Viator 45 No. 1 (2014) 99–120. 10.1484/J.VIATOR.1.103784

ARABIC SINGING GIRLS, THE POPE, AND THE ASTROLABE: ARABIC SCIENCE IN TENTH-CENTURY LATIN EUROPE

Marco Zuccato

Abstract: This article presents a new hypothesis related to the very earliest filtration of Arabic science to the Latin World during the tenth century. Contrary to the beliefs of current scholarship, it argues that the very earliest Latin astronomical texts derived from Arabic sources cannot be considered to be related to the written tradition of the mathematical school of Maslama al-Majr nor can they be regarded as translations from Arabic. It contends that these texts derive from a non-written Arabic tradition of practical astronomy that existed in al-Andalus before the time of Maslama. It offers new evidence supporting the thesis that such a tradition existed, and argues that traces of it can also be detected in the teaching of Gerbert of Aurillac, as described by Richer of Reims. It concludes with an alternative explanation of the very earliest filtration of Arabic science to the Latin World and a new reconstruction of the stages of composition for these earliest Latin astronomical texts. Keywords: Arabic singing-slave-girls, women in Al-Andalus, Gerbert of Aurillac, early medieval intellec-tual history, medieval Arabic intellectual history, Arabic practical astronomy, Arabic astronomy into Latin, teaching at the cathedral school of Reims during the tenth century, the infiltration of the astrolabe into tenth-century Latin Europe, qiyan.

1. INTRODUCTION Scholars believe that around the end of the tenth century, a number of Arabic astro-nomical writings and also one or, perhaps, a few astrolabes reached Catalonia, in the northeastern part of the Iberian Peninsula, from al-Andalus. These writings are repre-sented by the following:

1. An Arabic version (or parts of an Arabic version) of Ptolemy’s Planispherium that was circulating in the entourage of the school of Maslama al-Majr .1 2. An Arabic version of the treatise on the use of the astrolabe (Kit b al- `amal bi’l-as url b t) by Mu ammad ibn M s al-Khw rizm .2 3. A writing derived from the entourage of the school of Maslama al-Majr , including in-structions on how to project stars on the rete of an astrolabe.3 4. A writing from the school of Maslama al-Majr , that included a table of twenty-seven stars (star table type III4), which was used to project stars on the rete of an astrolabe.5

Division of History, Centro de Investigación y Dociencia Económicas, A.C., (Center for Research and Teaching in Economics; CIDE), Carretera México Toluca 3655, Col. Lomas de Santa Fe, 01210, Mexico City, Mexico. The research for this article was made possible by CNRS, France, during my stay in Paris as a Research Associate of the unit UMR 7219 of the Université Paris 7 Diderot. I am most grateful to the mem-bers of UMR 7219 and, in particular, Pascal Crozet, Gad Freudenthal, and Barbara Obrist for their kind advice and support. I also thank John Marenbon for his comments and feedback on an earlier version of this article and Miquel Forcada for his help and suggestions for finding the Arabic sources. Finally, I thank the two anonymous readers for Viator.

1 Paul Kunitzsch, “Fragments of Ptolemy’s Planisphaerium in an Early Latin Translation,” Centaurus 36 (1993) 97–101.

2 Paul Kunitzsch, “Al-Khw rizm as a source for the Sententiae astrolabii,” From Deferent to Equant. A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E. S. Ken-nedy (New York 1987) 227–236.

3 María Mercè Viladrich, “Dos capitulos de un libro perdido de Ibn al-Sam ,” Al-Qantara 7 (1986) 5–11.

4 Paul Kunitzsch, Typen von Sternverzeichnissen in astronomischen Handschriften des zehnten bis vierzehnten Jahrhunderts (Wiesbaden 1966) 23–30.

5 Julio Samsó, “Maslama al-Majr t and the Star Table in the Treatise De mensura astrolabii,” Sic Itur ad Astra. Studien zur Geschichte der Mathematik und Naturwissenschaften. Festschrift für den Arabisten Paul Kunitzsch zum 70. Geburtstag, ed. M. Folkerts and R. Lorch (Wiesbaden 2000) 506–522.

100 MARCO ZUCCATO

5. Other Arabic written texts which have not yet been identified.6

It is known that the earliest extant Latin European Astrolabe, or Destombes astrolabe (#3042), circulated in Catalonia during the second half of the tenth century.7 Addition-ally, a number of astrological writings also deriving from Arabic sources filtered to Catalonia and reached Limoges, in southern France, before the end of the tenth cen-tury.8 According to recent scholarship, such texts spurred a vivid interest in astronomy among the Catalan scholars. Thus, thanks to the above-mentioned Arabic writings, the astrolabe and, perhaps, the help of Mozarabs who aided in the understanding of the Arabic texts, the earliest Latin translations were produced. These translations show different stages of elaboration and can be classified as follows:

Stage 1. (from al-Andalus to the Latin World [Catalonia] soon after 978 AD9): At least one astrolabe (#3042) and some Arabic texts related to the astrolabe reached the Latin World soon after 978 AD. They were, most likely, translated into Latin. If so, none of those translations survives.

Stage 2. (Catalonia, between ca. 980–990 AD [?]) Crude Latin versions of Arabic material: on the construction of the astrolabe, De mensura astrolapsus (h’’); on the use of the astrolabe, Sententie astrolabii (J’); on the celestial/solid sphere, De orologio secundum alchoram (J’a); on the quadrans vetustissimus: Incipiunt regule de quarta parte astrolabii.

Stage 3. (France, Fleury, and Micy, ca. 995 AD [according to A. Borst10] or the first quarter of the eleventh century): Literary remodeling of De mensura astrolabii (h’) and De Utilitatibus astrolabii (J).

Stage 4. (Lotharingia, the second quarter of the eleventh century and, in any case, before 1054) Final stage, texts assembled by Hermann the Lame (Hermannus Con-tractus): on the construction of the astrolabe, De mensura astrolabii (h); on the use of the astrolabe, De Utilitatibus astrolabii (J) (from stage 3); on the construction of a vertical sundial and other issues, De horologio viatorum (K).

6 Paul Kunitzsch, “Traces of a Tenth-Century Spanish-Arabic Astrolabe,” Zeitschrift für Geschichte der Arabisch–Islamischen Wissenschaften 12 (1998) 113–120, esp. 114; and idem, “La Table des climats dans le corpus des plus anciens texts Latins sur l’Astrolabe,” Science antique, Science medieval (Autour d’Avranches 235). Actes du Colloque International (Mont-Saint-Michel, 4–7 septembre 1998), ed. L. Callebat et O. Desbordes (Hildesheim-Zürich-New York 2000) 391–399, esp. 392. These ideas have also passed into the most recent scholarship; see David Juste, Les Alchandreana primitifs. Recherches sur les plus anciens traités astrologiques latins d’origine arabe (Xe siècle) (Leiden-Boston 2007) esp. 5.

7 On the Destombes astrolabe, see Marcel Destombes, “Un astrolabe carolingien et l’origine de nos chiffres arabes,” Archives internationales d’Histoire des Sciences 15 (1962) 3–45; and the large collection of studies in Physis 32 (1995) 191–450. See also Julio Samsó, “El astrolabio ‘Carolingio’ de Marcel Des-tombes y la introducción del astrolabio en la Catalunya medieval,” Memorias de la Real Academia de Ciencias y Artes de Barcelona, Tercera época 60.10 (Barcelona 2003) 345–356.

8 These writings represent the astrological corpus that David Juste named Alchandreana; see the comprehensive study on this corpus by Juste, Les Alchandreana Primitifs (n. 6 above).

9 For an explanation of the terminus post quem 978 AD, see below. 10 Arno Borst, Astrolab und Klosterreform an der Jahrtausendwende. Sitzungsberichte der Heidelberger

Akademie der Wissenschaften (Heidelberg 1989) at 69: “Exakt beweisen kann ich es nicht, aber alle Indizien sprechen dafür, daß das erste lateinische Lehrbuch zum Astrolabi im Kreis um Konstantin von Fleury entstand, gegen 995, kurz vor Berns Heimkehr und längere Zeit vor Abbos Tod.”

ARABIC SINGING GIRLS, THE POPE, AND THE ASTROLABE 101

2. ALL ROADS LEAD TO ROME, BUT WHICH ROME? Recent scholarship has questioned the likelihood of this four-stage reconstruction. In particular, the rigidity that would be entailed in the process of creating a written transmission of Arabic texts by translating them into Latin is not reflected in what we actually see when we inspect the texts of this astronomical corpus.11 As a matter of fact, these texts do not convey the impression of being derived from Arabic writings that have undergone a series of organized stages of translation into Latin. These texts possess a very high degree of fluidity and instead appear to mirror a non-codified Arabic astronomical practice that Latin scholars attempted to crystallize and save into writings.12 However, if that was the case, the existence of this non-codified astronomi-cal practice in al-Andalus remains a mystery.

In a number of medieval manuscripts, one of the texts from the above-mentioned astronomical corpus, De Utilitatibus astrolabii, is often ascribed to a certain Gerbertus (also spelled Gilebertus or Girbertus).13 This author is none other than Gerbert of Aurillac, a well-known Latin scholar who was active during the second half of the tenth century, a schoolmaster at the prestigious cathedral school of Reims, the arch-bishop of Ravenna and, later, Pope Sylvester II. Gerbert also acquired a peculiar rep-utation among his contemporaries for excelling in the arts of the quadrivium and for having absorbed elements of a forbidden knowledge derived from the Arabs of Spain.14 Recently, however, both Gerbert’s authorship of De Utilitatibus astrolabii and the likelihood that he received any element of Arabic astronomy and mathematics have been dismissed by the vast majority of scholars, although the issue is far from being conclusively resolved.15 Yet, the strongest and most universally accepted argu-ment against the attribution of the De Utilitatibus Astrolabii to Gerbert of Aurillac

11 The most important contribution towards a critical rethinking of the various stages for the conversion of Arabic astronomical material into Latin during the 10th c. comes from Arianna Borrelli, Aspects of the Astrolabe.“Architectonica ratio” in tenth- and eleventh-century Europe (Stuttgart 2008).

12 Ibid. 99–112. 13 See the list of these manuscripts in Nicolaus Bubnov, Gerberti postea Silvestri II papae opera mathe-

matica (972–1003) (Berlin 1899) 112–114. 14 This reputation derives from the writings of the so-called Dark Legend of Gerbert. On the Dark Leg-

end, see Elly R. Truitt, “Celestial Divination and Arabic Science in Twelfth-Century England: The History of Gerbert of Aurillac’s Talking Head,” Journal of the History of Ideas 73.2 (2012) 201–222. See also Marco Zuccato, “Gerbert of Aurillac and a Tenth-Century Jewish Channel for the Transmission of Arabic Science to the West,” Speculum 80.3 (2005) 742–763, esp. 747. There is also a comprehensive study on the Dark Legend of Gerbert by Massimo Oldoni, Gerberto e il Suo Fantasma. Tecniche della fantasia e della letteratura nel Medioevo (Naples 2008).

