The Development of Mathematics in Medieval Europe: The Arabs, Euclid, Regiomontanus (Variorum Collected Studies Series)

The Development of Mathematics in Medieval Europe complements the previous collection of articles by Menso Folkerts, Essays on Early Medieval Mathematics, and deals with the development of mathematics in Europe from the 12th century to about 1500. In the 12th century European learning was greatly transformed by translations from Arabic into Latin. Such translations in the field of mathematics and their influence are here described and analysed, notably al-Khwarizmi's "Arithmetic" -- through which Europe became acquainted with the Hindu-Arabic numerals -- and Euclid's "Elements". Five articles are dedicated to Johannes Regiomontanus, perhaps the most original mathematician of the 15th century, and to his discoveries in trigonometry, algebra and other fields. The knowledge and application of Euclid's "Elements" in 13th- and 15th-century Italy are discussed in three studies, while the last article treats the development of algebra in South Germany around 1500, where much of the modern symbolism used in algebra was developed. Cover 1 Series 3 Half Title 4 Title 6 Copyright 7 Contents 8 Preface 12 Acknowledgements 15 I Arabic Mathematics in the West 16 II Early Texts on Hindu-Arabic Calculation 32 III Euclid in Medieval Europe 58 IV Probleme der Euklidinterpretation und ihre Bedeutung für die Entwicklung der Mathematik 122 V Die mathematischen Studien Regiomontans in seiner Wiener Zeit 154 VI Regiomontanus’ Role in the Transmission and Transformation of Greek Mathematics 190 VII Regiomontanus’ Approach to Euclid 216 VIII Regiomontanus’ Role in the Transmission of Mathematical Problems 232 IX Leonardo Fibonacci’s Knowledge of Euclid’s Elements and of Other Mathematical Texts 250 X Piero della Francesca and Euclid 276 XI Luca Pacioli and Euclid 298 XII Algebra in Germany in the Fifteenth Century 312 Index of Names 330 Index of Manuscripts 340 31.01 history of mathematics; Aufsatzsammlung; Euclid; Euclid Influence; Euclides ca. v3. Jh; Europa; Europa (geografie); Geschichte 500-1500; History (form); Influence (Literary,artistic,etc); Mathematics Europe History; Mathematics,Medieval; Mathematik; Mathématiques médiévales; Regiomontanus 1436-1476; Regiomontanus,Joannes,1436-1476; Wiskunde 31.01 history of mathematics,Aufsatzsammlung,Euclid,Euclid Influence,Euclides ca. v3. Jh,Europa,Europa (geografie),Geschichte 500-1500,History (form),Influence (Literary,artistic,etc),Mathematics Europe History,Mathematics,Medieval,Mathematik,Mathématiques médiévales,Regiomontanus 1436-1476,Regiomontanus,Joannes,1436-1476,Wiskunde The Development of Mathematics in Medieval Europe complements the previous collection of articles by Menso Folkerts, Essays on Early Medieval Mathematics, and deals with the development of mathematics in Europe from the 12th century to about 1500. In the 12th century European learning was greatly transformed by translations from Arabic into Latin. Such translations in the field of mathematics and their influence are here described and analysed, notably al-Khwarizmi's "Arithmetic" -- through which Europe became acquainted with the Hindu-Arabic numerals -- and Euclid's "Elements". Five articles are dedicated to Johannes Regiomontanus, perhaps the most original mathematician of the 15th century, and to his discoveries in trigonometry, algebra and other fields. The knowledge and application of Euclid's "Elements" in 13th- and 15th-century Italy are discussed in three studies, while the last article treats the development of algebra in South Germany around 1500, where much of the modern symbolism used in algebra was developed. Cover 1 Series 3 Half Title 4 Title 6 Copyright 7 Contents 8 Preface 12 Acknowledgements 15 I Arabic Mathematics in the West 16 II Early Texts on Hindu-Arabic Calculation 32 III Euclid in Medieval Europe 58 IV Probleme der Euklidinterpretation und ihre Bedeutung für die Entwicklung der Mathematik 122 V Die mathematischen Studien Regiomontans in seiner Wiener Zeit 154 VI Regiomontanus’ Role in the Transmission and Transformation of Greek Mathematics 190 VII Regiomontanus’ Approach to Euclid 216 VIII Regiomontanus’ Role in the Transmission of Mathematical Problems 232 IX Leonardo Fibonacci’s Knowledge of Euclid’s Elements and of Other Mathematical Texts 250 X Piero della Francesca and Euclid 276 XI Luca Pacioli and Euclid 298 XII Algebra in Germany in the Fifteenth Century 312 Index of Names 330 Index of Manuscripts 340 31.01 history of mathematics; Aufsatzsammlung; Euclid; Euclid Influence; Euclides ca. v3. Jh; Europa; Europa (geografie); Geschichte 500-1500; History (form); Influence (Literary,artistic,etc); Mathematics Europe History; Mathematics,Medieval; Mathematik; Mathématiques médiévales; Regiomontanus 1436-1476; Regiomontanus,Joannes,1436-1476; Wiskunde 31.01 history of mathematics,Aufsatzsammlung,Euclid,Euclid Influence,Euclides ca. v3. Jh,Europa,Europa (geografie),Geschichte 500-1500,History (form),Influence (Literary,artistic,etc),Mathematics Europe History,Mathematics,Medieval,Mathematik,Mathématiques médiévales,Regiomontanus 1436-1476,Regiomontanus,Joannes,1436-1476,Wiskunde Twelve articles consider the reception of Euclid in the Latin West from the 12th century to about 1500, and the contributions of Johannes Regiomontanus (1436-76) to Western mathematics. Two in German and five in English are reproduced from previous publication; two have been translated from German, another radically revised, and one is published here for the first time. Among the topics are early texts on Hindu-Arabic calculation, Regiomontanus' role in the transmission and transformation of Greek mathematics, and algebra in Germany in the 15th century. In an earlier volume of the series, Folkerts looks at the same themes from the eighth to the 11th centuries. Annotation :2006 Book News, Inc., Portland, OR (booknews.com) Erwähnt fünf Handschriften der Burgerbibliothek Bern: BBB Codd. A 50, 87, 212, 234, 299