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"Mathematics, Medieval Sources."
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Sourcebook in the mathematics of medieval Europe and North Africa /
Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This sourcebook presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time. Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments providing results on the conchoid--a curve previously unknown in medieval Europe; Levi ben Gershon's use of mathematical induction in combinatorial proofs; Al-Muʹtaman Ibn Hūd's extensive survey of mathematics, which included proofs of Heron's Theorem and Ceva's Theorem; and Muhyī al-Dīn al-Maghribī's interesting proof of Euclid's parallel postulate. This book includes a general introduction, section introductions, footnotes, and references. The Sourcebook in the Mathematics of Medieval Europe and North Africa will be indispensable to anyone seeking out the important historical sources of premodern mathematics. -- Inside jacket flap.
Book
Desire of teachers and realities in textbooks: dealing with history of mathematics in the new French curriculum and its impact on teacher training
Many international studies focus empirically on integrating the history of mathematics in mathematics education. Over the last 2 decades, some studies also revealed theoretical elements concerning the implementation of learning sessions and/or their didactical analysis and effectiveness. This paper has the aim of complementing these empirical studies with a more systematic approach in the French context. Defended for decades within the IREM (Institut de recherche sur l’enseignement des mathématiques), the history of mathematics is now officially introduced in the French curriculum. Nevertheless, is it really sufficient for teachers to change their habits by implementing the history of mathematics in their practices? To answer this question, I first present an unpublished survey with secondary school mathematics teachers (pupils from 10- to 18 years old) about the introduction of the history of mathematics in their classes. This survey allows the comparison of teachers’ desires (‘history of mathematics
in potentiality
’) and realities in classrooms (‘history of mathematics
in actuality
’). Then I focus on French mathematics textbooks (for pupils from 15- to 18 years old) in order to question their effectiveness as tools for the introduction of a historical perspective. I describe the historical/mathematical tasks available in these textbooks focusing on their reference to Fibonacci. Finally, I present a proposition to implement the history of mathematics in mathematics education starting from the textbooks, aiming to help mathematics teachers to redesign the tasks of their textbooks so as to be more relevant.
Journal Article
FICINO AND THE NODUS DIVINUS
This paper analyzes the compositional, cosmological, and metaphysical order in Marsilio Ficino’s Platonic Theology 1-4. It argues that Ficino conceived of this order according to Timaean and Iamblichean mean terms. It revises the accepted conclusion that the central bond in the Platonic Theology is the human soul, demonstrating instead that the mean term of the third substance in Ficino’s five grades of reality is the soul of the spheres. Examining Ficino’s arguments and ancient sources, it also discusses older traditions of mathematical theologies and cosmologies. It further analyzes the formal nature of cosmological, metaphysical, and theurgical arguments constructed with mathematical laws of mean terms.
Journal Article
Verse and Transmutation
Identifies and investigates a corpus of twenty-one anonymous Middle English recipes for the philosophers' stone dating from the fifteenth century. Verse and Transmutation: A Corpus of Middle English Alchemical Poetry identifies and investigates a corpus of twenty-one anonymous recipes for the philosophers’ stone dating from the fifteenth century. These were circulated and received in association with each other until the mid-seventeenth century, when a number of them appeared in Elias Ashmole’s Theatrum Chemicum Britannicum. These editions are the first to make this previously unidentified corpus available to researchers. The accompanying studies discover the complex histories of these alchemica, in plain and illuminated manuscripts, as anonyma and in attribution to famous authors, and in private and institutional, medical and academic book collections. Together, they offer novel insights into the role of alchemy and poetry in late medieval and early modern England.
eBook
Verse and Transmutation - A Corpus of Middle English Alchemical Poetry (Critical Editions and Studies)
Identifies and investigates a corpus of twenty-one anonymous Middle English recipes for the philosophers' stone dating from the fifteenth century. Verse and Transmutation: A Corpus of Middle English Alchemical Poetry identifies and investigates a corpus of twenty-one anonymous recipes for the philosophers’ stone dating from the fifteenth century. These were circulated and received in association with each other until the mid-seventeenth century, when a number of them appeared in Elias Ashmole’s Theatrum Chemicum Britannicum. These editions are the first to make this previously unidentified corpus available to researchers. The accompanying studies discover the complex histories of these alchemica, in plain and illuminated manuscripts, as anonyma and in attribution to famous authors, and in private and institutional, medical and academic book collections. Together, they offer novel insights into the role of alchemy and poetry in late medieval and early modern England. This title was made Open Access by libraries from around the world through Knowledge Unlatched.
eBook
Volume Functions of Historical Texts and the Amplitude Correlation Principle
A new empirico-statistical model is suggested to distinguish dependent narrative texts from independent narrative texts by means of their volume functions. A \"regard for information\" principle and an \"amplitude correlation\" principle are formulated. The model and both principles are examined experimentally using specific historical texts.
Journal Article
Roger Bacon and the Origins of \Perspectiva\ in the Middle Ages: A Critical Edition and English Translation of Bacon's \Perspectiva\ with Introduction and Notes
Unguru reviews \"Roger Bacon and the Origins of 'Perspectiva' in the Middle Ages: A Critical Edition and English Translation of Bacon's 'Perspectiva' with Introduction and Notes\" by Roger Bacon and edited and translated by David C. Lindberg.
Book Review