15 See, in particular, the recent work edited by Marie-Hélène Jullien, Clavis Des Auteurs Latins du Moyen Age. Territoire Français 735–987, Tomus III (Turnhout 2010) at 138, where De Utilitatibus Astro-labii is classified as an opera spuria. See also Charles Burnett, “King Ptolemy and Alchandreus the Philoso-pher: the Earliest texts on the Astrolabe and Arabic Astrology at Fleury, Micy and Chartres,” Annals of Science 55 (1998) 329–368, esp. 330–331; Paul Kunitzsch, “Les relations scientifiques entre l’Occident et le monde arabe a l’époque de Gerbert,” Gerbert l’Européen: Actes du colloque d’Aurillac, 4–7 juin 1996, ed. Nicole Charbonnel and Jean-Eric Iung (Aurillac 1997) 193–203; Emmanuel Poulle, “L’Astronomie de Gerbert,” Gerberto. Scienza, storia e mito. Atti del Gerberti Symposium (Bobbio 25–27 luglio 1983) (Bob-bio 1985) 597–617; Julio Samsó, “Maslama al-Majr and the star table in the treatise De mensura astro-labii,” Sic itur ad astra. Studien zur Geschichte der Mathematik und Naturwissenschaften. Festschrift für den Arabisten Paul Kunitzsch zum 70. Geburtstag, ed. M. Folkerts and R. Lorch (Wiesbaden 2000) 500–522; and Julio Samsó “Els inicis de la introducció de la ciència àrab a Europa a través de Catalunya,” La Ciència en la Història dels Països Catalans, vol. I dels Àrabs al Renaixement (Valencia 2004) 115–159.

102 MARCO ZUCCATO comes from Paul Kunitzsch. This scholar, in an article that appeared in 1996, has argued that the year 978 should be considered the terminus post quem for the intro-duction of the study of the astrolabe into the Latin World. Indeed, according to a refer-ence included in MS Paris, BnF, ar. 4821, fol. 81v, in this year Maslama al-Majr 16 (a well-known Andalusian scholar and founder of a mathematical and astronomical school who was active in al-Andalus during the tenth century) compiled a star table that was directly connected to his studies on the astrolabe. Kunitzsch claimed that the work of the school of Maslama inaugurated the studies on the astrolabe in al-Andalus. In fact, the activity of the school of Maslama inspired a vivid interest in this astro-nomical instrument among Latin scholars after 978. However, it is known that Gerbert resided in Spain from 967 until 970. Thus, knowledge of the astrolabe could not have reached Gerbert of Aurillac during these years.17 This argument has had a profound influence on modern scholarship.18

Furthermore, scholars have universally stressed the prominence and the crucial im-portance of the school of Maslama al-Majr in relation to the earliest introduction of advanced mathematical, astronomical, and astrological studies in al-Andalus, which also included specialized studies on the use and construction of the astrolabe. This emphasis generated an overwhelming scholarly interest on the birth and activity of the school of Maslama al-Majr . In particular, Maslama’s mathematical and astronomical achievements became a matter of great importance because they elucidate the links that this school and, more broadly, the entire Andalusian intellectual life of this period were able to establish with the rival and more acculturated eastern part of Islam, which was under the control of the ‘Abb s ds, in terms of the books and scientific writings that could be imported to al-Andalus from Baghdad.19

In this article, I have no intention of delving into the specifics of the protracted, technical debate over the exact attribution of the above-mentioned Latin corpus on the astrolabe. However, the question of whether Gerbert of Aurillac did participate in the compilation of at least one of the writings of this corpus and whether he transmitted

16 Below, I discuss the work of the school of Maslama al-Majr . 17 Kunitzsch, “Les Relations Scientifiques” (n. 15 above) at 196: “Dans ce contexte, il traita aussi des

problems de l’astrolabe; une table d’étoiles établie de sa main date de 978. On peut penser que c’est bien le travail de Maslama et de son école sur l’astrolabe (dont le rayonnement se fit sentir jusqu’en Catalogne chrétienne) qui suscita l’intérêt des clercs latins de cette région pour cet instrument.” In addition, ibid. 199: “Il est certes connu que Gerbert séjourna entre 967 à 970 à Ripoll, en Catalogne, pour ses études sur le quadrivium. Cependant, il est vraisemblable qu’à cette époque les études d’astrolabes arabes n’y avaient pas encore commencé (la tabla d’étoiles de Maslama date de 978!). Gerbert n’est donc sans doute pas entré en contact avec la science arabe à Ripoll.”

18 See the works of two of the most authoritative scholars in this field. Charles Burnett states, “For this reason, among others, the attribution of De utilitatibus astrolabii to Gerbert d’Aurillac is unlikely. When he was still very young, Gerbert spent 967–970 in the cathedral school at Vich as a student studying the quadr-ivium; this was before Maslama had drawn up his star table.” Burnett, “King Ptolemy and Alchandreus the Philosopher” (n. 15 above) at 331–332. Julio Samsó claims, “Aquest és el cas, per exemple, del De mensura astrolabii que, com veurem, conté una taula d’estels que sembla que deriva, en darrer terme, d’una altra taula de l’astrònom andalusí Maslama al-Majriti, que és posterior a l’any 978: és correcta, per tant, l’opinió de Kunitzsch quan afirma que Gerbert no hauria pogut accedir a aquest text entre els anys 967 i 970.” Samsó, La Ciència en la Història dels Països Catalans, (n. 15 above) at 117. See also Juste, Les Alchandre-ana primitifs (n. 6 above) 5–6.

19 See Julio Samsó, Las ciencias de los Antiguos en al-Andalus (Madrid 1992; repr. Almería 2011) esp. 80–110.

ARABIC SINGING GIRLS, THE POPE, AND THE ASTROLABE 103 this advanced astronomical knowledge to the Latin West, has engendered a considera-ble amount of debate and uncertainty.20

In the first part of this article, I seek to dissipate at least part of this uncertainty by discussing the following issues. First, I offer a cursory description of the school of Maslama al-Majr . Second, I examine whether it is true that in this period the Anda-lusian intellectual and scientific landscape was immobilized in a straightjacket that was determined by the scientific activity of Maslama al-Majr and his school. Third, by examining the astronomical teaching of Gerbert of Aurillac at the cathedral school of Reims, I investigate whether it is possible to detect any element that conveys the idea of a break or a significant discontinuity with the traditional astronomical teaching normally cultivated in the Latin world.

3. MASLAMA AL-MAJR AND HIS SCHOOL

During the tenth century, the development of a school of astronomy and mathematics in al-Andalus was in large part due to Maslama al-Majr (d. ca. 1007/1008).21 cid al-Andalus (1029–1070) in his Kit b abaq t al-umam (Book of the Categories of the Nations) tells us that Maslama was “the chief mathematician in al-Andalus during his time and better than all the astronomers who came before him.”22 Indeed, the famous q of Toledo goes on to tell us that Maslama “left behind an excellent group of stu-dents, better than any group formed by any other scholar of al-Andalus. Among his best known students, we name ibn al-Sam , ibn al- aff r, al-Zahraw , al-Kirm n , and ibn Khald n.”23 The activity of this school appears to have continued for at least three generations of scholars. Nonetheless, of all of the writings belonging to these scholars, only some of the works ascribed to Maslama, ibn al-Sam and ibn al- aff r are pre-served.

20 See Guy Beaujouan, “Les Apocryphes mathématiques de Gerbert,” Gerberto. Scienza, storia e mito. Atti del Gerberti Symposium (Bobbio 25–27 luglio 1983) (Bobbio 1985) 645–658; Werner Bergmann, Innovationen im Quadrivium des 10. und 11. Jahrhunderts. Studien zur Einführung von Astrolab und Aba-kus im Lateinischen Mittelalter (Stuttgart 1985); Borst, Astrolab und Klosterreform an der Jahrtausend-wende (n. 10 above); Max Büdinger, Über Gerberts wissenschaftliche und politische Stellung (Marburg 1851); Burnett, “King Ptolemy and Alchandreus the Philosopher” (n. 15 above); David Juste, Les Alchan-dreana primitifs (n. 6 above); Paul Kunitzsch, “Les relations scientifiques” (n. 15 above); Uta Lindgren, Gerbert von Aurillac und das Quadrivium (Wiesbaden 1976); Josè Millàs Vallicrosa, Assaig d’història de les idees físiques i matemàtiques a la Catalunya Medieval. «Estudis Universitaris Catalans», Sèrie Monogràfica I (Barcelona 1931); Antoni Pladevall i Font, “Entorn de l’estada de Gerbert a Catalunya (967–970). L’existència de biblioteques privades perdudes,” Actes del Congrés Internacional Gerbert d’Orlhac i el seu temps: Catalunya i Europa a la fi del 1r milleni. Vic-Ripoll, 10–13 de novembre de 1999 (Vic 1999) 651–663; Emmanuel Poulle, “Note sur l’autorité des traités de l’astrolabe,” Autour de Gerbert d’Aurillac. Le pape de l’an Mil (Paris 1996) 343–345; and idem, “L’Astronomie de Gerbert,” (n. 15 above) 597–617; Gemma Puigvert I Planagumà, Astronomia i Astrologia al Monestir de Ripoll (Barcelona 2000); Julio Samsó, “Cultura científica àrab i cultura científica llatina a la Catalunya altmedieval: el monestir de Ripoll i el naixement de la ciència catalana,” Symposium internacional sobre els origins de Catalunya (segles VIII–XI) (Barcelona 1991) 253–269; Andrè Van de Vyver, “Les premières traductions latines (Xe–XIe s.) de traités arabes sur l’astrolabe,” Premier Congrès International de Géographie Historique, II: Mémoires (Bruxelles 1931) 266–290; and Zuccato, “Gerbert of Aurillac” (n. 14 above).

21 cid al-Andalusi, Science in the Medieval World.“Book of the Categories of the Nations,” trans. and ed. Sema ‘an I. Salem and Alok Kumar (Austin 1996) 64.

