The Abacus And The Cross Part 13

232 "the black arts": "the black arts": William of Malmesbury, 279-289. David Rollo explains the literary allusion in William of Malmesbury, 279-289. David Rollo explains the literary allusion in Glamorous Sorcery Glamorous Sorcery, 3-20.

235 Gerbert died: Gerbert died: Roland Allen, "Gerbert, Pope Silvester II," 661, 664-668; Robert Favreau, "Le souvenir officiel: L'epitaphe de Silvestre II a Saint-Jean-de-Latran," in Olivier Guyotjeannin and Emmanuel Poulle, eds., Roland Allen, "Gerbert, Pope Silvester II," 661, 664-668; Robert Favreau, "Le souvenir officiel: L'epitaphe de Silvestre II a Saint-Jean-de-Latran," in Olivier Guyotjeannin and Emmanuel Poulle, eds., Autour de Gerbert d'Aurillac Autour de Gerbert d'Aurillac, 336-341; and Pierre Riche, Gerbert d'Aurillac Gerbert d'Aurillac, 232-233. Both Allen and Riche quote Canon Caesar Raspo's account of the opening of Gerbert's tomb in 1648.

236 "white mantle of churches": "white mantle of churches": Ralph the Bald, 115. The discovery of the second head of John the Baptist is told by Richard Landes in Ralph the Bald, 115. The discovery of the second head of John the Baptist is told by Richard Landes in Relics, Apocalypse, and the Deceits of History Relics, Apocalypse, and the Deceits of History, 47; he also details Ademar's forgeries and the riots over Saint Martial's relics, 269-279.

237 "relic jamborees": "relic jamborees": Landes, 47; he also cites Ademar of Chabanne's report of the collective pilgrimage to Jerusalem, 155. R. I. Moore, Landes, 47; he also cites Ademar of Chabanne's report of the collective pilgrimage to Jerusalem, 155. R. I. Moore, Formation of a Persecuting Society Formation of a Persecuting Society, points out the change from miserere n.o.bis miserere n.o.bis to to dona n.o.bis pacem dona n.o.bis pacem, 320.

238 heretics: heretics: Ralph the Bald, 139-151; Ademar of Chabannes in Landes, 128. A monk from Ripoll who was present at the burning, Landes adds, "wrote his abbot soon thereafter with the news," according to the Ralph the Bald, 139-151; Ademar of Chabannes in Landes, 128. A monk from Ripoll who was present at the burning, Landes adds, "wrote his abbot soon thereafter with the news," according to the Life of Gauzlin Life of Gauzlin . For the heretics' connection to Gerbert, see Moore, 12-15. On "The Condemnation of Aristotle's Books on Natural Philosophy in 1210 at Paris," see Edward Grant, . For the heretics' connection to Gerbert, see Moore, 12-15. On "The Condemnation of Aristotle's Books on Natural Philosophy in 1210 at Paris," see Edward Grant, A Source Book in Medieval Sciences A Source Book in Medieval Sciences, 42-43.

238 religious intolerance: religious intolerance: Ralph the Bald blames the destruction of the Holy Sepulchre on the Jews, 133-137, as does Ademar of Chabannes in Landes, 40. Moore quotes Guibert of Nogent's description of the ma.s.sacres of Jews, 28, and the general change in att.i.tude toward Jewish citizens, 28-30, 76-83. The rise of intolerance in Spain is chronicled by Maria Rosa Menocal, Ralph the Bald blames the destruction of the Holy Sepulchre on the Jews, 133-137, as does Ademar of Chabannes in Landes, 40. Moore quotes Guibert of Nogent's description of the ma.s.sacres of Jews, 28, and the general change in att.i.tude toward Jewish citizens, 28-30, 76-83. The rise of intolerance in Spain is chronicled by Maria Rosa Menocal, The Ornament of the World The Ornament of the World, 96-103. She writes, "The old Andalusian order, with its political unity and cultural grandeur, exploded like a star," 100. On the importance of the filioque filioque in dividing East and West, see John Man, in dividing East and West, see John Man, Atlas of the Year 1000 Atlas of the Year 1000, 35; Norwich finds additional reasons, 315-322.

