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Jordanus de Nemore, 13th century mathematical innovator: an essay on intellectual context, achievement, and failure

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Bibliography

  • Archibald, R. C. (ed.), 1915. Euclid's Book on the Division of Figures with a Restoration Based on Woepcke's Text and on the Practica Geometriae of Leonardo Pisano. Cambridge: Cambridge University Press.

    Google Scholar 

  • [Aristotle, all works:] The Works of Aristotle. Translated into English under the Editorship of Sir David Ross. Oxford: The Clarendon Press, 1908–1952.

  • Baron, R., 1955. “Hugues de Saint-Victor, auteur d'une ‘practica geometriae’”. Mediaeval Studies 17, 107–116.

    Google Scholar 

  • Baron, R., 1955a. “Sur l'introduction en Occident des termes ‘geometria theorica et practica’”. Revue de l'Histoire des Sciences 8, 298–302.

    Google Scholar 

  • Baron, R. (ed.), 1956. “Hugonis de Sancto Victore Practica Geometriae: Introduction, texte”. Osiris 12, 176–224.

    Google Scholar 

  • Baur, L. (ed.), 1903. “Dominicus Gundissalinus, De divisione philosophiae, herausgegeben und philosophiegeschichtlich untersucht”. Beiträge zur Geschichte der Philosophie des Mittelalters. Texte und Untersuchungen, Bd. IV, Heft 2–3 (Münster).

  • Beati Alberti Magni, Ratisbonensis Episcopi, Ordinis Praedicatorum, Operum Tomus Secundus. Lyons 1651.

  • Beaujouan, G., 1961. “Le symbolisme des nombres à l'époque romane”. Cahiers de Civilisation Médiévale 4, 159–169.

    Google Scholar 

  • Bergmann, W., 1985. Innovationen im Quadrivium des 10. und 11. Jahrhunderts. Studien zur Einführung von Astrolab und Abakus im lateinischen Mittelalter. (Sudhoffs Archiv, Beihefte, 26). Wiesbaden: Franz Steiner.

    Google Scholar 

  • Birkenmajer, A., 1970/1922. “La bibliothèque de Richard de Fournival, poète et érudit français du début du XIII siècle, et son sort ultérieur”, in A. Birkenmajer, Études d'histoire des sciences et de la philosophie du Moyen Âge, pp. 117–215. (Studia Copernicana I). Wroclaw: Ossolińskich, 1970.

    Google Scholar 

  • Björnbo, A. A., 1905. “Gerhard von Cremonas Übersetzung von Alkhwarizmis Algebra und Euklids Elementen”. Biblioteca Mathematica, 3. Folge 6 (1905–1906), 239–248.

    MATH  Google Scholar 

  • Boncompagni, B., 1851. “Della vita e delle opere di Gherardo Cremonese, traduttore del secolo duodecimo, e di Gherardo da Sabbionette astronomo del secolo decimoterzo”. Atti dell' Accademia pontificia de' Nuovi Lincei 4 (1850–51), 387–493.

    Google Scholar 

  • Boncompagni, B. (ed.), 1857. Il Liber abaci di Leonardo Pisano. Roma: Tipografia delle Scienze matematiche e fisiche.

    Google Scholar 

  • Boncompagni, B. (ed.), 1857a. Trattati d'aritmetica. I–II [consecutive pagination]. Roma: Tipografia delle Scienze fisiche e matematiche.

    Google Scholar 

  • Boncompagni, B. (ed.), 1862. Leonardi Pisani Practica geometriae ed Opusculi. Roma: Tipografia delle Scienze matematiche e fisiche.

    Google Scholar 

  • Brewer, J. S. (ed.), 1859. Fr. Rogeri Bacon Opera quaedam hactenus inedita. Vol. I containing i, Opus tertium. ii, Opus minus, iii, Compendium philosophiae. (Rerum Britannicorum Medii Aevi Scriptores). London.

  • Bridges, J. H. (ed.), 1897. The Opus majus of Roger Bacon. I–II. London: The Clarendon Press. Suppl. volume, London: Williams & Norgate, 1900.

    Google Scholar 

  • Brown, J. E., 1967. “The Scientia de ponderibus in the Later Middle Ages”. Dissertation, The University of Wisconsin.

  • Brown, J. E., 1967a. [Abstract of Brown 1967]. Dissertation Abstracts International A 28 (1967–68), 3097.

    Google Scholar 

  • Bubnov, N. (ed.), 1899. Gerberti postea Silvestri II papae Opera mathematica. Berlin: Friedländer.

    Google Scholar 

  • Burke, R. B. (transl.), 1928. The Opus majus of Roger Bacon. I–II. Philadelphia: University of Pennsylvania Press.

    Google Scholar 

  • Busard, H. L. L., 1968. “L'algèbre au Moyen Âge: ‘Liber mensurationum’ d'Abu Bekr”. Journal des Savants, avril-juin, 65–125.