22 Ibid. 64. 23 Ibid. 64.

104 MARCO ZUCCATO

The q of Toledo tells us that “he [Maslama] wrote a good book, titled Thim r ‘Ilm al-‘Adad [Fruits of the Science of Numbers], which has come to mean to us the ‘mathematics of business transactions,’” (al-muc mal t).24 The same type of mathematical work is also ascribed to two other members of Maslama’s school, ibn al-Sam and al-Zahraw .25 Furthermore, with regards to the mathematics cultivated in this school, cid al-Andalus adds that ibn al-Sam wrote two mathematical books: the first is al-Madkha ila al-Handasah [Introduction to Geometry], in which he ex-plained the work of Euclid, and the second is a book titled abicat al-cAdad [The Na-ture of Numbers].26 Ibn al-Sam also wrote “a great treatise on geometry in which he exhausted the study of straight, curved, and broken lines.”27 It has also been suggested that some of these mathematical treatises compiled by Maslama and his disciples likely included sections devoted to the study of algebra.28

However, the school of Maslama excelled, in particular, in the field of astronomy. The Andalusian scholar, aside from making several astronomical observations, studied and adapted the astronomical tables of al-Khw rizm (the famous Z j al-Sindhind); he studied the Z j authored by al-Batt n ; he devoted great effort to the study of Pto-lemy’s Almagest; and, most importantly, he commented upon the Kit b Tas bas al-kura, known in Latin as the Planispherium by Ptolemy.29 This work is of crucial im-portance in particular for astrolabe studies because it offers a mathematical explana-tion of the theory of stereographic projections. This theory allows for the representa-tion of the celestial sphere on a plane, in such a way that the circles on the sphere are correctly represented by the circles on the plane.

Works such as the Z j al-Sindhind by al-Khw rizm , the Alamgest and the Plani-spherium by Ptolemy, or the Z j by al-Batt n , were obviously imported from the east-ern part of Islam, which indicates that Maslama was the first known scholar to start a systematic scholarly work of study toward the assimilation of the important scientific texts coming from the most culturally evolved part of Islam, i.e., the ‘Abb s d Cali-phate. Thus, it is clear that in this period, an important cultural channel had been opened between the Umayyad Caliphate of Cordoba and the ‘Abb s d Caliphate of Baghdad. However, as we shall see below, it would be erroneous to consider it the only cultural channel that connected al-Andalus to the rest of Islam.

4. AL-ANDALUS AND FATIMID NORTH AFRICA: A NEW SCENARIO.

There is no question that the school of Maslama al-Majr played an important role in the intellectual life of al-Andalus during the tenth century. It is also true that Maslama had a number of important mathematical and astronomical books imported from Baghdad to Cordoba. However, it would be facile to observe the Andalusian intellec-

24 Ibid. 64. 25 Ibid. 64–65. 26 Ibid. 64. 27 Ibid. 64. 28 See Ahmed Djebbar, “Quelques aspects de l’Algèbre dans la tradition mathématique arabe de

l’Occident Musulman,” Actes du Premier Colloque International d’Alger sur l’Histoire des Mathématiques Arabes (Alger 1988) 101–123, esp. 102–106.

29 See Paul Kunitzsch and Richard Lorch, Maslama’s Notes on Ptolemy's Planisphaerium and Related Texts (Munich 1994).

ARABIC SINGING GIRLS, THE POPE, AND THE ASTROLABE 105 tual culture of this period solely under the monochromatic perspective determined by the scientific production of the school of Maslama al-Majr and its contacts with the ‘Abb sid east. In fact, recent studies have shown that, at least during the tenth century, the Fatimid world held a significant intellectual influence on primarily, but not only, al-Andalus via Qayrawan, one of the most important cultural centers of the Fatimid Caliphate in North Africa. The evidence is as follows:

First, Fatimid emissaries (da‘is or summoners) were sent to Cordoba, including Ab ‘Abd All h ibn al- ay am, an agent particularly learned in philosophy.30 It is very likely that several additional agents were dispatched to al-Andalus by the Fati-mids, and it is known that religious-political, but also cultural-philosophical propa-ganda were the core tasks of these agents.31

Second, Ibn Masarra (883–931) was the first mystic in al-Andalus to make exten-sive use of neoplatonic philosophy in his writings. He was the founder of a religious sect that was declared heretical and persecuted by the caliph of Cordoba. A recent work by Sarah Stroumsa and Sara Sviri has detected some important Ismaili-Fatimid influence in Ibn Masarra’s doctrine.32

Third, a well-known work on magic and astrology titled Gh yat al- ak m (trans-lated into Latin as Picatrix) and a work on alchemy titled Rutbat al- ak m were cir-culating in al-Andalus during the tenth century; these works had initially been at-tributed to Maslama al-Majr (though later regarded as eleventh-century works by pseudo-Maslama), but were in fact composed by the Andalusian b in 33 Maslama ibn Q sim al-Qur ub (d. 964), who was influenced both by Masarr s and Ismailis and who knew the Ras ’il Ikhw n al- af ’ (a collection of epistles on philosophical and scien-tific knowledge that acquired very great importance for Ismaili doctrine).34

Fourth, it has been shown that Ab Yusuf asd y ben Is q ben Shapr , head of the Andalusian Jewish community and right-hand man and adviser of two Caliphs in Cordoba (‘Abd al-Ra m n III and his son al- akam II), maintained and developed some important intellectual exchange with the Jewish community of Fatimid North Africa as well as with the Jewish scholars who were active at the Fatimid court in Qayrawan. This exchange also comprised the transmission of astronomical, astrologi-cal and perhaps medical works.35

Fifth, a recent study has hypothesized that Gerbert of Aurillac did assimilate some crucial elements of Arabic astronomy that originated in Qayrawan via al-Andalus.36

30 See Miquel Forcada, Ética e ideología de la Ciencia. El médico-filósofo en Al-Andalus (siglos X–XIII) (Almería 2011) 168.

31 See Heinz Halm, The Fatimids and their Traditions of Learning (London-New York 1997). On the role of the da‘is, see also Farhad Daftary, The Assassin Legends. Myths of the Isma‘ilis (London 1994) esp. 8–48.

32 Sarah Stroumsa and Sara Sviri, “The beginning of mystical philosophy in al-Andalus: Ibn Masarra and his Epistle on contemplation,” Jerusalem Studies in Arabic and Islam 36 (2009) 201–253.

33 B in in the general sense indicates someone who is interested in the esoteric interpretation of the sa-cred texts. B in sm is known to have been a fundamental component of Ismaili-Fatimid doctrine. See Halm, The Fatimids and their Traditions of Learning (n. 31 above) 4–55.

34 See the ground-breaking article by Maribel Fierro, “Maslama b. Q sim al-Qur ub (d. 353/964), Au-thor of the ‘Rutbat al- ak m’ and the ‘Gh yat al- ak m (Picatrix),’” Studia Islamica 84 (1996) 87–112.

35 See Forcada, Ética e ideología de la Ciencia (n. 30 above) 196–198. 36 Zuccato, “Gerbert of Aurillac” (n. 14 above) esp. 755–763. I discuss Zuccato’s thesis below.

106 MARCO ZUCCATO Indeed, a medieval source informs us that Gerbert made use of a number of celestial globes and instruments for the teaching of astronomy at the cathedral school of Reims. This unusual astronomical pedagogy fits very well with the astronomical pedagogy proposed by the Jewish scholar Dun sh ibn Tam m al-Qaraw as propaedeutic to the understanding and use of the astrolabe. There is evidence of a Jewish channel through which Dun sh’s work could have been transmitted from Qayrawan via al-Andalus to a circle of savants in Catalonia that was connected to Gerbert of Aurillac.37

This evidence attenuates the claim of the predominant intellectual and scientific role attributed to the school of Maslama al-Majr during this period as well as its role as a privileged channel of cultural transmission between Cordoba and Baghdad. In-deed, some important cultural and scientific influence reached al-Andalus from Fati-mid North Africa and Qayrawan. Among these influences one, in particular, that con-cerns a new astronomical pedagogy, appears even to have been received by Gerbert of Aurillac in the north eastern corner of the Iberian Peninsula outside of the Muslim territories.38 If these influences were present, the traces of this new pedagogy should be detected in Gerbert’s astronomical teaching. Indeed, there is evidence that corrobo-rates this claim.

5. GERBERT’S TEACHING AT REIMS Manuscript Bamberg Staatsbibliothek Hist. 5, E. 5.3 can rightly be considered one of the most interesting documents regarding the history of the tenth century.39 This manuscript includes the Historia Francorum, an original writing by Richer, cantor and canon of the cathedral of Reims and later monk at the prestigious abbey of St. Remi. It appears that this work was neither recopied nor read in the Middle Ages, and the Bamberg manuscript is the only known extant copy as well as Richer’s own copy of the Historia Francorum. Richer wrote this history between 995 and 998. The work was dedicated to Gerbert, archbishop of Reims, who was in all likelihood Richer’s master at the cathedral school of Reims.40 Gerbert, monk of Aurillac, held the title of archbishop of Reims sometime between 991 and 998 before becoming archbishop of Ravenna and then Pope Sylvester II in 999.41 When he was still a young monk, Ger-

37 Ibid. 763. 38 Ibid. 755–763. 39 For a detailed description of this manuscript, see Jason Glenn, Politics and History in the Tenth Cen-

tury. The Work and World of Richer of Reims (Cambridge 2004), in particular Appendices A, D, E, 269–273 and 285–300.

40 Ibid. 67. Glenn writes “Richer never identifies himself as Gerbert´s student.” Furthermore, ibid. 67–68, he claims: “to compose his account, Richer could surely have drawn on his own observations, on written texts found in the library of the cathedral, or on the oral testimony of Gerbert’s students or friends.” This claim contrasts with the information provided by a recent study authored by Courtney DeMayo, “The Stu-dents of Gerbert of Aurillac’s Cathedral School at Reims: An Intellectual Genealogy,” Medieval Prosopog-raphy 27 (2012) 97–117, esp. 112, where Richer of St. Remi is identified as a student of Gerbert. As I argue below, the astronomical teaching delivered by Gerbert at Reims follows an unorthodox methodology cen-tered on the use of practical astronomical instruments. There is no evidence that such an astronomical practice was ever recorded into writing. Thus, it is very unlikely that Richer could have found any written source illustrating this teaching. In fact, the very detailed description of Gerbert’s teaching, especially as related to astronomy, displays an intimate familiarity with the didactic methods employed by Gerbert, and this familiarity appears to suggest that Richer did attend at least some of Gerbert’s classes focusing on astronomy.