240 Gerbert's reputation: Gerbert's reputation: "great genius" is from Richer of Saint-Remy (before 998), vol. 2, 51. Helgaud of Fleury (c. 1041) and the son of Count Borrell are quoted by Riche, "great genius" is from Richer of Saint-Remy (before 998), vol. 2, 51. Helgaud of Fleury (c. 1041) and the son of Count Borrell are quoted by Riche, Gerbert d'Aurillac Gerbert d'Aurillac, 202, 234. Sergius IV (c. 1009- 1012) is translated by Anna Marie Flusche, The Life and Legend of Gerbert of Aurillac The Life and Legend of Gerbert of Aurillac, 75. "Surpa.s.sed his contemporaries," is from Thietmar of Merseburg (1013-1018), 303. "Acutely intelligent" is from Ralph the Bald (writing before 1030), 27. "Happy the state" is from Sigebert of Gembloux (c. 1070-1100), quoted by Henry Mayr-Harting, Church and Cosmos in Early Ottonian Germany Church and Cosmos in Early Ottonian Germany, 60. "Among those shining, shone exceedingly" is quoted by Landes, 312.

241 Beno: Beno: Allen traces the "dark legend of Gerbert" to Benno of Osnabruck and imputes to it a political reason, 664-668; as does Riche, Allen traces the "dark legend of Gerbert" to Benno of Osnabruck and imputes to it a political reason, 664-668; as does Riche, Gerbert d'Aurillac Gerbert d'Aurillac , 10; see also Darlington, "Gerbert the Teacher," 462. I follow Flusche in spelling his name "Beno"; rather than the German Benno from Osnabruck, the author of the dark legend was more likely the Italian Beno, cardinal-priest of the Church of SS Martino e Silvestro in Rome. The two may also be the same person; see Flusche, 82-86. The first to record the "R to R to R" joke was Helgaud of Fleury in his , 10; see also Darlington, "Gerbert the Teacher," 462. I follow Flusche in spelling his name "Beno"; rather than the German Benno from Osnabruck, the author of the dark legend was more likely the Italian Beno, cardinal-priest of the Church of SS Martino e Silvestro in Rome. The two may also be the same person; see Flusche, 82-86. The first to record the "R to R to R" joke was Helgaud of Fleury in his Life of King Robert Life of King Robert; see Riche, Gerbert d'Aurillac Gerbert d'Aurillac, 234.

241 Meridiana: Meridiana: Walter Map, Walter Map, De nugis curialium De nugis curialium, edited and translated by M. R. James, C. N. L. Brooke, and R. A. B. Mynors, 351-365.

242 Saracen philosopher: Saracen philosopher: William of Malmesbury, 279-289. William of Malmesbury, 279-289.

243 talking head: talking head: For Ibn Juljul's description, see Julio Samso, "Astrology, Pre-Islamic Spain, and the conquest of al-Andalus," in For Ibn Juljul's description, see Julio Samso, "Astrology, Pre-Islamic Spain, and the conquest of al-Andalus," in Islamic Astronomy and Medieval Spain Islamic Astronomy and Medieval Spain, Chap. 2, 86.

243 "best necromancer": "best necromancer": Michael Scot (c. 1175-1234), in Lynn Thorndike, Michael Scot (c. 1175-1234), in Lynn Thorndike, Michael Scot Michael Scot, 93-94.

243 Martin the Pole: Martin the Pole: Pascale Bourgain, "Silvestre II dans le Pascale Bourgain, "Silvestre II dans le Liber pontificalis Liber pontificalis," in Guyotjeannin and Poulle, 354-357.

244 Luther's disciples: Luther's disciples: Riche mentions the use of Gerbert's writing by the Protestants in his introduction to Gerbert's Riche mentions the use of Gerbert's writing by the Protestants in his introduction to Gerbert's Correspondance Correspondance, edited and translated (into French) by P. Riche and J.-P. Callu, xiv-xv; Riche discusses Cardinal Baronius in the same work, xvii-xix. See also Claude Grimmer, "Gerbert vu par le carme Geraud Vigier," in Guyotjeannin and Poulle, 358-360. Jules Michelet is quoted by Riche, Gerbert d'Aurillac Gerbert d'Aurillac, 13, and Les grandeurs de l'an mil Les grandeurs de l'an mil, 14.

247 "ancient chronicle": "ancient chronicle": Richard Erdoes, Richard Erdoes, A.D. 1000: Living on the Brink of Apocalypse A.D. 1000: Living on the Brink of Apocalypse , 1, 8. , 1, 8.