  • Busard, H. L. L., 1971. “Die Traktate De Proportionibus von Jordanus Nemorarius und Campanus”. Centaurus 15 (1970–71), 193–227.

    MATH  MathSciNet  Google Scholar 

  • Busard, H. L. L., 1972. “The Translation of the Elements of Euclid from the Arabic into Latin by Hermann of Carinthia (?), Books VII, VIII and IX”. Janus 59, 125–187.

    MATH  MathSciNet  Google Scholar 

  • Campbell, D. T., 1979. “A Tribal Model of the Social System Vehicle Carrying Scientific Knowledge”. Knowledge: Creation, Diffusion, Utilization 1, 181–200. (Also under a different title in Communication and Cognition 12 (1979), 245–264.)

    Google Scholar 

  • Cantin, A., 1974. “Sur quelques aspects des disputes publiques au XIe siècle latin”, in Études de civilisation médiévale (IX e–XIIe siècles). Mélanges offerts à Edmond-René Labande, pp. 89–104. Poitiers: C.E.S.C.M.

    Google Scholar 

  • Cantor, M., 1865. “Über einen Codex des Klosters Salem”. Zeitschrift für Mathematik und Physik 10, 1–16.

    Google Scholar 

  • Cantor, M., 1900. Vorlesungen über Geschichte der Mathematik. II. 2. Auflage. Leipzig: Teubner.

    Google Scholar 

  • Cantor, M., 1907. Vorlesungen über Geschichte der Mathematik. I. 3. Auflage. Leipzig: Teubner.

    Google Scholar 

  • Clagett, M., 1953. “The Medieval Latin Translations from the Arabic of the Elements of Euclid, with Special Emphasis on the Versions of Adelard of Bath”. Isis 44, 16–42.

    MATH  MathSciNet  Google Scholar 

  • Clagett, M., 1954. “The De curvis superficiebus Archimenidis: A Medieval Commentary of Johannes de Tinemue on Book I of the De sphaera et cylindro of Archimedes”. Osiris 11, 295–358.

    MATH  MathSciNet  Google Scholar 

  • Clagett, M., 1956. “The Liber de motu of Gerard of Brussels and the Origins of Kinematics in the West”. Osiris 12, 73–175.

    Article  MATH  MathSciNet  Google Scholar 

  • Clagett, M., G. Post & R. Reynolds (eds), 1961. Twelfth-Century Europe and the Foundations of Modern Society. Madison, Wisconsin: University of Wisconsin Press.

    Google Scholar 

  • Clagett, M., 1964. Archimedes in the Middle Ages. Vol. I. The Arabo-Latin Tradition. Madison, Wisconsin: University of Wisconsin Press.

    Google Scholar 

  • Clagett, M., 1971. “Archimedes in the Late Middle Ages”, in H. D. Roller (ed.), Perspectives in the History of Science and Technology, pp. 239–259. Norman, Oklahoma: University of Oklahoma, Press.

    Google Scholar 

  • Clagett, M., 1984. Archimedes in the Middle Ages. Vol. V. Quasi-Archimedean Geometry in the Thirteenth Century. (Memoirs of the American Philosophical Society 157 A+B). Philadelphia: The American Philosophical Society.

    Google Scholar 

  • Clerval, A., 1889. “L'enseignement des arts libéraux à Chartres et à Paris dans la première moitié du XIIe siècle, d'après l'Heptateuchon de Thierry de Chartres”, in Congrès Scientifque International des Catholiques, Paris 1888, vol. II pp. 277–297. Paris.

  • Colebrooke, H. T. (ed., transl.), 1817. Algebra, with Arithmetic and Mensuration from the Sanscrit of Brahmagupta and Bhascara. London: John Murray. Reprint Wiesbaden: Martin Sändig, 1973.

    Google Scholar 

  • Curtze, M. (ed.), 1887. “Jordani Nemorarii Geometria vel De triangulis Libri IV”. Mitteilungen des Coppernicusvereins für Wissenschaft und Kunst zu Thorn 6 (Thorn/Toruń).

  • Curtze, M., 1891. “Commentar zu dem ‘Tractatus de Numeris Datis’ des Jordanus Nemorarius”. Zeitschrift für Mathematik und Physik, Historisch-literarische Abteilung 36, 1–23, 41–63, 81–95, 121–138.

    MATH  Google Scholar 

  • Curtze, M., 1898. “Über eine Algorismusschrift des XII. Jahrhunderts”. Abhandlungen zur Geschichte der mathematischen Wissenschaften 8, 1–27.

    MATH  Google Scholar 

  • Curtze, M. (ed.), 1899. Anaritii in decem libros priores Elementorum Euclidis commentarii. Ex interpretatione Gherardi Cremonensis in Codice Cracoviensi 569 servata. (Euclidis Opera Omnia, supplementum). Leipzig: Teubner.