41 For an exhaustive biography of Gerbert see Pierre Riché, Gerbert d’Aurillac, le pape de l’an mil (Paris 1987).

ARABIC SINGING GIRLS, THE POPE, AND THE ASTROLABE 107 bert spent three years in Catalonia from 967 to 970 studying mathesis,42 and in 971 he was invited by Archbishop Adalbero to teach the quadrivium at the cathedral school of Reims.

In Book III (chapters 46 to 54) of the Historia Francorum, Richer offers an account of Gerbert’s teaching at the cathedral school of Reims.43 This teaching includes the disciplines of the trivium and the quadrivium, as one would expect when considering the teaching of the period. Gerbert’s teaching in the trivium is described in three chapters, 46 to 48.44 Chapter 46 is devoted to dialectica and chapters 47–48 focus on grammatica and rhetorica. Chapter 46, titled Quem ordinem librorum in docendo servaverit, explains the book order followed by Gerbert in the teaching of logic. Ger-bert introduced his students to Porphyry’s Isagoge, in the translation by Victorinus the rhetorician, and proceeded to explain these works following Boethius.45 Gerbert also explained the treatise of Aristotle on the categories. He then moved to Aristotle’s Peri Hermeneias and concluded with Boethius’s commentary on Cicero’s topics.46

Chapter 47 and the brief chapter 48 are dedicated to Gerbert’s teaching of grammar and rhetoric, Quid Provehendis Rhetoricis Providerit (how Gerbert prepared his stu-dents to receive instruction in rhetoric) and Cur Eis Sophistam Adhibuerit (why Ger-bert entrusted his students to a sophist).47 Gerbert commented on several works of Boethius before familiarizing his students with the modes of locution (locutionum modis) of the classical Latin poets. Here, authors such as Virgil, Statius, Terence, Juvenal, Persius, Horace, and Lucan are mentioned as auctoritates to be assimilated by the students before moving on to rhetoric. This latter subject was subsequently exer-cised and practiced in actual discussions and controversies with the aid of a sophist.

Chapters 49 to 54 describe Gerbert’s teaching in mathematics, astronomy, music, and geometry, the arts of the quadrivium. However, it is noteworthy that musica and matematica are very briefly condensed in one chapter (chapter 49, Qui Labor ei in Mathematicis [impensus] sit).48 Here, Richer tells us that Gerbert began to instruct his disciples in arithmetic, which is the first art of the quadrivium [Matheseos]. He then taught music in depth, which at that time was completely ignored among the Gauls.49

42 Hartmut Hoffmann, Richer Von Saint-Remi Historiae MGH SS, XXXVIII (Hannover 2000) at 192: “Dux itaque non abnuens, petenti liberaliter favit, ac fratrum consensu G(erbertum) assumptum duxit, atque Hattoni…episcopo instruendum commisit. Apud quem etiam in mathesi plurimum et efficaciter studuit.”

43 For the Latin text, see the critical edition by Hoffmann, Richer Von Saint-Remi Historiae (n. 42 above) esp. 191–200. See also Robert Latouche, Histoire de France, 2 vols. (Paris 1930 and 1937, re-ed. 1964 and 1967).

44 On Gerbert’s teaching in the trivium, see John Marenbon, Early Medieval Philosophy (480–1150) (London-New York 1988) esp. 80–89. See also Stephen Jaeger, “Philosophy, CA. 950–CA. 1050” Viator 40 (2009) 17–40.

45 “Boethius wrote two commentaries on the Isagoge, the first one using Victorinus’s translation, the second his own. Richer tells us that Gerbert expounded the Isagoge both in Victorinus’s translation and in Boethius’s. One might surmise that, in the first case, he used Boethius’s first commentary as his guide, and in the second case, Boethius’s second commentary.” I owe this comment to John Marenbon in a private communication.

46 Hoffman, Richer Von Saint-Remi Historiae (n. 42 above) 193–194. 47 Ibid. 194–195. 48 Ibid. 195. 49 The word mathesis is often translated as mathematics, sometimes in the sense of the sciences of the

quadrivium, unproblematically. But a more balanced view would be that the term retained some ambiguity.

108 MARCO ZUCCATO Richer provides a very short description of Gerbert’s musical teaching, reporting that he showed his students the disposition of the notes on the monochord and demon-strated the mathematical divisions of the monochord into tones and semi-tones.

Geometry is described in chapter 54 (Confectio Abaci).50 Here, Richer describes the abacus built by Gerbert to teach geometry to his students:

Gerbert employed the offices of a shield maker to make an abacus, i.e., a board fitted with divisions of measurement. He divided its length into 27 columns of which he marked nine with a numeral, these signifying all possible numbers. In the likeness of which [i.e., the col-umns marked with Arabic numerals] he made 1000 counters of horn, which, by being moved around through the 27 columns of the abacus, could show the multiplication or division of any number you like. This instrument enabled performing very quickly some mathematical operations such as division and multiplication.51

Richer’s account of Gerbert’s astronomical teaching covers four chapters (50 to 53). Here, Richer describes four demonstrational instruments used by Gerbert for the teaching of astronomy: one hemisphere showing only celestial circles, one armillary sphere, and two globes displaying stars and constellations. Although Richer’s account lacks specific technical details, it is nonetheless possible to offer a concise description of the instruments that he mentions.

The first sphere is described in chapter 50, titled Sperae Solidae Compositio.52 This instrument is an armillary sphere displaying the northern and southern constellations. The sphere features a horizon ring that is said to regulate (regere) the position of the

Indeed, there is evidence that mathesis can also be translated as astronomy/astrology. For instance, the term mathesis appears in the title of the most important astrological treatise of late antiquity, i.e., Mathesis Iulii Firmici Materni. In addition, some important evidence appears in a document from the monastery of Ripoll coeval with Richer’s Historia Francorum, i.e., the so-called Glossarium of Ripoll, a miscellaneous collec-tion of rare mottos, glosses and unusual or difficult words, which are listed with an explanation. On the Glossarium of Ripoll see Gemma Puigvert i Planagumà, Astronomia i Astrologia al Monestir de Ripoll. Edició i estudi dels manuscrits científics astronomicoastrològics del monestir de Santa Maria de Ripoll (Barcelona 2000); and Michel Zimmermann, “Un formulaire du Xème siècle conserve à Ripoll,” Faventia 4.2 (1982) 25–86. A tenth-century manuscript, Barcelona, Archivo de la Corona de Aragon (ACA), MS Ripoll 74, fols. 37r and 71r, includes part of the Glossarium. This part bears the title Liber glosarum et timologiarum and includes both the terms mathesis and matematica. Mathesis is explained as “stellarvm inspeccio; ars scilicet per qvam genitvrae hominvm colligvntvr. Vnde matematica ars dicitvr doctrinalis scientia.” Matematica is explained as “g.[rece] l.[atine] doctrinalis sciencia dicitvr.” This terminology could have reached Richer through the teachings of Gerbert, who, while in Catalonia, could have accessed the library of the monastery of Ripoll, which was the most important Catalan library at the time.

50 Hoffman, Richer Von Saint-Remi Historiae (n. 42 above) 198. 51 For an exhaustive description of this abacus see the Charles Burnett, “The Abacus at Echternach in ca.

1000 A.D.,” Sciamus 3 (2002) 91–109. See also Alain Schärlig, Un Portrait de Gerbert d´Aurillac. Inven-teur d´un abaque, utilisateur précoce des chiffres arabes, et pape de l’an mil (Lausanne 2012).

52 Hoffman, Richer Von Saint-Remi Historiae (n. 42 above) 195–196: “[50] Sperae solidae compositio – Ratio vero astronomiae quanto sudore collecta sit dicere inutile non est, ut et tanti viri sagacitas advertatur, et artis efficacia lector commodissime capiatur. Quae cum pene intellectibilis sit, tamen non sine admira-tione quibusdam instrumentis ad cognitionem adduxit. Inprimis enim mundi speram ex solido ac rotundo ligno argumentatus, minoris similitudine, maiorem expressit. Quam cum duobus polis obliquaret, signa septe(n)trionalia polo erectiori dedit, australia vero deiectiori adhibuit. Cuius positionem eo circulo rexit, qui a Graecis orizon, a Latinis limitans sive determinans appellatur, eo quod in eo signa quae videntur ab his quae non videntur distinguat ac limitet. Qua in orizonte sic collocata, ut et ortum et occasum signorum utiliter ac probabiliter demonstraret, rerum naturas dispositis insinuavit, instituitque in signorum compre-hensione. Nam tempore nocturno ardentibus stellis operam dabat, agebatque ut eas, in mundi regionibus diversis obliquatas, tam in ortu quam in occasu notarent.”

ARABIC SINGING GIRLS, THE POPE, AND THE ASTROLABE 109 constellations and to demarcate the visible from the invisible constellations. This ex-ternal horizon ring is adjustable: it can be accommodated to display the stars’ positions under different geographical latitudes.53

A second instrument is described in chapter 51 in a section titled Intellectibilium Circulorum Comprehensio.54 This instrument shows the classical five parallels of the Aratean tradition, i.e., the arctic circles, the tropic circles, and the equator. Addition-ally, the construction of this hemisphere is explained in more detail in a letter that Gerbert sent to Constantine of Fleury.55 We learn from Richer that this hemisphere is divided by a diameter that is represented by a fistula (sighting tube), with the two poles marked at the extremities of this tube. Then, the hemisphere is divided in thirty parts from one pole to the other. We have, therefore, 180° divided by thirty, so that each part measures 6°. Subsequently, Gerbert placed other sighting tubes (all of the same size) in the following order: the first tube (indicating the arctic circle) is placed in the sixth part from the North Pole, the second tube (indicating the tropic circle) in the fifth part from the first tube, and the third tube (indicating the equator) in the fourth part from the second tube. He then repeated the same process, adopting the identical subdivision and starting from the South Pole. As a result, given that each part measures 6°, we have the following subdivisions: the two arctic circles are placed at 36° from the poles; the tropic circles are placed at 30° from the arctic circles; and the equator is placed at 24° from the tropic circles. Such an instrument is correctly ori-ented, with its convexity upwards, by observing the polestar through the polar fistulae, seeing through both as if through one. The purpose of this sphere is to teach invisible circles and impress them deep in the memory, i.e., to show, by looking through the fistulae, the positions of the five classical celestial parallels of the Aratean tradition, each of them possibly marked by a star.

Chapter 52 is titled Sperae compositio planetis cognoscendis aptissima and de-scribes a sphere that aims to show the planetary revolutions.56 Richer tells us that this

53 See Marco Zuccato, “Gerbert’s Islamicate Celestial Globe,” Gerberto d’Aurillac-Silvestro II Linee per una sintesi. Atti del Convegno Internazionale. Bobbio, Auditorium di S. Chiara, 11 Settembre 2004, ed. Flavio G. Nuvolone (Bobbio 2005) 167–186.