247 rediscover the Scientist Pope: rediscover the Scientist Pope: See Tim Roufs, "Inter-facing the Inevitable: Appropriate Technology in the 21st Century"; "Y1K: Web-Only Supplement to See Tim Roufs, "Inter-facing the Inevitable: Appropriate Technology in the 21st Century"; "Y1K: Web-Only Supplement to The Millennium Issue The Millennium Issue," Searcher Magazine Searcher Magazine, http://www.infotoday. com/searcher/jan00/y1k.htm.; Jay Ryan, "Gerbert d'Aurillac: Y1K's Science Guy," Sky & Telescope Sky & Telescope (February 2000): 38. See Pope John Paul II's letter at (February 2000): 38. See Pope John Paul II's letter at http://www.vatican.va/holy_father/john_paul_ii/speeches/1999/april. Also Keith Devlin's "The Mathematical Legacy of Islam," MAA On-line MAA On-line , , http://www.maa.org/devlin/devlin_0708_02.html; Kalpana Sahni's editorial from the Pakistan Daily Times Daily Times, October 21, 2006, http://dailytimes.com.pk/default.asp?page=2006%5C10%5C21%5Cstory_21-10-2006 _pg3_3; Pope Benedict XVI's message on the Year of Astronomy, http://www.vatican.va/holy_father/benedict_xvi/angelus/2008/doc.u.ments/hf_ben-xvi_ang_20081221_en.html.

BIBLIOGRAPHY.

Medieval Sources Abbo of Fleury and Ramsey. Commentary on the Calculus of Victorius of Aquitaine Commentary on the Calculus of Victorius of Aquitaine. Ed. A. M. Peden. Oxford University Press, 2003.

Adalbero (Ascelin) of Laon. Poeme au roi Robert Poeme au roi Robert. Ed. and tr. (into French) Claude Carozzi. Les Belles Lettres, 1979.

Ademar of Chabannes. Chronique Chronique. Ed. J. Chavanon. Collection de textes pour servir a l'etude et a l'enseignement de l'histoire 20, 1897.

Adso of Montier-en-Der. "Book of the Antichrist." In Apocalyptic Spirituality: Treatises and Letters of Lactantius, Adso of Montier-en-Der, Joachim of Fiore, the Spiritual Franciscans, Savonarola Apocalyptic Spirituality: Treatises and Letters of Lactantius, Adso of Montier-en-Der, Joachim of Fiore, the Spiritual Franciscans, Savonarola. Tr. Bernard McGinn. Cla.s.sics of Western Spirituality. Paulist Press, 1979.

Aelfric of Eynsham. AElfric's Colloquy AElfric's Colloquy. Tr. G. N. Garmonsway. University of Exeter Press, 1978.

Anon. Le Calendrier de Cordoue Le Calendrier de Cordoue. Ed. R. Dozy. Tr. (into French) Ch. Pellat. Brill, 1961.

Augustine of Hippo. The City of G.o.d The City of G.o.d. Tr. Marcus Dods. Christian Cla.s.sics Ethereal Library at Calvin College. Http://www.ccel.org/ccel/schaff/npnf102.iv.XVI.9.html.

---. The Literal Meaning of Genesis. The Literal Meaning of Genesis. Tr. J. H. Taylor. Newman Press, 1982. Tr. J. H. Taylor. Newman Press, 1982.

Benedict of Aniane. Saint Benedict's Rule for Monasteries Saint Benedict's Rule for Monasteries. Tr. Leonard J. Doyle. Order of Saint Benedict, 1948; reprint, 2001. Http://www.osb.org/rb/text/toc.html#toc.

Bernard of Angers. "Liber miraculorum sancte Fidis." In The Book of Sainte Foy The Book of Sainte Foy. Tr. Pamela Sheinborn. University of Pennsylvania Press, 1995.

Bernelin. Libre d'abaque Libre d'abaque. Ed. Beatrice Bakhouche and Jean Ca.s.sinet. Princi Neguer, 1999.

Boethius. The Consolation of Philosophy The Consolation of Philosophy. Tr. E. Watts. Penguin Books, 1969.

---. De inst.i.tutione arithmetica De inst.i.tutione arithmetica. In Boethian Number Theory Boethian Number Theory. Ed. and tr. Michael Masi. Rodopi, 1983.

---. De inst.i.tutione musica De inst.i.tutione musica. Selections in Source Readings in Music History Source Readings in Music History. Ed. O. Strunk. Norton, 1950.