  • Curtze, M. (ed.), 1902. “Urkunden zur Geschichte der Mathematik im Mittelalter und der Renaissance”. Abhandlungen zur Geschichte der mathematischen Wissenschaften 12–13.

  • Dante, Inferno, in F. Chiapeplli (ed.), Opere di Dante Alighieri, pp. 449–567. Milano: Ugo Mursia, 1965.

    Google Scholar 

  • Delisle, L., 1868. Le cabinet des manuscrits de la Bibliothèque nationale. I–III. (Histoire générale de Paris. Collection de documents). Paris: Imprimerie nationale, 1868, 1874, 1881.

    Google Scholar 

  • Denifle, H., 1885. “Die Constitutionen des Prediger-Ordens vom Jahre 1228”. Archiv für Literatur- und Kirchengeschichte des Mittelalters 1, 165–227.

    Google Scholar 

  • Denifle, H., & É. Chatelain (eds), 1889. Chartularium Universitatis Parisiensis. I. Ab anno MCC ad annum MCCLXXXVI. Paris: Frères Delalain.

    Google Scholar 

  • [DSB:] Dictionary of Scientific Biography. I–XVI. New York: Scribner, 1970–80.

    Google Scholar 

  • Duby, G., 1973. Guerriers et Paysans. VII–XII e siècle: Premier essor de l'économie européenne. Paris: Gallimard.

    Google Scholar 

  • Eneström, G., 1906. “Über die ‘Demonstratio Jordani de algorismo’”. Bibliotheca Mathematica, 3. Folge 7 (1906–1907), 24–37.

    MATH  Google Scholar 

  • Eneström, G., 1907. “Über eine dem Nemorarius zugeschriebene kurze Algorismusschrift”. Bibliotheca Mathematica, 3. Folge 8 (1907–1908), 135–153.

    MATH  Google Scholar 

  • Eneström, G., 1912. “Der ‘Algorismus de integris’ des Meister Gernardus”. Bibliotheca Mathematica, 3. Folge 13 (1912–13), 289–332.

    MATH  Google Scholar 

  • Eneström, G., 1913. “Der ‘Algorismus de minutiis’ des Meister Gernardus”. Bibliotheca Mathematica, 3. Folge 14 (1913–14), 99–149.

    Google Scholar 

  • Eneström, G., 1913a. “Das Bruchrechnen des Nemorarius”. Bibliotheca Mathematica, 3. Folge 14 (1913–14), 41–54.

    MATH  Google Scholar 

  • Euclidis Megarensis mathematici clarissimi Elementorum libri XV. Cum expositione Theonis in priores XIII à Bartholomeo Veneto Latinitate donata, Campani in omnes & Hypsiclis in duos postremos ... Basel: Johannes Hervagius, 1546.

  • Evans, G. R., 1975. “The Influence of Quadrivium Studies in the Eleventh and Twelfth Century Schools”. Journal of Mediaeval History 1, 151–164.

    Google Scholar 

  • Evans, G. R., 1976. “The Rithmomachia: A Mediaeval Mathematical Teaching Aid?” Janus 63, 257–271.

    MATH  MathSciNet  Google Scholar 

  • Evans, G. R., 1976a. “The ‘Sub-Euclidean’ Geometry of the Earlier Middle Ages, up to the Mid-Twelfth Century”. Archive for History of Exact Sciences 16 (1976–77), 105–118.

    Article  MATH  MathSciNet  Google Scholar 

  • Evans, G. R., 1978. “Introductions to Boethius's ‘Arithmetica’ of the Tenth to the Fourteenth Century”. History of Science 16, 22–41.

    MathSciNet  Google Scholar 

  • Evans, G. R., 1981. “Boethius' Geometry and the Four Ways”. Centaurus 25, 161–165.

    MATH  Google Scholar 

  • Folkerts, M., 1970. ‘Boethius’ Geometrie II. Ein mathematisches Lehrbuch des Mittelalters. Wiesbaden: Franz Steiner.

    Google Scholar 

  • Friedlein, G. (ed.), 1867. Anicii Manlii Torquatii Severini Boetii De institutione arithmetica libri duo, De institutione musica libri quinque. Accedit Geometria quae fertur Boetii. Leipzig: Teubner.

    Google Scholar 

  • Gauss, J., 1966. “Anselm von Canterbury. Zur Begegnung und Auseinandersetzung der Religionen”. Saeculum 17, 277–363.

    Google Scholar 

  • Gibson, S. (ed.), 1931. Statuta antiqua Universitatis Oxoniensis. Oxford: The Clarendon Press.

    Google Scholar 

  • Gilson, É., 1955. History of Christian Philosophy in the Middle Ages. London: Sheed and Ward.

