologna, MS A. 51, sec. XIV.
    Johannis de Sacro Bosco, Tractatus de algorismo.
    Johannis de Sacro Bosco, Tractatus de sphera.
    (Roberti Linclonensis), Tractatus de Computo.
    Ignoto, Cautelae in divinationum computatione.
    Ignoto, Tabulae de computo.
    Johannis de Sacro Bosco, Tractatus de arte quadrantis.
    Pseudo Severino Boezio, Tractatus de doctrina scholarium.
    Biblioteca Comunale Archiginnasio Bologna, MS A. 142, sec. XV.
    Severino Boezio, De arithmetica libri IV.
    Hermanni Contracti, De mensura astrolabii liber.
    Hermanni Contracti, De utilitatibus astrolabii libri II.
    Ignoto, Tabula de positione stellarum.
    Biblioteca Comunale Archiginnasio Bologna, MS 198, sec XIV-XV.
    Ignoto, Tabulae motuum planetarum (date estreme 1335-1393)
    Ignoto, Altitudo Solis ... in Mediolano.
    Tabulae astronomicae, vulgo dictae Alphonsinae, cum canonibus Magistri Johannis de Lineriis.
    Ignoto, Tabulae XII signorum Zodiaci pro horoscopis inferendis .... .
    Biblioteca Universitaria Bologna, MS 154 (132), sec. XIV.
    Alcabitii, Introductorium... interpretatus a Iohanne hispalensi.
    (Gherardo da Cremona), Theorica Planetarum.
    Magister Petro de Sancto Hodomaro, Theoricam motuum latitudinis Planetarum secundum regulas Albategni.
    (Roberti Linclonensis), Liber de prognosticatione sive prescientia dispositionis temporum.
    (Messahala), Liber totus astronomicus.
    Magistri Campani Novariensi, Theorica planetarum.
    Ignoto, Liber cursus Lunae.
    Alfargani, Liber differentiae.
    (Messahala), Tractatus Astrolabii.
    (Iohannes Lineriis), Tabula positionis stellarum.
    (Robertus Anglicus), Tractatus quadrantis moderni
    s. Ignoto, Tabulae Solis.
    (Johannis de Sacro Bosco), Algorismus.
    Johannis de Sacro Bosco, Tractatus de sphera.
    Fratris Fuci de Ferraria, Calendarium (1311-1386, per Milano)
    Ignoto, Theorica Planetarum.
  9. - L. Thorndike: 1949, The sphere of Sacrobosco and his commentators, Chicago, p. 371.
  10. - L. Thorndike: A history of magic and experimental science op. cit., III, cap.XXXVI.