54 Hoffman, Richer Von Saint–Remi Historiae (n. 42 above) 196–197: “[51] Intellectibilium circulo-rum comprehensio – Circuli quoque qui a Graecis paralleli, a Latinis aequistantes dicuntur, quos etiam incorporales esse dubium non est, hac ab eo arte comprehensi noscuntur. Effecit semicirculum recta dia-metro divisum. Sed hanc diametrum fistulam constituit, in cujus cacuminibus duos polos boreum et austronothum notandos esse instituit. Semicirculum vero a polo ad polum xxx partibus divisit. Quarum sex a polo distinctis, fistulam adhibuit, per quam circularis linea arctici signaretur. Post quas etiam quinque diductis, fistulam quoque adjecit, quae aestivalem circulationem indicaret. Abinde quoque quatuor divisis, fistulam identidem addidit, unde aequinoctialis rotunditas commendaretur; reliquum vero spatium usque ad notium polum eisdem dimensionibus distinxit. Cujus instrumenti ratio in tantum valuit ut, ad polum sua diametro directa ac semicirculi productione superius versa, circulos visibus inexpertos scientiae daret atque alta memoria reconderet.”

55 The letter to Constantine of Fleury is edited in Bubnov, Gerberti postea Silvestri II papae (n. 13 above) 24–28. An Eng. trans. of this letter is contained in Harriet Pratt Lattin, The letters of Gerbert with his papal privileges as Sylvester II (New York 1961) 36–39.

56 Hoffman, Richer Von Saint-Remi Historiae (n. 42 above) 197: “[52] Sperae compositio planetis cognoscendis aptissima – Errantiumque siderum circuli cum intra mundum ferantur et contra contendant, quo tamen artificio viderentur scrutanti non defuit. Inprimis enim speram circularem effecit; hoc est ex solis circulis constantem. In qua circulos duos qui a Graecis coluri, a Latinis incidentes dicuntur, eo quod in sese incidant complicavit; in quorum extremitatibus polos fixit. Alios vero quinque circulos, qui paralleli di-

110 MARCO ZUCCATO sphere displays rings indicating the two colures (either of two great circles on the celestial sphere, one of which passes through the celestial poles and the equinoxes and the other through the poles and the solstices) and again the five classical circles of the Aratean tradition. These circles are placed in exactly the same order that Gerbert adopted for his hemisphere: two arctic circles at 36° from the poles, two tropic circles at 30° from the arctic circles, and the circle of the equator at 24° from the two tropic circles. In addition, a ring indicating the Ecliptic is obliquely set on the parallel circles. Richer says that “planetary circles are suspended inside this oblique circle thanks to a marvelous device” (Intra hunc obliquum errantium circulos miro artificio suspendit), but he offers no further details on the structure of such a mechanism. He observes that this sphere can show “in a very effective way planetary apsides, altitudes and relative distances.”57

Finally, chapter 53, titled Aliae Sperae Compositio signis cognoscendis idonea, features a star globe that displays no celestial circles but carries constellation figures designed by iron and copper wires.58 A fistula is added for the purpose of orienting the axis of the globe towards the celestial poles. Richer notes that such an instrument “has something divine in itself as, even those ignorant in this science (i.e., astronomy), if they were shown one of the constellations, could then recognize all the other constel-lations thanks to the sphere and without the aid of a master.”59 Therefore, the purpose of this star sphere is more practical than theoretical, i.e., it is meant to be a practical aid to help students to observe and correctly recognize the various constellations.

Richer continues his account by stating that Gerbert’s reputation as an exceptional teacher spread beyond the borders of Gaul, attracting many students from Germany and Italy. That Gerbert’s knowledge of mathesis appeared very advanced to his con-temporaries is also corroborated by Richer’s earlier statement that when Gerbert, still a young monk, visited Rome in 970, both Pope John XIII and Emperor Otto I were so impressed by the young monk’s knowledge in the Quadrivium (mathesim optime nosset) that Gerbert was first appointed as the mentor of the emperor’s young son Otto

cuntur, coluris transposuit, ita ut a polo ad polum xxx partes sperae medietatem dividerent; idque non vulgo neque confuse. Nam de xxx dimidiae sperae partibus a polo ad primum circulum sex constituit; a primo ad secundum quinque; a secundo ad tertium, quatuor; a tertio ad quartum, itidem quatuor; a quarto ad quintum, quinque; a quinto usque ad polum sex. Per hos quoque circulos eum circulum obliquavit, qui a Graecis loxos vel zoe, a Latinis obliquus vel vitalis dicitur, eo quod animalium figuras in stellis contineat. Intra hunc obliquum errantium circulos miro artificio suspendit. Quorum absidas, et altitudines a sese etiam distantias, efficacissime suis demonstravit. Quod quemadmodum fuerit, ob prolixitatem hic ponere commodum non est, ne nimis a proposito discedere videamur.”

57 Regarding this sphere, see David Juste, “La sphère planétaire du ms. Vatican, BAV, Pal. lat. 1356 (XIIe siècle). Une pièce inédite de l’astronomie de Gerbert?” Mélanges offerts à Hossam Elkhadem par ses amis et élèves, ed. Frank Daelemans, Jean-Marie Duvosquel, Robert Halleux, and David Juste (Bruxelles 2007) 205–221.

58 Hoffman, Richer Von Saint-Remi Historiae (n. 42 above) 197–198: “[53] Aliae sperae compositio signis cognoscendis idonea – Fecit praeter haec speram alteram circularem, intra quam circulos quidem non collocavit, sed desuper ferreis atque aereis filis signorum figuras complicavit; axisque loco fistulam trajecit, per quam polus coelestis notaretur ut, eo perspecto, machina coelo aptaretur. Unde et factum est ut singulorum signorum stellae singulis hujus sperae signis clauderentur. Illud quoque in hac divinum fuit quod, cum aliquis artem ignoraret, si unum ei signum demonstratum foret, absque magistro cetera per speram cognosceret; inde etiam suos liberaliter instruxit. Atque haec actenus de astronomia.”

59 Ibid. 198: “Illud quoque in hac divinum fuit quod, cum aliquis artem ignoraret, si unum ei signum demonstratum foret, absque magistro cetera per speram cognosceret.”

ARABIC SINGING GIRLS, THE POPE, AND THE ASTROLABE 111 II and was subsequently asked to teach the quadrivium at the cathedral school of Reims.

Additionally, Richer’s narrative here is echoed by a large number of medieval tes-timonies spanning from the eleventh until at least the sixteenth century, from Adalbero seu Ascelinus, episcopus Laudunensis (977–1030), Thitmarus of Magdeburg, Ade-marus of Chabannes until Trithemius (d. 1516), Buxerius, and Arnoldus Vuion. All of these testimonies celebrate the depth of knowledge of the “sciences” of the quadri-vium shown by Gerbert. The historical evidence that attests how Gerbert, still a young Benedictine monk, became teacher of the Quadrivium at one of the most prestigious cathedral school of that time adds credibility to Richer’s testimony.60

There is, however, something out of place in Gerbert’s teaching at Reims. Cer-tainly, just a quick glimpse at the first part of Richer’s account (chapters 46 and 47 in particular) reveals the number, variety and quality of medieval sources adopted by Gerbert for teaching the trivium: here auctoritates, such as Victorinus, Porphyry, Bo-ethius, Aristotle, Cicero, Virgil, Statius, Terence, Juvenal, Persius, Horace, and Lucan, are known and studied. However, if we consider Richer’s description of Gerbert’s teaching in the quadrivium, the situation changes completely. Indeed, what is quite striking is that no medieval authorities whatsoever are mentioned for the teaching of the quadrivium. One cannot find even a single mention of Boethius, Pliny, Martianus Capella, Macrobius, or Calcidius, who were all very popular sources of scientific knowledge, in particular for astronomy, during the early Middle Ages.61 This fact is inexplicable, especially in the light of the fact that Gerbert was quite familiar with such authors: this familiarity clearly emerges from the letters preserved in Gerbert’s correspondence.62 In particular, Boethius is mentioned in several of Gerbert’s letters. There is, in fact, good evidence that Boethius’s De Musica, De arithmetica, and even the De astrologia (de astronomia) were quite well known to Gerbert.63

Instead, in Gerbert’s quadrivium we have a teaching that relies entirely on the use of technical instruments: the monochord for music, the abacus for mathematics and geometry and four celestial spheres for astronomy. Thus, it is possible to infer from Richer’s testimony that Gerbert’s students were instructed in these disciplines through a practical/oral method that did not draw on the use of any Latin auctoritas. An ex-haustive analysis of the four disciplines of the quadrivium as taught by Gerbert at the cathedral school of Reims would transcend the scope of this article. However, as noted already, the greatest part of Richer’s description is devoted to astronomy, and this appears to indicate that astronomy had a predominant position in Gerbert’s teachings.

60 These testimonies are listed in Bubnov, Gerberti postea Silvestri II papae (n. 13 above) 382–393. 61 The most recent work about the teaching and study of astronomy in this period is Bruce S. Eastwood,

Ordering the Heavens. Roman Astronomy and Cosmology in the Carolingian Renaissance (Leiden-Boston 2007). See also Stephen C. McCluskey, Astronomies and Cultures in Early Medieval Europe (Cambridge 1998); Wesley M. Stevens, Cycles of Time and Scientific Learning in Medieval Europe (Collected Studies) (Ashgate 1995); and Barbara Obrist, La cosmologie médiévale. Textes et images. I. Les fondements antiques (Florence 2004).

62 See the analysis carried out by Pratt Lattin, The Letters of Gerbert (n. 55 above) at 128 and 189–191. 63 Bubnov, Gerberti postea Silvestri II papae (n. 13 above). See, in particular, the following letters by

Gerbert: n. 3, 39–41; n. 4, 41–44; n.15, 54–55; n. 132, 163–164; n. 138, 168–169. I follow the Eng. ed. Pratt Lattin, The Letters of Gerbert (n. 55 above).

112 MARCO ZUCCATO The importance of astronomy to Gerbert is also corroborated by the fact that Richer uses the term mathesis to indicate the disciplines of the quadrivium, but, if we accept the lectio furnished by MS Barcelona, ACA, Ripoll, 74,64 then we can safely assume that the focus of Gerbert’s scientific teaching was astronomy, whereas mathematics, geometry, and music occupied an ancillary position that was integrated into the astro-nomical teaching. I shall, therefore, focus my analysis on astronomy and show that what emerges from Richer’s description is not consistent with the medieval tradition of astronomical teaching. In fact, Gerbert’s astronomical teaching represents a neat break with such a tradition.