    Google Scholar 

  • Glacken, C. J., 1967. Traces on the Rhodian Shore. Nature and Culture in Western Thought from Ancient Times to the End of the Eighteenth Century. Berkeley & Los Angeles: University of California Press.

    Google Scholar 

  • Goldat, G. D., 1957. “The Early Medieval Traditions of Euclid's Elements”. Dissertation, The University of Wisconsin.

  • Grabmann, M., 1930. “Mitteilungen aus Münchner Handschriften über bisher unbekannte Philosophen der Artistenfakultät (Codd. lat. 14246 and 14383)”, in Festschrift für Georg Leidinger zum 60. Geburtstag am 30. December 1930, pp. 73–83. München: Hugo Schmidt.

    Google Scholar 

  • Grabmann, M., 1941. “I divieti ecclesiastici di Aristotele sotto Innocenzo III e Gregorio IX”. Miscellanea Historiae Ecclesiasticae in Pontificiae Universitate Gregoriana, vol. V. 1 (collectionis totius n. 7). (Roma: Saler).

    Google Scholar 

  • Grant, E. (ed.), 1974, A Source Book in Mediaeval Science. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Grossmann, U., 1954. “Studien zur Zahlensymbolik des Frühmittelalters”. Zeitschrift für Katholische Theologie 76, 19–54.

    Google Scholar 

  • Günther, S., 1887. Geschichte des mathematischen Unterrichts im deutschen Mittelalter. (Monumenta Germaniae Paedagogica III). Berlin.

  • Haskins, Ch. H., 1924. Studies in the History of Medieaval Science. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Haskins, Ch. H., 1976. The Renaissance of the Twelfth Century. Cambridge, MA: Harvard University Press. 1st ed. 1927.

    Google Scholar 

  • Heiberg, J. L. (ed.), 1907. Claudii Ptolemaei Opera astronomica minora. Leipzig: Teubner.

    Google Scholar 

  • Heitz, C., 1976. “Symbolisme et architecture. Les nombres et l'architecture religieuse du haut Moyen Âge”. Settimane di studio del Centro Italiano di Studi sull'alto Medioevo 23 (Spoleto), 387–418, tav. 1–24, discussione 421–427.

  • Hermelink, H., 1978. “Arabic Recreational Mathematics as a Mirror of Age-Old Cultural Relations Between Eastern and Western Civilizations”, in A. Y. Al-Hassan et al. (eds), Proceedings of the First International Symposium for the History of Arabic Science, April 5–12, 1976, vol. II pp. 44–52. Aleppo: Institute for the History of Arabic Science.

    Google Scholar 

  • Holmes, U. T., 1961. “Transitions in European Education”, in Clagett et al. 1961: 15–38.

  • Høyrup, J., 1980. “Influences of Institutionalized Mathematics Teaching on the Development and Organization of Mathematical Thought in the Pre-Modern Period”. Materialien und Studien. Institut für Didaktik der Mathematik der Universität Bielefeld 20, 7–137.

    Google Scholar 

  • Høyrup, J., 1985. “Varieties of Mathematical Discourse in Pre-Modern Socio-Cultural Contexts: Mesopotamia, Greece, and the Latin Middle Ages”. Science & Society 49 (1985), 4–41.

    Google Scholar 

  • Hughes, B. B., 1970. “The De numeris datis of Jordanus de Nemore: A Critical Edition, Analysis, Evaluation and Translation, Latin Text”. Dissertation, Stanford University.

  • Hughes, B. B., 1972. “Johann Scheubel's Revision of Jordanus de Nemore's De numeris datis: An Analysis of an Unpublished Manuscript”. Isis 63, 221–234.

    MATH  MathSciNet  Google Scholar 

  • Hughes, B. B., 1975. “Biographical Information on Jordanus de Nemore to Date”. Janus 62, 151–156.

    MathSciNet  Google Scholar 

  • Hughes, B., 1981. Jordanus Nemorarius, De numeris datis. A Critical Edition and Translation. (Publications of the Center for Medieval and Renaissance Studies, UCLA, 14). Berkeley: University of California Press.

    Google Scholar 

  • Hunt, R. W., 1955. “The Library of Robert Grosseteste”, in D. A. Callus (ed.), Robert Grosseteste. Scholar and Bishop, pp. 121–145. Oxford: Oxford University Press.

    Google Scholar 

  • Ito, S., 1980. The Medieval Latin Translation of the Data of Euclid. Basel, Boston, Stuttgart: Birkhäuser/Tokyo: University of Tokyo Press.

    Google Scholar 

  • Jones, Ch. W. (ed.), 1943. Bedae Opera de temporibus (The Mediaeval Academy of America, Publication N° 41). Cambridge, MA: The Medieval Academy of America.

