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Cette thèse se propose de déterminer les apports d’Oronce Fine (1494-1555) à la philosophie des mathématiques de la Renaissance. En tant que premier titulaire de la première chaire royale de mathématiques, ce mathématicien a joué un rôle important dans la revalorisation de l’enseignement des mathématiques dans la France du XVIe siècle. Dans cette mesure, sa conception des mathématiques permet de montrer l’évolution du statut épistémologique et institutionnel de ces disciplines dans le milieu académique parisien de cette période. Parmi les thèmes abordés par Fine dans sa définition du statut des mathématiques, nous avons choisi d’étudier, dans une première partie, la nature des objets du mathématicien, le statut épistémologique de l’astronomie, la nature des procédures démonstratives et des principes des mathématiques, ainsi que la fonction du quadrivium dans le processus éducatif. Dans une seconde partie, notre analyse de la pensée de Fine porte sur le statut des mathématiques pratiques et des disciplines subalternes des mathématiques, à savoir la perspective et la géométrie, ainsi que sur le profit qui peut être obtenu de l’apprentissage du quadrivium. / The aim of this study is to determine the contributions of Oronce Fine (1494-1555) to Renaissance philosophy of mathematics. As first Royal lecturer in mathematics, Fine played a major part in the reassertion of the value of mathematical teaching in sixteenth-century France. Thus, his thought concerning mathematics allows to set forth the evolution of the epistemological and institutional status of these sciences within the parisian academic context of the period. Among the questions tackled by Fine in his definition of the status of mathematics, we consider, in a first part, the ontological status of mathematical things, the epistemological status of astronomy, the nature of mathematical demonstrations and principles, as well as the function of the quadrivium in the educative process. In a second part, our analysis of Fine’s conception on mathematics deals with the status of practical mathematics and of the sciences which are subalternated to mathematics, that is optics and geography, concluding with the definition of the profit which may be obtained from learning mathematics.

O tratado Speculum Musicae do Magister Jacobus de Ispania (ou Jacobus Leodiensis) não recebeu a devida visibilidade nas instituições de ensino e de investigação intelectual tanto de sua época quanto posteriormente. A partir da segunda metade do século XX o tratado foi gradualmente ganhando maior visibilidade e nos últimos anos tem recebido por parte de diversos estudiosos um maior esforço de investigação. A presente dissertação visa expor o contexto filosófico e teológico desse tratado, investigando os seus principais conceitos norteadores a partir de uma leitura dos primeiros capítulos do seu primeiro livro. A partir da exposição dessas concepções fundamentais, buscamos então esclarecer algumas das questões mais fundamentais a respeito da musica speculativa, a saber, sua função no programa das artes liberais, sua concepção enquanto ciência e sua relação com a teologia sagrada. / Magister Jacobus de Ispania\'s treatise, Speculum Musicae, did not receive the due visibility in the educational and scholarly institutions of its time as well as later. From the second half of the twentieth century the treatise gradually gained more visibility and in recent years has received from several scholars a greater research effort. The present dissertation aims at exposing the philosophical and theological context of this treatise and investigating its main guiding concepts through a reading of the first chapters of its first book. Through the exposition of these fundamental conceptions, we seek to clarify some of the most fundamental questions regarding speculative music, namely, its function in the liberal arts program, its conception as a science and its relation to sacred theology.

O tratado Speculum Musicae do Magister Jacobus de Ispania (ou Jacobus Leodiensis) não recebeu a devida visibilidade nas instituições de ensino e de investigação intelectual tanto de sua época quanto posteriormente. A partir da segunda metade do século XX o tratado foi gradualmente ganhando maior visibilidade e nos últimos anos tem recebido por parte de diversos estudiosos um maior esforço de investigação. A presente dissertação visa expor o contexto filosófico e teológico desse tratado, investigando os seus principais conceitos norteadores a partir de uma leitura dos primeiros capítulos do seu primeiro livro. A partir da exposição dessas concepções fundamentais, buscamos então esclarecer algumas das questões mais fundamentais a respeito da musica speculativa, a saber, sua função no programa das artes liberais, sua concepção enquanto ciência e sua relação com a teologia sagrada. / Magister Jacobus de Ispania\'s treatise, Speculum Musicae, did not receive the due visibility in the educational and scholarly institutions of its time as well as later. From the second half of the twentieth century the treatise gradually gained more visibility and in recent years has received from several scholars a greater research effort. The present dissertation aims at exposing the philosophical and theological context of this treatise and investigating its main guiding concepts through a reading of the first chapters of its first book. Through the exposition of these fundamental conceptions, we seek to clarify some of the most fundamental questions regarding speculative music, namely, its function in the liberal arts program, its conception as a science and its relation to sacred theology.

Auteur romain du 6ème siècle connu pour ses traductions en latin des textes en grec d’Aristote, Boèce a aussi rédigé une traduction-adaptation d’un texte de Nicomaque de Gérase sur l’arithmétique. La première partie de ce mémoire de maîtrise est consacrée à l’étude de Boèce en tant que passeur de savoir. Sa relation avec son père adoptif est mise en valeur afin de soutenir l’hypothèse selon laquelle Boèce aurait acquis sa connaissance du grec et son éducation tout en restant à Rome, sans avoir séjourné dans les écoles athéniennes ou alexandriennes. La deuxième partie porte sur le contenu mathématique du De institutione arithmetica. Après avoir montré comment le De arithmetica était relié à l’oeuvre de traduction par Boèce des philosophes grecs, le choix de l’Introduction à l’Arithmétique de Nicomaque comme point de départ du traité d’arithmétique de Boèce est étudié. Un catalogue raisonné des concepts mathématiques présentés est ensuite proposé, organisé autour des notions de quantité en soi et quantité relative qui conservent l’opposition entre le Même et l’Autre et rappellent l’opposition fondamentale entre Limité et Illimité, si chère aux pythagoriciens. Ce mémoire se termine par une analyse de la transmission du De institutione arithmetica et de son influence sur les mathématiques et l’enseignement du quadrivium au Moyen-Âge. / Roman author of the 6th century known for his Latin translations of Aristotle’s Greek texts, Boethius has also composed a translation-adaptation of a treatise on arithmetics written by Nicomachus of Gerasa. The first section of this master’s thesis focuses on characterizing Boethius as a intermediary, transferring Greek knowledge to the Latin West. His relationship with Symmachus is highlighted in order to argue that Boethius had been able to learn Greek and reach such a high level of learning in Rome, without the need to study in the Athenian or Alexandrian schools of his time. The mathematical content of the De institutione arithmetica is the main topic of the second section. After showing how the De arithmetica is related to Boethius’ magnum opus – the Latin translation of the Greek philosophers – the choice of Nicomachus of Gerasa’ Introduction to Arithmetics as the source of Boethius’ treaty on arithmetics is studied. Then, a catalogue raisonné of the mathematical concepts showcased is provided, organized around the notions of quantity constant of itself and relative quantity which retain the opposition between the Same and the Other and stems from the pythagoricians’ fondamental opposition between the Limited and the Unlimited. This masters’ thesis ends with an analysis of the medieval transmission of the De institutione arithmetica and of its influence on medieval mathematics and education through the quadrivium.