Commencing with the Carolingian Renaissance and the educational reform of Al-cuin of York (737–804), the teaching and practice of astronomy was safely anchored to the written tradition. Alcuin himself drew on a wide variety of sources in his at-tempt to revitalize astronomical studies at the Carolingian court. As Bruce Eastwood noted, “the works of Pliny the Elder and Macrobius were supplemented by Roman translations of Aratus’s Phaenomena as well as by Isidore of Seville’s De natura re-rum and Etymologies and Bede De natura rerum and De temporum ratione.”65 In particular “the copying of texts, sometimes involving recovery as well, was clearly of primary importance for the advancement of such monastic schooling as Alcuin and others practiced.”66

The eighth and early ninth centuries, in particular, represent a period of great im-portance for understanding the general trend in astronomical studies, which would dictate the leitmotiv of “scientific” scholarship until the time of Gerbert. The copying, transmission, and diffusion of scientific manuscripts in this period were paramount to the Carolingian program of knowledge revival. Not only basic texts on computus, a distinct ecclesiastical study that used a very limited body of astronomical information, but also more advanced astronomical works such as Hyginus’s De Astronomia and Pliny’s astronomical excerpts began to circulate in this period.

For instance, if we look at a library catalogue of 821/822 of the monastery of Reichenau on Lake Constance, we see the various names of medical books, the Prog-nostica Democriti, Boethius’s arithmetic and geometry, and an Aratea. But, by the 840s, the library displays Vitruvius’s De Architectura, Hyginus’s Astronomia, Boe-thius’s De Musica, copies of Isidore, and Bede’s De natura rerum, containing circular cosmological and computistical images, and several illustrated copies of Pliny’s astro-nomical excerpts.67

Bruce Eastwood tells us that “by ca. 840—perhaps some years earlier—the astron-omy (Book VIII) of Martianus Capella’s Marriage of Philology and Mercury was not only being studied but also submitted to an enormous effort of commentary, resulting in what we now call the Anonymus Commentary, which traveled in many versions and had tremendous influence on scholars such as John Scottus Eriugena and Re-migius of Auxerre in the ninth century. The more demanding astronomy of Calcidius’s

64 See n. 49 above. 65 Eastwood, Ordering the Heavens (n. 61 above) 9. 66 Ibid. 9. 67 Ibid. 9–10.

ARABIC SINGING GIRLS, THE POPE, AND THE ASTROLABE 113 Commentary on Plato’s Timaeus was being studied and excerpted by the mid-ninth century and was being copied and corrected later in the century.”68

When Dungal wrote his reply to Charlemagne’s inquiry about the two solar eclip-ses that occurred in 810, he heavily relied on Macrobius’s Commentary to answer the question. Similarly, in Alcuin’s letters, we find computistical questions and conversa-tions about potentially ominous events in the heavens, for instance, an unusually long invisibility of the planet Mars. Alcuin formulated his astronomical explanations of such celestial phenomena using Book Two of Pliny’s Naturalis Historia.69 Astronomy in this period was cultivated through the written verbum and was sapientia scripta first and foremost. Astronomical questions, problems and the like were addressed and solved through the use of Latin auctoritates, precious information stored in scripta authored by Pliny, Macrobius, Martianus Capella, Calcidius, Hyginus, and Boethius, which were widely circulating in the monasteries’ scriptoria in this period.70

Against this background, Richer’s narration appears to be a strangely anomalous account of a very unconventional type of quadrivium. In Richer’s description, the external form of Gerbert’s teaching appears to be the classical quadripartition of sci-entific knowledge into the four liberal arts of mathematics, geometry, astronomy, and music. However, the standard contents of the quadrivium have completely disap-peared, its classical auctoritates washed away and replaced by actual physical objects meant to represents visual and tactile aids for the understanding of a mostly oral teaching. Again, if we take astronomy as a paradigmatic case, Gerbert’s students were no longer mentored through the pages of Calcidius, Macrobius, Pliny, Martianus, etc., but rather they were instructed via an “astronomical practice” that relied on the aid of spherical instruments. This emphasis on practices can explain why Richer is silent on the names of the classical authorities in the quadrivium. At least a significant part of the teaching took place neither in a monastic scriptorium nor in a classroom of the cathedral school, but rather in the open air, as Richer himself clearly states in chapter 50 of Book III of his Historia: “at night [Gerbert] paid attention to the shining stars, and he brought it about that [his students] noticed how [these stars] were oblique in different parts of the world, both in their rising and in their setting.”71 Most important, the knowledge transmitted by Gerbert appears to be encapsulated in an astronomical practice that relies on astronomical instruments as opposed to written information derived from manuscripts, verba scripta. To my knowledge, Richer’s description stands alone in the ocean of early Latin medieval testimonies concerning the study and teaching of astronomy using a method that is not based on written information and that completely ignores all of the Latin astronomical authorities available during that pe-

68 Ibid. 12–13. 69 Ibid. 17–19. 70 MS St. Gallen, Stiftsbibliothek, Cod. Sang. 18, fol. 43r, includes a drawing of an astronomical clock

described by Pacificus of Verona (d. 884). This instrument is commonly used for nocturnal timekeeping, a branch of computus. The astronomical clock is quite different from Gerbert’s spheres because it does not convey any knowledge of the physical structure of the cosmos. On this instrument see McCluskey, Astron-omies and Cultures (n. 61 above) 112.

71 Hoffman, Richer Von Saint-Remi Historiae (n. 42 above) 196: “Nam tempore nocturno ardentibus stellis operam dabat, agebatque ut eas, in mundi regionibus diversis obliquatas, tam in ortu quam in occasu notarent.”

114 MARCO ZUCCATO riod. In fact, it appears that we are dealing here with an alien tradition that pseudo-morphed into the liberal arts of the classical Latin Quadrivium.72 If we are addressing an alien tradition, then the origin of this tradition must be sought outside of the Latin World.

In chapter 43 of Book III of his Historia Francorum, Richer tells us that that a Count Borrell, on pilgrimage, visited the monastery of Saint-Géraud in Aurillac and, when asked by the abbot of that monastery “whether in Spain there were men profi-cient in the arts, he positively replied with no hesitation.” Then, having been per-suaded by the abbot to take Gerbert with him, the count entrusted the young monk to Bishop Atto “with whom [Gerbert] studied many things in mathesis with excellent results.”73

It has been established that Gerbert spent approximately three years in the Iberian Peninsula (967–970), and much has been written and conjectured about Gerbert’s whereabouts during this period: whether he visited Cordoba, whether he received any teaching from Islamic scholars, and, if so, what sort of teaching he could assimilate. Yet, there can be little doubt that Gerbert’s training in the quadrivium was primarily carried out during his sojourn in Spain74 and that, once Gerbert arrived in Rome in 970, his knowledge in musica and astronomia, in particular, greatly impressed both the papal and the imperial courts.75

As noted above, it has been conjectured that it was approximately during this pe-riod that important mathematical and astronomical works filtered from Qayrawan (Tunisia) to al-Andalus and possibly to Catalonia, reaching Catalan scholars who were very close to Gerbert. One of these works displays the concept of ‘ilm al-hay’a (the science of the structure of the world, which is “physical” astronomy76) and urged

72 I refer here to the concept of historical pseudomorphosis first proposed by Oswald Spengler, Der Untergang des Abendlandes: Umrisse euner Morphologie der Weltgeschichte (Munich 1923).

73 Hoffman, Richer Von Saint-Remi Historiae (n. 42 above) 191–192: “Qui a loci abate humanissime ex-ceptus, post sermones quotlibet, an in artibus perfecti in Hispaniis habeantur sciscitatur. Quod cum promptissime assereret, ei mox ab abbate persuasum est ut suorum aliquem susciperet, secumque in artibus docendum duceret. Dux itaque non abnuens petenti liberaliter favit ac fratrum consensu G[erbertum] as-sumptum duxit, atque Hattoni episcopo instruendum commisit. Apud quem etiam in mathesi plurimum et efficaciter studuit.”

74 See Michael Zimmermann, “La Catalogne de Gerbert,” Gerbert l’Européen: Actes du colloque d’Aurillac, 4–7 juin 1996 ed. Nicole Charbonnel and Jean-Eric Iung (Aurillac 1997) 79–101, esp. 85; Pierre Riché, Gerbert d’Aurillac (n. 41 above) 25–27; Antoni Pladevall i Font, Silvestre II (Gerbert d’Orlhac) (Barcelona 1998) esp. 31–33; Jaime Tarracó, “Formación Cultural de Gerberto (Silvestre II) en San Geraldo de Aurillac y en la Marca Hispánica,” Annals 1997–1998 del Centre d’estudis comarcals del Ripollès (Ripoll 1999) 1–58. Lluis Nicolau y d’Olwer, “Gerbert (Silvestre II) y la cultura catalana del Siegle X”, Estudis Universitaris Catalans 4 (1910) 332–358, esp. 333–334, believes that Gerbert travelled to Cordova for his training in the quadrivium, but offers no further arguments to support this claim aside from a testi-mony of Adhemar de Chabannes.

75 Hoffman, Richer Von Saint-Remi Historiae (n. 42 above) 192: “Nec latuit papam adolescentis indus-tria, simulque et discendi voluntas. Et quia musica et astronomia in Italia tunc penitus ignorabantur, mox papa O[ttoni], regi Germaniae et Italiae, per legatum, indicavit illuc hujusmodi advenisse juvenem, qui mathesis optime nosset, suosque strenue docere valeret.”

76 For a clarification of ‘ilm al-hay’a in the Arabic astronomical tradition see Tzvi Langermann, “Arabic Cosmology” Early Science and Medicine 2.2 (1997) 185–213. See also Jamil Ragep, Nasir al-Din al-Tusi’s Memoir on Astronomy (al-Tadhkira fi `ilm al-hay’a). Edition, Translation, Commentary and Introduction. 2 vols. (New York 1993) esp. 1.38–41. See also the review essay by A. I. Sabra, “Config-uring the Universe: Aporetic, Problem Solving, and Kinematic Modeling as themes of Arabic Astron-omy,” Perspectives on Science 6.3 (1998) 288–330; and the reply by George Saliba, “Arabic versus

ARABIC SINGING GIRLS, THE POPE, AND THE ASTROLABE 115 astronomers to adopt the use of celestial globes to achieve a correct understanding of the kinematics of the heavens as a basic propaedeutic training for the use of the astro-labe.77 This suggestion is quite plausible because, as has been shown, Qayrawan dur-ing the tenth century did exert some important cultural influence over al-Andalus.