    Google Scholar 

  • Jones, L. W. (ed., transl.), 1946. An Introduction to Divine and Human Reading, by Cassiodorus Senator. Translated with an Introduction and Notes. New York: Columbia University Press.

    Google Scholar 

  • Karpinski, L. Ch., 1911. “The Algebra of Abu Kamil Shoja° ben Aslam”. Biblioteca Mathematica, 3. Folge 12 (1911–12), 40–55.

    MATH  Google Scholar 

  • Karpinski, L. Ch. (ed. transl.), 1915. Robert of Chester's Latin Translation of the Algebra of al-Khowarizmi. (University of Michigan Studies, Humanistic Series, vol. 11). New York: Macmillan.

    Google Scholar 

  • Katzenellenbogen, A., 1961. “The Representation of the Seven Liberal Arts”, in M. Clagett et al. 1961: 39–55.

  • King, J. E. (transl.), 1930. Baedae Opera historica. Vol. I. Cambridge, MA: Harvard University Press/London: Heinemann.

    Google Scholar 

  • Klebs, A. C., 1938. “Incunabula scientifica et medica”. Osiris 4, 1–359.

    Article  MATH  Google Scholar 

  • Klinkenberg, H. M., 1959. “Der Verfall des Quadriviums im frühen Mittelalter”, in J. Koch (ed.), Artes liberales von der Antiken Bildung zur Wissenschaft des Mittelalters, pp. 1–32. (Studien und Texte zur Geistesgeschichte des Mittelalters, Bd. 5). Leiden & Köln: Brill.

    Google Scholar 

  • Krasnova, S. A. (ed., transl.), 1966. “Abu-l-Vafa al-Buzdžani, Kniga o tom, čto neobchodimo remeslenniku iz geometričeskich postroenij”, in Fiziko-matematičeskie nauki v stranach Vostoka. Sbornik statej i publikacij, vypusk I (IV), pp. 42–140. Moscow: Izdatel'stvo “Nauka”.

    Google Scholar 

  • Kristeller, O., 1961. Renaissance Thought. The Classic, Scholastic, and Humanistic Strains. New York: Harper & Brothers.

    Google Scholar 

  • [Le Fevre d'Étaples, Jacques (ed.)] 1514. In hoc opere contenta/Arithmetica decem libris demonstrata. Musica libris demonstrata quatuor. Epitome in libros Arithmeticos diui Seuerini Boetij. Rithmimachie ludus qui et pugna numerorum appellatur. Paris: Henricus Stephanus.

    Google Scholar 

  • Lemay, R., 1962. Abu Ma°shar and Latin Aristotelianism in the Twelfth Century. The Recovery of Aristotle's Natural Philosophy through Arabic Astrology. Beirut: American University of Beirut.

    Google Scholar 

  • Levey, M. (ed., transl.), 1966. The Algebra of Abū Kāmil, Kitāb fī al-jābr wa'l-muqābala, in a Commentary by Mordecai Finzi. Hebrew Text, Translation, and Commentary with Special Reference to the Arabic Text. Madison, Milwaukee, London: University of Wisconsin Press.

    Google Scholar 

  • L'Huillier, Gh., 1980. “Regiomontanus et le Quadripartitum numerorum de Jean de Murs”. Revue d'Histoire des Sciences 33, 193–214.

    MATH  MathSciNet  Google Scholar 

  • Libri, G., 1838. Histoire des sciences mathématiques en Italie. I–IV. Paris: 1838–1841. Reprint Hildesheim: Olms, 1967.

    Google Scholar 

  • Lubar, S., 1977. “The Algebra of Jordanus of Nemore: The Arabic Influence”. Synthesis. The Undergraduate Journal in the History and Philosophy of Science 3: 4, 33–43.

    Google Scholar 

  • Luckey, P., 1941. “\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{T} \)abit b. Qurra über den geometrischen Richtigkeitsnachweis der Auflösung der quadratischen Gleichungen”. Berichte der Mathematisch-Physischen Klasse der Sächsischen Akademie der Wissenschaften zu Leipzig 93, 93–114.

    MATH  MathSciNet  Google Scholar 

  • Manitius, K. (ed., transl.), 1912. Des Claudius Ptolemäus Handbuch der Astronomie. I-II. Leipzig: Teubner.

    Google Scholar 

  • Matvievskaya, G. P., 1981. “On Some Problems of the History of Mathematics and Astronomy of the Middle East”, in XVIth International Congress of the History of Science. Papers by Soviet Scientists: The 1000th Anniversary of Ibn Sina's Birth (Avicenna), pp. 21–31. Moscow: “Nauka”.

    Google Scholar 

  • Meerssemann, G. C., 1958. “In libris gentilium non studeant. L'étude des classiques interdite aux clercs au Moyen Âge?”. Italia Medioevale e Umanistica 1 (Padova), 1–13.

