scholarly journals Guillaume des Moustiers’ treatise on the armillary instrument (1264) and the practice of astronomical observation in medieval Europe

2021 ◽  
pp. 1-17
Author(s):  
C. Philipp E. Nothaft

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 book 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 proving results on the conchoid—a curve previously unknown in medieval Europe; Levi ben Gershon's use of mathematical induction in combinatorial proofs; Al-Muʾtaman 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. The book includes a general introduction, section introductions, footnotes, and references.


Author(s):  
Chris Wickham

Amid the disintegration of the Kingdom of Italy in the eleventh and twelfth centuries, a new form of collective government—the commune—arose in the cities of northern and central Italy. This book takes a bold new look at how these autonomous city-states came about, and fundamentally alters our understanding of one of the most important political and cultural innovations of the medieval world. The book provides richly textured portraits of three cities—Milan, Pisa, and Rome—and sets them against a vibrant backcloth of other towns. It argues that, in all but a few cases, the élite of these cities and towns developed one of the first nonmonarchical forms of government in medieval Europe, unaware that they were creating something altogether new. The book makes clear that the Italian city commune was by no means a democracy in the modern sense, but that it was so novel that outsiders did not know what to make of it. It describes how, as the old order unraveled, the communes emerged, governed by consular elites “chosen by the people,” and subject to neither emperor nor king. They regularly fought each other, yet they grew organized and confident enough to ally together to defeat Frederick Barbarossa, the German emperor, at the Battle of Legnano in 1176. This book reveals how the development of the autonomous city-state took place, which would in the end make possible the robust civic culture of the Renaissance.


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