Byrhtferth of Ramsey. Byrhtferth's Manual, A.D. 1011 Byrhtferth's Manual, A.D. 1011. Ed. and tr. S. J. Crawford. Early English Text Society, 1929.

Fulbert of Chartres. The Letters and Poems of Fulbert of Chartres The Letters and Poems of Fulbert of Chartres. Tr. Frederick Behrends. Clarendon Press, 1976.

Gerbert of Aurillac. Correspondance Correspondance. Ed. and tr. (into French) P. Riche and J.-P. Callu. Les Belles Lettres, 1993.

---. The Letters of Gerbert, with His Papal Privileges as Sylvester II The Letters of Gerbert, with His Papal Privileges as Sylvester II. Tr. Harriet Pratt Lattin. Columbia University Press, 1961.

---. Opera mathematica (972-1003) Opera mathematica (972-1003). Ed. Nicolai Bubnov. Berolini, 1899.

Guibert of Nogent. A Monk's Confession A Monk's Confession. Tr. Paul J. Archambault. Pennsylvania State University Press, 1996.

Hasdai ibn Shaprut. "The Epistle of R. Chisdai, Son of Isaac (of Blessed Memory) to the King of the Khozars (ca. 960)." In Jewish Travellers Jewish Travellers. Tr. Elkan Nathan Adler. Routledge, 1930.

Hrotsvit of Gandersheim. Hrotsvit of Gandersheim: A Florilegium of Her Works Hrotsvit of Gandersheim: A Florilegium of Her Works. Tr. Katharina Wilson. D. S. Brewer, 1998.

Ibn Hauqal, Muhammad. Configuration de la terre (Kitab surat al-Ard) Configuration de la terre (Kitab surat al-Ard). Tr. (into French) J. H. Kramers and G. Wiet. Commission internationale pour la traduction des chefs-d'oeuvre, 1964.

Ibn Juljul. "On the Translation of Dioscorides." In "The Early Growth of the Secular Sciences in Andalusia." Tr. George Hourani. Studia Islamica Studia Islamica 32 (1970): 155-156. 32 (1970): 155-156.

Isidore of Seville. Etymologies, Book II Etymologies, Book II. Tr. Peter K. Marshall. Les Belles Lettres, 1983.

Jean de Saint-Arnoul. La Vie de Jean, Abbe de Gorze La Vie de Jean, Abbe de Gorze. Ed. and tr. (into French) Michel Parisse. Picard, 1999.

John of Salerno. "The Life of Saint Odo of Cluny." In St Odo of Cluny St Odo of Cluny. Tr. Gerard Sitwell. Sheed and Ward, 1958.

Leo of Synada. "Amba.s.sade de Leon de Synades, envoye de Basile II a Otton III et au pape." In Epistoliers byzantins du Xe siecle Epistoliers byzantins du Xe siecle. Tr. (into French) J. Darrouzes. Archives de l'Orient chretien, 1960.

---. The Correspondence of Leo, Metropolitan of Synada and Syncellus The Correspondence of Leo, Metropolitan of Synada and Syncellus. Ed. and tr. Martha Pollard Vinson. Dumbarton Oaks Research Library and Collection, 1985.

Liudprand of Cremona. The Works of Liudprand of Cremona The Works of Liudprand of Cremona. Tr. F. A. Wright. Routledge, 1930.

Odilo of Cluny. "The Epitaph of Adelheid." In Queenship and Sanct.i.ty Queenship and Sanct.i.ty. Tr. Sean Gilsdorf. Catholic University of America Press, 2004.

Odo of Cluny. "The Life of Saint Gerald of Aurillac." In St Odo of Cluny St Odo of Cluny. Tr. Gerard Sitwell. Sheed and Ward, 1958.

Radulf of Liege and Ragimbold of Koln. "Letters." In Memoires scientifiques Memoires scientifiques. Ed. Paul Tannery. Vol. 5, 229-303. E. Privat, 1887-1921.

Ralph the Bald (Rodulfus Glaber). The Five Books of the Histories The Five Books of the Histories. Tr. John France, Neithard Bulst, and Paul Reynolds. Clarendon Press, 1989.

Richer of Saint-Remy. Histoire de France (888-995) Histoire de France (888-995). Ed. and tr. (into French) Robert Latouche. H. Champion, 1930-1937.