    Google Scholar 

  • Meyer, H., 1975. Die Zahlenallegorese im Mittelalter: Methode und Gebrauch. (Münstersche Mittelalter-Schriften, 25). München: Wilhelm Fink.

    Google Scholar 

  • Moody, E. A., & M. Clagett (eds., transl.), 1952. The Medieval Science of Weights (Scientia de ponderibus). Treatises Ascribed to Euclid, Archimedes, Thabit ibn Qurra, Jordanus de Nemore and Blasius of Parma. Madison: Wisconsin: University of Wisconsin Press.

    Google Scholar 

  • Muckle, J. T., C. S. B., (ed.), 1950. “Abelard's Letter of Consolation to a Friend (Historia calamitatum)”. Mediaeval Studies 12, 163–213.

    Google Scholar 

  • Müller, M. (ed.), 1934. “Die Quaestiones naturales des Adelardus von Bath, herausgegeben und untersucht”. Beiträge zur Geschichte der Philosophie des Mittelalters. Texte und Untersuchungen Bd. XXXI Heft 2 (Münster).

  • Murdoch, J. E., 1968. “The Medieval Euclid: Salient Aspects of the Translations of the Elements by Adelard of Bath and Campanus of Novara”. Revue de Synthèse 89, 67–94.

    Google Scholar 

  • Murray, A., 1978. Reason and Society in the Middle Ages. Oxford: Oxford University Press.

    Google Scholar 

  • Palencia, Á. G. (ed., transl.), 1953. Al-Fārābī, Catálogo de las ciencias. Segunda edición. Madrid: Consejo Superior de Investigaciones Científicas, Instituto Miguel Asín.

  • Pidal, R. M. (ed.), 1963. Poema de mío Cid. Sexta edición. (Colección Crisól, 96). Madrid: Aguilar.

    Google Scholar 

  • [PL:] Patrologiae cursus completus, series latina, accurante J.-P. Migne. 221 vols. Paris, 1844–64. Reprints Paris: Garnier, & Turnhout: Brepols.

  • Rashdall, H., 1936. The Universities of Europe in the Middle Ages. A New Edition in three Volumes Edited by F. M. Powicke & A. B. Emden. Oxford: The Clarendon Press. 1st ed. 1895.

    Google Scholar 

  • Reynolds, R. E., 1979. “‘At sixes and Sevens’—and Eights and Nines: The Sacred Mathematics of Sacred Orders in the Early Middle Ages”. Speculum 54, 669–684.

    Google Scholar 

  • Riché, P., 1979. Les écoles de l'Occident chrétien de la fin du V e siècle au milieu du XI e siècle. Paris: Aubier Montaigne.

    Google Scholar 

  • Robinson, J., 1964. Economic Philosophy. Harmondsworth, Middlesex: Penguin. 1st ed. 1962.

    Google Scholar 

  • Rose, P. L., 1975. The Italian Renaissance of Mathematics. Studies on Humanists and Mathematicians from Petrarch to Galileo. (Travaux d'humanisme et renaissance CXLV). Genéve: Droz.

    Google Scholar 

  • Rosen, F. (ed., transl.), 1831. The Algebra of Muhammed ben Musa. London: The Oriental Translation Fund.

    Google Scholar 

  • Rouse, R. H., 1967. “The Early Library of the Sorbonne”. Scriptorium 21, 42–71.

    Google Scholar 

  • Rouse, R. H., 1971. “The A Text of Seneca's Tragedies in the Thirteenth Century”. Revue d'Histoire des Textes 1, 93–121.

    Google Scholar 

  • Rouse, R. H., 1973. “Manuscripts Belonging to Richard de Fournival”. Revue d'histoire des Textes 3, 253–269.

    Google Scholar 

  • Rousset, P., 1963. “La notion de Chrétienté aux XIe et XIIe siècles”. Le Moyen Âge 69, 191–203.

    Google Scholar 

  • Saidan, A. S. (ed., transl.), 1978. The Arithmetic of al-Uqlīdisī. Dordrecht: Reidel.

    Google Scholar 

  • Sarton, G., 1931. Introduction to the History of Science. II. From Rabbi ben Ezra to Roger Bacon. [In two parts, consecutive pagination]. Baltimore: William & Wilkins.

    Google Scholar 

  • Sarton, G., 1947. Introduction to the History of Science. III: Science and Learning in the Fourteenth Century. [In two parts, consecutive pagination]. Baltimore: Wiliam & Wilkins, 1947–48.

    Google Scholar 

  • Sayili, A., 1962. Logical Necessities in Mixed Equations by ° Abd al Hamîd ibn Turk and the Algebra of His Time. Ankara: Türk Tarih Kurumu Basımevi.

    Google Scholar 

  • Sesiano, J., 1984. “Une arithmétique médiévale en langue provençale”. Centaurus 27, 26–75.