Still, a serious obstacle for this hypothesis comes from the above-mentioned thesis proposed by Paul Kunitzsch. If the text or teaching that reached Gerbert from Qay-rawan was centered on an important pedagogy that was propaedeutic to the use of the astrolabe, how could Gerbert have grasped the meaning of this pedagogy without any knowledge of the astrolabe? How could Gerbert have understood the importance of teaching astronomy through the use of celestial globes, as Dun sh ibn Tam m al-Qaraw had proposed, when he completely lacked any knowledge of the astronomical instrument, i.e., the astrolabe, that this teaching was meant to ground? As a matter of fact, Dunash’s astronomical pedagogy, based on the use of celestial spheres, had a profound connection to the understanding of the astrolabe and its use. It is true that medieval sources do connect the name of Gerbert of Aurillac to at least one of the texts of the early astrolabe corpus, i.e., De Utilitatibus Astrolabii. However, these sources should be dismissed because, according to Kunitzsch, Gerbert could not have possessed any knowledge of the astrolabe at the time because studies on the astrolabe did not commence in al-Andalus before the work of the school of Maslama and there-fore could not have reached Catalonia before 978. How to solve this riddle?

6. NEW EVIDENCE

A very interesting story emerges from two thirteenth-century sources: the Takmila li-kit b al- ila by Ibn al-Abb r78 and the Al-Dayl wa-l-takmila by Ibn ‘Abd al-Malik al-Marr kuš (VIII-2, n. 285).79 Both sources tell us that al- akam II (915–976) had a young slave, who was a k tiba of great intelligence. Therefore, the caliph sent her to Ab l-Q sim Sulaym n ibn A mad ibn Sulaym n al-An r al-Ru f al-Qass m “to learn astronomy (ta‘d l) and the use of the astrolabe and similar things.” The slave devoted all of her energies to learning those subjects, and within three years, she had acquired such a profound knowledge of astronomy and the astrolabe that it caused great admiration among the Caliph and his court. Al- akam sent her to work on what she had learnt in the alcazar. Sulaym n was rewarded with a great gift and by the increased esteem that al- akam held for him.80

Greek Astronomy: a Debate over the Foundations of Science,” Perspectives on Science 8.4 (2000) 328–341.

77 Zuccato, “Gerbert of Aurillac” (n. 14 above) 742–763. 78 Ibn al-Abb r, Takmila li-kit b al- ila ed. F. Codera (Madrid 1887); Miscelánea de Estudios y textos

árabes ed. M. Alarcón and C.A. González Palencia (Madrid 1915) 147–690. 79Ibn ‘Abd al-Malik al-Marr kuš , Al-Dayl wa-takmila (Beirut 1964–1965) VIII–2 n. 285. 80 On such a crucial testimony, see Maria Luisa Ávila, “Las Mujeres ‘Sabias’ en Al-Andalus,” La Mujer

en Al-Andalus. Reflejos históricos de su actividad y categorías sociales, Actas de las V jornadas de investi-gación interdisciplinaria. I: Al-Andalus. Edición a cargo de María J. Viguera (Sevilla 1989) 139–184, esp. 180 n. 113: “Una esclava ( riya) al- akam II (s. IV/X). Al- akam envió una joven sierva (wa fa) que había en el alcázar, que era una k tiba de gran inteligencia, a Abý l-Q sim Sulaym n b. A mad b. Sulaym n al-An r al-Ru f al-Qass m para que le enseñara astronomía (ta‘d l), el manejo del astrolabio y cosas parecidas. Se dedicó a ello haciéndose una experta, a lo que la ayudó su natural inclinación a esta ciencia que llegó a dominar en unos tres años, al cabo de los quales causó la admiración del califa que la puso a

116 MARCO ZUCCATO

Before I can proceed with my argument and show why these testimonies are so im-portant, the following basic questions should be asked. First, do we have two inde-pendent accounts of the same incident, so that they reinforce each other, or is one dependent on the other, or the two on a third, lost source? Second, are there good grounds for believing that these sources are accurate?

The work by Ibn al-Abb r (Takmila li-kit b al- ila) follows the classical stereotype of Andalusian biographical dictionaries, providing information such as the person’s name, place of birth, profession, his teachers, qualities as a scholar, disciples and fi-nally his date of death.81 In fact, the Takmila was meant to complement the biograph-ical dictionary Kit b al- ila f ta’r kh a’immat al-Andalus (1139) by the Andalusian traditionist, historian and jurist, Ibn Bashkuw l (1101–1183). This writing is a collec-tion of some 1400 biographies of ‘ulam ’ (religious scholars) from the eleventh to the twelfth centuries. This work was a continuation of a biographical dictionary compiled by Ibn al-Fara (962–1012) titled Ta’r kh ‘ulam ’ al-Andalus.

It is quite clear that the Al-Dayl wa-l-takmila by Ibn ‘Abd al-Malik al-Marr kuš is based on Ibn al-Abb r’s Takmila; however it does not appear that this latter work is based or at least draws on the same sources used by Ibn Bashkuw l’s Kit b al- ila or al-Farad ’s Ta’r kh. As a matter of fact, the information described above concerning al- akam’s young slave does not appear in either Ibn Bashkuw l’s Kit b al- ila or al-Fara ’s Ta’r kh. For a philological analysis of the above-mentioned information pro-vided by Ibn Al-Abb r’s Takmila, one should be able to access the original sources used by Ibn al-Abb r. However, it is not possible to access these sources because they are either lost or yet to be found. At any rate, a recent study by María Luisa Ávila has established that the authors of Andalusian biographical dictionaries normally had strict criteria for selecting the scholars to be included in their works and that the author covered one period exclusively. For earlier periods covered by later works, these crite-ria became far less strict primarily because of the need to expand the works of prede-cessors. These relaxed criteria explains why, for instance, the slave girl described in the thirteenth-century works by Ibn al-Abb r and Ibn ‘Abd al-Malik did not match the strict criteria for inclusion in the eleventh- and twelfth-century biographical dictionar-ies by Ibn Bashkuw l and al-Fara .82 For instance, as María Luisa Ávila notes, “of the forty-one women living up to the end of the tenth century (the period covered by Ibn al-Fara ) only two are mentioned by him; the rest appear in later dictionaries and many of them are included simply for having been the wife or slave of some distin-guished person.”83

trabajar en lo que había aprendido en el alcázar. A Sulaym n lo recompensó con un gran regalo y le duplicó la estima que sentía por él.” See also Manuela Marín, Mujeres en Al–Ándalus, (Madrid 2000) 653–654; and Marie G. Balty–Guesdon, Médecins et hommes de sciences en Espagne Musulmane (IIe/VIIIe–Ve/Xie s.). Thése pour le doctorat (arêté du 23 novembre 1988), présentée par Marie Geneviève Balty-Guesdon sous la direction de Mohammed Arkoun, Université de La Sorbonne Nouvelle-Paris III. 3 vols (Paris 1992) 405 and 635.

81 On the biographical dictionaries, see Christian Muslim relations: a bibliographical history, ed. David Thomas and Alex Mallet with Juan Pedro Monferrer Sala, et al. (Leiden-Boston 2011) vol. 3, esp. 453.

82 See María Luisa Ávila, “Women in Andalusi Biographical Sources,” Writing the Feminine. Women in Arab Sources, ed. Manuela Marín and Randi Deguilhem (London-New York 2002) 149–163.

83 Ibid. 154.

ARABIC SINGING GIRLS, THE POPE, AND THE ASTROLABE 117

At all events, there are good grounds to believe that Ibn al-Abb r’s Takmila and Ibn ‘Abd al-Malik’s Al-Dayl wa-l-takmila are accurate. Indeed, the information that we receive from these sources is coherent with the historical scenario described by other contemporary Arabic sources. To begin with, it is well known that the caliphal court of Cordoba, in particular during the reign of al al- akam II (961–976), was populated by many qiyan, i.e., singing-slave-girls, who were not only trained in music but also medicine, philosophy, astronomy, astrology, and mathematics. The main function of these girls was to entertain the caliph, the nobles, and aristocrats at the caliphal court in Cordoba.84 During this period and earlier, science and philosophy were traded and cultivated in Cordoba as courtly luxury goods. Indeed, the polymath Abu l-Hasan ‘Ali Ibn Nafi‘ (789–857), better known by the nickname Ziryab (the black bird), served at the court of Emir ‘Abd al-Ra m n II (788–852) in Cordoba and was the first scholar to establish the court etiquette of the Andalusian emirate. He used art, science, and philosophy as luxury products that eventually became highly sought after by the no-bles and aristocrats orbiting around the emir and his court. It was during this period that Cordoba acquired the reputation as the stylistic capital of the Western World. Ziryab was also the first scholar that we know about who trained qiyan in the sciences of the ancients in Cordoba, and he most likely sold qiyan also.85 Ibn Bass m (d. 1147), in his anthology titled Dhakh rah f ma sin ahl al-jaz rah, reports that Ibn al-Katt n , the famous physician of al- akam II and al-Man r bi-llah (938 – 1002), used to train his slave-girls in medicine, geometry, music, astronomy, astrology, and logic, and then sold them for 3000 dinars.86 Furthermore, we know of another slave girl of al- akam II, named Lubna, who was trained in mathematics, grammar and poetry and became an expert in is b (calculus).87

If we accept the this testimony by Ibn al-Abb r and Ibn ‘Abd al-Malik al-Marr kuš , then we obtain at least four important pieces of information: 1. The use of the astrolabe was known in al-Andalus definitely before 978. The astrolabe was used and studied as the pivotal instrument for practicing ta‘d l, i.e., practical astronomy, outside of the school of Maslama al-Majr . 2. Sometime during 961–976 at the ca-liphal court in Cordoba, there was at least one scholar we know about, Ab l-Q sim Sulaym n ibn A mad ibn Sulaym n al-An r al-Ru f al-Qass m, who possessed enough knowledge of this subject to be able to teach practical astronomy and the use of the astrolabe. 3. Transmission of information concerning practical astronomy (ta‘d l) and the use of the astrolabe, at least in the form of oral teaching, took place at the caliphal court in Cordoba under al- akam al-Mustan ir bi-ll h (961–976). 4. At least one student who we know about, i.e., a slave girl of al- akam, was successful in

84 See Forcada, Ética e ideología de la Ciencia (n. 30 above) 185–196. See also Manuela Marín, Vidas de mujeres andalusíes (Malaga 2006) esp. 113–134.