Synesius of Cyrene. "On the Astrolabe." In Livius.org: A Website on Ancient History . Tr. A. Fitzgerald. . Tr. A. Fitzgerald. Http://www.livius.org.

Thietmar of Merseberg. "Chronicon." In Ottonian Germany Ottonian Germany. Tr. David Warner. Manchester University Press, 2001.

Walter Map. De nugis curialium De nugis curialium. Ed. and tr. M. R. James, C. N. L. Brooke, and R. A. B. Mynors. Clarendon Press, 1983.

William of Malmesbury. Gesta Regum Anglorum Gesta Regum Anglorum. Tr. R. A. B. Mynors, R. M. Thomson, and M. Winterbottom. Vols. 1 and 2. Clarendon Press, 1998.

Modern Sources Allen, Roland. "Gerbert, Pope Silvester II." English Historical Review English Historical Review 7 (1892): 625-668. 7 (1892): 625-668.

Althoff, Gerd. Otto III Otto III. Pennsylvania State University Press, 2003.

Barthelemy, Dominique. L'an mil et la paix de Dieu L'an mil et la paix de Dieu. Fayard, 1999.

Bedos-Rezak, Brigitte. "Review of Autour de Gerbert d'Aurillac Autour de Gerbert d'Aurillac." Speculum Speculum 73 (1998): 528-531. 73 (1998): 528-531.

Bekken, Otto B. "Algorismus of Hauksbok Hauksbok." Http://home.hia.no/~ottob/.

Berggren, J. L. Episodes in the Mathematics of Medieval Islam Episodes in the Mathematics of Medieval Islam. Springer-Verlag, 1986.

Berkhofer, Robert F. Day of Reckoning Day of Reckoning. University of Pennsylvania Press, 2004.

---, ed. The Experience of Power in Medieval Europe The Experience of Power in Medieval Europe. Ashgate, 2005.

Bischoff, Bernhard. Ma.n.u.scripts and Libraries in the Age of Charlemagne Ma.n.u.scripts and Libraries in the Age of Charlemagne. Cambridge University Press, 1994.

Bonnery, Andre. L'abbaye Saint-Michel de Cuixa L'abbaye Saint-Michel de Cuixa. MSM, 2005.

Borrelli, Arianna. Aspects of the Astrolabe: "Architectonica Ratio" in Tenth- and Eleventh-Century Europe. Aspects of the Astrolabe: "Architectonica Ratio" in Tenth- and Eleventh-Century Europe. Franz Steiner Verlag, 2008. Franz Steiner Verlag, 2008.

Borst, Arno. The Ordering of Time The Ordering of Time. University of Chicago Press, 1993.

Bouchard, Constance Brittain. "Those of My Blood": Constructing n.o.ble Families in Medieval Francia "Those of My Blood": Constructing n.o.ble Families in Medieval Francia. University of Pennsylvania Press, 2001.

Bowman, Jeffrey. Shifting Landmarks Shifting Landmarks. Cornell University Press, 2004.

Bradbury, Jim. The Capetians The Capetians. Hambledon Continuum, 2007.

Brockett, Clyde W. "The Frontispiece of Paris, Bibl. Nat. Ms. Lat. 776: Gerbert's Acrostic Pattern Poems." Ma.n.u.scripta Ma.n.u.scripta 39 (1995): 3-25. 39 (1995): 3-25.

Brownrigg, Linda L., ed. Making the Medieval Book Making the Medieval Book. Anderson-Lovelace, 1995.

Bruce, Scott G. Silence and Sign Language in Medieval Monasticism Silence and Sign Language in Medieval Monasticism. Cambridge University Press, 2007.

Brunterc'h, Jean-Pierre. "Gerbert, archeveque de Ravenne et pape en Italie." In Gerbert: Moine, eveque, et pape Gerbert: Moine, eveque, et pape, 225-268. a.s.sociation catalienne pour la commemoration du pape Gerbert, 2000.

Bukofzer, F. "Speculative Thinking in Mediaeval Music." Speculum Speculum 17 (1942): 178-180. 17 (1942): 178-180.

Burnett, Charles. "The Abacus at Echternach in ca. 1000 AD." SCIAMVS SCIAMVS 3 (2002): 91-108. 3 (2002): 91-108.

---. "Algorismi vel helcep decentior est diligentia: The Arithmetic of Adelard of Bath and His Circle." In Mathematische Probleme im Mittelalter Mathematische Probleme im Mittelalter, ed. Menso Folkerts, 221-331. Harra.s.sotiz, 1996.