    MATH  MathSciNet  Google Scholar 

  • Smith, D. E., & C. C. Eaton, 1911. “Rithmomachia, the Great Medieval Number Game”. American Mathematical Monthly 18: 4, 73–80.

    MathSciNet  Google Scholar 

  • Southern, R. W., 1953. The Making of the Midlde Ages. London: Hutchinson.

    Google Scholar 

  • Southern, R. W., 1962. Western Views of Islam in the Middle Ages. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Southern, R. W., 1970. Medieval Humanism and Other Studies. Oxford: Blackwell.

    Google Scholar 

  • Stahl, W. H., 1971. Martianus Capella and the Seven Liberal Arts. I. The Quadrivium of Martianus Capella. Latin Traditions in the Mathematical Sciences, 50 B. C.-A. D. 1250. New York: Columbia University Press.

    Google Scholar 

  • Steele, R. (ed.), 1940. Communia mathematica fratris Rogeri partes prima et secunda. (Opera hactenus inedita Rogeri Baconi, fasc. XVI). Oxford: The Clarendon Press.

    Google Scholar 

  • Steenberghen, F. van, 1966. La philosophie au XIII e siècle. Louvain: Publications Universitaires/Paris: Béatrice-Nauwelaerts.

    Google Scholar 

  • Steinschneider, M., 1865. Die ‘mittleren Bücher’ der Araber und ihre Bearbeiter”. Zeitschrift für Mathematik und Physik 10, 456–498.

    Google Scholar 

  • Steinschneider, M., 1904. “Die europäischen Übersetzungen aus dem arabischen bis Mitte des 17. Jahrhunderts. I. Schriften bekannter Übersetzer”. Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften in Wien, philosophisch-historische Klasse, Bd. CXLIX/iv.

  • Stevens, W. M., 1971. “Walahfrid Strabo—a Student at Fulda”. Canadian Historical Association. Historical Papers 1971, 13–20.

  • Stevens, W. M., 1979. “Compotistica et astronomica in the Fulda School”, in M. H. King & W. M. Stevens (eds), Saints, Scholars, and Heroes: Studies in Medieval Culture in Honour of Charles W. Jones, vol. II pp. 27–63. Collegeville, Minnesota: St. John's University Press.

    Google Scholar 

  • Suter, H., 1909. “Die Abhandlung des Abū Kāmil Shōǵā° b. Aslam ‘über das Fünfeck und Zehneck’”. Bibliotheca Mathematica, 3. Folge 10 (1909–10), 15–42.

    Google Scholar 

  • Suter, H., 1910. “Das Buch der Seltenheiten der Rechenkunst von Abū Kāmil el-Mi\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{s} \)rī”. Bibliotheca Mathematica, 3. Folge 11 (1910–11), 100–120.

    MATH  Google Scholar 

  • Tannery, P., 1922. Mémoires Scientifiques. Tôme V. Sciences exactes au Moyen Âge, 1887–1921. Toulouse: Edouard Privat/Paris: Gauthier-Villars.

    Google Scholar 

  • Thaer, C. (ed., transl.), 1962. Die Data von Euklid. Nach Menges Text aus dem Griechischen übersetzt und herausgegeben. Berlin: Springer.

    Google Scholar 

  • Thompson, J. W., 1929. “The Introduction of Arabic Science into Lorraine in the Tenth Century”. Isis 12, 184–193.

    Article  MATH  Google Scholar 

  • Thomson, R. B., 1974. “Jordanus de Nemore and the University of Toulouse”. The British Journal of the History of Science 7, 163–165.

    MATH  MathSciNet  Google Scholar 

  • Thomson, R. B., 1976. “Jordanus de Nemore: Opera.” Mediaeval Studies 38, 97–144.

    Google Scholar 

  • Thomson, R. B. (ed., transl.), 1978. Jordanus de Nemore and the Mathematics of astrolabes: DE PLANA SPERA. An Edition with Introduction, Translation and Commentary. Toronto: Pontifical Institute of Mediaeval Studies.

    Google Scholar 

  • Thomson, W., & G. Junge (eds, transl.), 1930. The Commentary of Pappus on Book X of Euclid's Elements. (Harvard Semitic Series, vol. VIII). Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Thorndike, L., 1944. University Records and Life in the Middle Ages. New York: Columbia University Press.

    Google Scholar 

  • Trabucco, J. (ed., transl.), 1960. Saint Augustin, Les Confessions. I–II. Paris: Garnier.

    Google Scholar 

  • Treutlein, P., 1877. “Intorno ad alcuni scritti inediti relativi al calcolo dell'abaco”. Bulletino di bibliografia e di storia delle scienze matematiche e fisiche 10, 589–594.

    MATH  Google Scholar 

  • Treutlein, P., 1877a. “Scritti inediti relativi al calcolo dell'abaco”. Bulletino di bibliografia e di storia delle scienze matematiche e fisiche 10, 595–647.