85 On Ziryab, see Forcada, Ética e ideología de la Ciencia (n. 30 above) 192–193; and Marín, Vidas de mujeres andalusíes (n. 84 above) 184–186.

86 Ibn Bass m al-Shantar n , Dhakh rah f ma sin ahl al-jaz rah / ta l f Ab al- asan (Beirut 1979) 3.320.

87 Luisa Ávila, “Las Mujeres ‘Sabias’ en Al-Andalus,” (n. 80 above) 166 n. 59; and Manuela Marín, Mujeres en Al-Ándalus (n. 80 above) 653.

118 MARCO ZUCCATO acquiring a good knowledge of astronomy (ta‘d l) and the use of the astrolabe at the caliphal court of Cordoba under the reign of Caliph al- akam (again, before 978).

7. CONCLUSIONS

The information listed above should be analyzed against the background of the recep-tion of the Arabic astrolabe in the Latin West. Here we have the following: 1. Sometime around the end of the tenth century, a Latin written corpus concerning the use and construction of the astrolabe appears in Catalonia and France. This corpus does not appear to be a translation derived from Arabic written sources. One of the texts of this corpus concerning the use of the astrolabe was ascribed by a number of medieval sources to Gerbert of Aurillac. 2. Gerbert of Aurillac in Reims delivered a very unorthodox astronomical oral teach-ing based on practical astronomy, i.e., the use of a number of spherical objects and celestial spheres, whose didactic purpose was to transfer astronomical knowledge directly through the observation of planets and stars and their motion. This method had no precedent in Latin astronomical teaching. 3. It has been claimed that Gerbert, while he was in Spain (967–970), could have ac-cessed an important Arabic astronomical writing from Qayrawan authored by Dun sh ibn Tam m al-Qaraw . This text offered an astronomical pedagogy based on the use of celestial spheres and pivoted around the astrolabe. However, the work on the astrolabe by the school of Maslama al-Majr could not have been introduced to the Latin world earlier than 978. Thus, if Gerbert did acquire any knowledge of the astrolabe in Spain, his source was not Maslama al-Majr . 4. It is therefore reasonable to conjecture that if Gerbert’s astronomical knowledge derived from the Arabic world, then we must look for a source with the following features: (a) a source in which astronomical knowledge is transferred primarily through oral/practical teaching, possibly via the use of astronomical instruments simi-lar to those used by Gerbert in Reims; (b) a source in which the teaching of astronomy is coherent with the pedagogy proposed by Dun sh ibn Tam m’s work, i.e., practical astronomy, the use of celestial spheres, and astronomical observations (not writings) related to the use and understanding of the astrolabe, must be the core of such a teaching; (c) a source that does not include the written advanced mathematical techni-calities proper to the school of Maslama al-Majr ; and (d) a source that must be available (and transmittable) in the Iberian peninsula during the 967–970 period.

Any single one of these eight pieces of information would be insufficient on its own to detect the source of Gerbert’s astronomy, but, taken together, and in the ab-sence of contrary evidence, they provide a good basis for the following conclusions. If knowledge of ta‘d l and the astrolabe was actually circulating in al-Andalus (Cordoba) before Maslama began his studies on the astrolabe, then it is possible to postulate the existence of two different traditions of astronomical studies in al-Andalus. The first and oldest tradition addresses what I would call “astronomical practice.” We gain knowledge of this tradition only through indirect evidence. It is possible that such a tradition dates back to the time of the emir ‘Abd al-Ra m n II, i.e., as early as the

ARABIC SINGING GIRLS, THE POPE, AND THE ASTROLABE 119 ninth century when Ziryab was active at the court of the emir of Cordoba.88 In this tradition, we do not have evidence of a proper mathematical-astronomical school in place that is capable of producing technical writings related to the astrolabe. Instead, what we have is the presence of astrolabe experts or “practitioners” orbiting around the caliph and his court, who knew and used the astrolabe for various purposes, from astrology to the complementing of astronomical knowledge, etc. These scholars cer-tainly knew how to use an astrolabe, and they could teach its use. They probably knew how to build an astrolabe. For instance, we have some interesting evidence in MS, Paris, BnF 7412, fol. 23v where, from a drawing of an astrolabe, it is possible to de-rive the name of an otherwise unknown Andalusian astrolabe maker of the tenth cen-tury named Khalaf ibn al-Muc dh, who did not appear to operate in the entourage of Maslama’s school.89 These court astrologers could transfer their expertise through oral explanations, practice, demonstrations and so on, but, it appears that they did not pro-duce advanced astronomical-mathematical writings, which we see instead coming from astronomical-mathematical schools, such as the school of Maslama al-Majr .

The second and most recent tradition, which began with Maslama al-Majr and his disciples, most likely around or after 978, is much more technical and could be de-fined as a proper mathematical-astronomical tradition that is based on written works. We gain knowledge of this tradition through direct evidence. Indeed, we possess good written evidence of the existence of such a tradition from the advanced mathematical and astronomical writings, treatises on the astrolabe and the like, that were produced by Maslama and his school. In this tradition, knowledge of the astrolabe is inserted into a complicated mathematical and astronomical framework, that entails knowledge of several advanced texts such as, for instance, Ptolemy’s Planispaerium, al-Batt n z j, star tables, mathematical methods for computing how to projects stars on the rete of an astrolabe, etc. Contrary to the first tradition, this tradition produced several writings.

88 Ali ibn Musa ibn Said al–Maghribi in his Al-Mugrib f ul al-Magrib (Book of the Maghrib) (I, 126) reports an anecdote that occurred during the reign of ‘Abd al-Ra m n II (788–852). Ibn Said tells us that one day ‘Abd al-Ra m n II challenged his best court astrologer, Ibn al-Šamir, to predict from which door he would exit a room which had four doors. Ibn al-Šamir cast the horoscope and wrote his answer on a sealed sheet. As soon as the astrologer sealed the sheet, the emir ordered his carpenters to open a new door in the room, and once that was made, he exited the room through the new door. But, when ‘Abd al-Ra m n opened the sealed sheet, he was struck to see that Ibn al-Šamir had predicted exactly all that had happened. As amusing as such an anecdote may be, there is a layer of truth in it: (1) We know that ‘Abd al-Ra m n II had a particular interest in astrology and was indeed surrounded by many court astrologers. (2) The astro-labe is the most obvious tool for aiding astrologers in casting their horoscopes and setting forth their predic-tions. Julio Samsó, Las ciencias de los Antiguos (n. 19 above) 51, describes this episode and writes that Ibn al-Šamir used an astrolabe to cast the horoscope: “Sin perder la seriedad, Ibn al-Šamir toma su astrolabio, levanta el horóscopo y escribe sus conclusiones en un pliego que cierra a continuación.” However, in the 2011 2nd ed. of the work he corrects the former statement by claiming that the sources do not mention an astrolabe (459). Yet, although it is true that the astrolabe is not explicitly mentioned here by the Arabic source, if one considers the widespread use of astrolabes, especially among court astrologers in the Islamic East during this period, it is possible to conjecture that astrolabes were also circulating and used by court astrologers in al-Andalus during this period.

89 This author is not mentioned in the list of Andalus scholars and astronomers by cid al-Andalus . See David King, “Bringing Astronomical Instruments back to Earth—The Geographical Data on Medieval Astrolabes (to CA. 1100),” Between Demonstration and Imagination. Essays in the History of Science and Philosophy Presented to John D. North (Leiden-Boston-Köln 1999) 3–54, at 23.

120 MARCO ZUCCATO

Modern scholarship has always noted the discrepancy between what we see in Ger-bert’s astronomical teaching in Reims and the scientific depth of the second tradition, ignoring, however, the existence of the first tradition.90 Yet, if we assume that it was the first tradition, “the astronomical practice,” that entered Catalonia during the second half of the tenth century, these difficulties disappear, and we can propose a simpler reconstruction in two stages:

Stage 1. The “astronomical practice” of the first tradition filtered from al-Andalus to Catalonia around the middle of the tenth century but definitely before 976 (i.e., the year of al- akam’s death). It is likely that the channels used to transmit this practice were primarily political-diplomatic channels.91 Gift exchange played a vital role in this transmission, and we can assume that the earliest surviving Latin astrolabe, the Des-tombes astrolabe, arrived in Catalonia via a political and diplomatic channel. Similar to what had happened with the study of the Materia Medica of Dioscorides in Cor-doba,92 it is possible that someone with knowledge of the first tradition was sent from al-Andalus to Catalonia to help Latin scholars in the understanding and use of the gifts received. By 967 at the latest, we have scholars in Catalonia who have mastered the astronomy of the first tradition. Gerbert of Aurillac learned such a practice during his sojourn in Catalonia 967–970.

Stage 2. Via Gerbert of Aurillac this “astronomical practice” of the first tradition reached France approximately 972. This practice pseudomorphed into the quadrivium, where it became known as mathesis and was taught in the cathedral school of Reims during the third quarter of the tenth century. The abacus with Arabic numerals and Gerbert’s celestial spheres were central to this new teaching. This teaching quickly arrived in Lotharingia before 980 and was then metabolized by scholars such as Con-stantine of Fleury, Ascelin of Augsburg, Bern of Prüm, Abbo of Fleury, and possibly other of Gerbert’s students. This teaching was put into writing around the end of the tenth century, generating a vast written corpus of astronomical texts.

Thus, an astronomical practice centered on the use of the astrolabe and practical astronomy (ta‘d l), was eventually “neutralized” and reassimilated by French scholars according to the standard epistemological criteria that dominated the Latin World during the early middle ages: it was transformed into verba scripta and transferred into a complex written corpus of astronomical writings centered on the astrolabe.

90 See Emmanule Poulle, “L’Astronomie de Gerbert” (n. 15 above); and idem, “Note sur l’autorité des traités de l’astrolabe” (n. 20 above). See also Guy Beaujouan, “Les Apocryphes mathématiques de Gerbert” (n. 20 above).

91 The existence of political-diplomatic channels between Catalonia and al-Andalus from at least 940 AD is illustrated in Zuccato, “Gerbert of Aurillac” (n. 14 above) 750–754.

92 See Ibn Abi U aybica, ‘Uyûn al-Anabâ’ fî T’abaqât al-At’ibbâ’, trans. Henri Jahier and Abdelkader Noureddine, Sources d’informations sur les classes des medecins (Alger 1958) 38–41. See also George F. Hourani, “The early growth of the secular sciences in Andalusia,” Studia Islamica 32 (1970) 143–156; Julio Samsó, Las ciencias de los Antiguos (n. 19 above) 111–113; and Thomas F. Glick, Islamic and Christian Spain in the Early Middle Ages (Princeton 1979) 256.