---. "King Ptolemy and Alchandreus the Philosopher." Annals of Science Annals of Science 55 (1998): 329-368. 55 (1998): 329-368.

---. Magic and Divination in the Middle Ages Magic and Divination in the Middle Ages. Ashgate, 1996.

---, ed. The Second Sense The Second Sense. Warburg Inst.i.tute, 1991.

Celli-Fraentzel, Anna. "Contemporary Reports on the Mediaeval Roman Climate." Speculum Speculum 7 (1932): 96-106. 7 (1932): 96-106.

Charbonnel, Nicole, and Jean-Eric Iung, eds. Gerbert l'Europeen: Acts du colloque d'Aurillac 4-7 juin 1996 Gerbert l'Europeen: Acts du colloque d'Aurillac 4-7 juin 1996. Societe des lettres, sciences et arts "La Haute-Auvergnes," 1997.

Chelini, Jean. "Rome et le Latran au temps de Sylvestre II." In Gerbert: Moine, eveque, et pape Gerbert: Moine, eveque, et pape, ed. Pierre Riche and Paul Poupard, 213-233. a.s.sociation catalienne pour la commemoration du pape Gerbert, 2000.

Clemens, Raymond, and Timothy Graham. Introduction to Ma.n.u.script Studies Introduction to Ma.n.u.script Studies. Cornell University Press, 2007.

Constable, Giles. "Dictators and Diplomats in the Eleventh and Twelfth Centuries." Dumbarton Oaks Papers Dumbarton Oaks Papers 46 (1992): 37-46. 46 (1992): 37-46.

Cushing, Kathleen G. Reform and the Papacy in the Eleventh Century Reform and the Papacy in the Eleventh Century. Manchester University Press, 2005.

Darlington, Oscar G. "Gerbert, 'obscuro loco natus.'" Speculum Speculum 11 (1936): 509-520. 11 (1936): 509-520.

---. "Gerbert the Teacher." American Historical Review American Historical Review 52 (1947): 456-476. 52 (1947): 456-476.

Davids, Adelbert, ed. The Empress Theophano The Empress Theophano. Cambridge University Press, 1995.

Des...o...b..s, Marcel. "Un astrolabe carolingien et l'origine de nos chiffres arabes." Archives internationales d'histoire des sciences Archives internationales d'histoire des sciences 15 (1962): 3-45. 15 (1962): 3-45.

Duckett, Eleanor. Death and Life in the Tenth Century Death and Life in the Tenth Century. University of Michigan Press, 1967.

Eastwood, Bruce. "Calcidius's Commentary on Plato's Timaeus Timaeus in Latin Astronomy of the Ninth to Eleventh Centuries." In in Latin Astronomy of the Ninth to Eleventh Centuries." In Between Demonstration and Imagination Between Demonstration and Imagination , ed. A. Nauta and A. Vanderjagt, 171-209. Brill, 1999. , ed. A. Nauta and A. Vanderjagt, 171-209. Brill, 1999.

---. "Invention and Reform in Latin Planetary Astronomy." In Latin Culture in the Eleventh Century: Proceedings of the Third International Conference on Medieval Latin Studies Latin Culture in the Eleventh Century: Proceedings of the Third International Conference on Medieval Latin Studies, ed. Michael W. Herren, C. J. McDonough, and Ross G. Arthur, 264-291. Brepols, 2003.

---. Ordering the Heavens Ordering the Heavens. Brill, 2007.

---. Planetary Diagrams for Roman Astronomy in Medieval Europe Planetary Diagrams for Roman Astronomy in Medieval Europe. American Philosophical Society, 2004.

---. The Revival of Planetary Astronomy in Carolingian and Post-Carolingian Europe The Revival of Planetary Astronomy in Carolingian and Post-Carolingian Europe. Ashgate, 2002.

Erdoes, Richard. A.D. 1000: Living on the Brink of Apocalypse A.D. 1000: Living on the Brink of Apocalypse. HarperCollins, 1988.

Evans, Gillian R. "Difficillima et Ardua: Theory and Practice in Treatises on the Abacus, 950-1150." Theory and Practice in Treatises on the Abacus, 950-1150." Journal of Medieval History Journal of Medieval History 3 (1977): 21-38. 3 (1977): 21-38.