    MATH  Google Scholar 

  • Tropfke, J., 1980. Geschichte der Elementarmathematik. 4. Auflage. Bd. 1. Arithmetik und Algebra. Vollständig neu bearbeitet von Kurt Vogel et al. Berlin & New York: de Gruyter.

    Google Scholar 

  • Ullman, B. L., 1964. “Geometry in the Medieval Quadrivium”, in Studi di Bibliografia e di Storia in Onore di Tammaro di Marinis, vol. IV, pp. 263–285. Verona: Giovanni Mardersteig.

    Google Scholar 

  • Van der Vyver, A., 1929. “Les étapes du développement philosophique du haut Moyen-Âge”. Revue Belge de Philologie et d'Histoire 8, 425–452.

    Google Scholar 

  • Van der Vyver, A., 1936. “Les plus anciennes Traductions latines médiévales (Xe–XIe siècles) de Traités d'Astronomie et d'Astrologie”. Osiris 1, 658–691.

    MATH  Google Scholar 

  • van Ryzin, Sister Mary St. Martin, 1960. “The Arabo-Latin Tradition of Euclid's Elements in the Twelfth Century”. Dissertation, University of Wisconsin.

  • Ver Eecke, P. (ed., transl.), 1926. Diophante d'Alexandrie, Les six livres arithmétiques et Le livre des nombres polygones. Bruges: De Brouwer.

    Google Scholar 

  • Vleeschauwer, H. J. de, 1965, “La BIBLIONOMIA de Richard de Fournival du manuscrit 636 de la Bibliothèque de la Sorbonne. Texte en facsimilé avec la transcription de Léopold Delisle”. Mousaion 62 (Pretoria).

  • Vogel, K. (ed.), 1963. Mohammed ibn Musa Alchwarizmi's Algorismus. Aalen: Zeller.

  • Vogel, K., 1982. “Zur Geschichte der Stammbrüche und der aufsteigenden Kettenbrüche”. Sudhoffs Archiv 66, 1–19.

    MATH  MathSciNet  Google Scholar 

  • Vossen, P. (ed., transl.), 1962. Der Libellus Scolasticus des Walther von Speyer. Ein Schulbericht aus dem Jahre 984. Berlin: De Gruyter.

    Google Scholar 

  • Vuillemin-Diem, G. (ed.), 1970. Aristoteles latinus XXV i-i a: Metaphysica lib. i–iv. 4, Translatio Iacobi sive ‘Vetustissima’ cum scholiis et Translatio Composita sive ‘Vetus’. Leiden: Brill.

    Google Scholar 

  • Waters, E. G. R., 1928. “A Thirteenth Century Algorism in French Verse”. Isis 11, 45–84.

    MATH  Google Scholar 

  • Watt, W. Montgomery, 1973. “L'influence de l'Islam sur l'Europe médiévale”. Revue des études islamiques 41, 129–156.

    Google Scholar 

  • Werner, E., 1976. “Stadtluft macht frei: Frühscholastik und bürgerliche Emancipation in der ersten Hälfte des 12. Jahrhunderts”. Sitzungsberichte der sächsischen Akademie der Wissenschaften zu Leipzig, Philologisch-historische Klasse 118, Heft 5.

  • Wickersheimer, E., 1936. Dictionnaire biographique des médecins en France au Moyen Âge. I–II. Paris: Droz.

    Google Scholar 

  • Wiedemann, E., 1970/1926. “Über eine besondere Art des Gesellschaftsrechnens nach Ibn al Haitam”, in id., Aufsätze zur arabischen Wissenschaftsgeschichte II, pp. 616–621. Hildesheim & New York: Olms. Reprint from Sitzungsberichte der Physikalisch-Medizinischen Sozietät zu Erlangen 58–59 (1926–27), 616–621.

  • Wiesen, D. S. (transl.), 1968. Saint Augustine, The City of God Against the Pagans, vol. III. London: Heinemann/Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Woepcke, F., 1853. Extrait du Fakhrî, traité d'algèbre par Aboû Bekr Mohammed ben Alhaçan Alkharkî; précédé d'un mémoire sur l'algèbre indéterminé chez les arabes. Paris: Imprimerie Impériale.

    Google Scholar 

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  1. Institute of Educational Research Media Studies & Theory of Science, Roskilde University Centre, Denmark

    Jens Høyrup

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Communicated by J. D. North

Franz Woepcke, Moritz Cantor, Maximilian Curtze, Heinrich Suter and Axel Anthon Bjørnbo in memoriam

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Høyrup, J. Jordanus de Nemore, 13th century mathematical innovator: an essay on intellectual context, achievement, and failure. Arch. Hist. Exact Sci. 38, 307–363 (1988). https://doi.org/10.1007/BF00357064

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