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.

This book deals with the mathematics of the medieval West between ca. 500 and 1100, the period before the translations from Arabic and Greek had their impact. Four of the studies appear for the first time in English. Among the topics treated are: the Roman surveyors (agrimensores); recreational mathematics in the period of Bede and Alcuin; geometrical texts compiled in Corbie and Lorraine from Latin sources from late antiquity; the abacus at the time of Gerbert (pope Sylvester II.); and a board-game invented in the first half of the 11th century (the 'Rithmimachia') to help people to learn mathematics. Included in the volume are critical editions of several texts, e.g. that of Franco of Liege on squaring the circle, Bede and Alcuin on recreational mathematics, and part of Pseudo-Boethius' Geometry I. The book opens with a survey of mathematics in the Middle Ages, and ends with a history of Rithmimachia up to the 17th century, when the game fell into disuse.

Eine sehr reizvolle Aufgabe mathematikhistorischer Forschung besteht darin, die Geschichte bestimmter mathematischer Aufgabentypen und Loesungsmethoden zu erforschen. Es ist schon lange bekannt, dass oft dieselben Probleme zu verschiedenen Zeiten und in von einander weit entfernten Kulturkreisen behandelt wurden. Dabei nimmt man an, dass manche Probleme des augewandten Rechnens Bestandteil der Literatur vieler Voelker sind, ohne dass man eine gegenseitige Beeinflussung vermuten darf. Wenn allerdings eine Aufgabe mit denselben nicht zu einfachen Zahlenwerten in verschiedenen Quellen uberliefert wird, muss man an eine Abhangigkeit denken. Es ist jedoch auch in diesen Fallen gegenwartig noch nicht moeglich, zu sicheren Erkenntnissen uber den Weg eines Problems zu gelangen; dazu sind die kulturellen Beziehungen zwischen den Voelkern zu komplex und in den Einzelheiten zu wenig geklart. Gemeinsam mit Mathematikhistorikern mussten hier Vertreter anderer historischer Disziplinen wie Wirtschafts- und Sozialgeschichte, aber auch die Philologen mitarbeiten. Eine solche Arbeit koennte dazu beitragen,_ die kulturellen Leistungen der be teiligten Voelker, die Gemeinsamkeiten, aber auch die Unterschiede ihrer wissenschaftlichen Entwicklung herauszuarbeiten und dabei insbesondere den europazentrischen Standpunkt zu uberwinden, der immer noch viele wissenschaftshistorische Darstellungen beherrscht. Als Vorarbeit fur eine derart anspruchsvolle Untersuchung stellt sich dem Mathematik historiker zunachst die Aufgabe, die zahlreichen Sammlungen praktischer Mathematik zu untersuchen, festzustellen, wo das einzelne Problem oder die verwendete Methode sich erst mals findet, und - wenn moeglich - Aussagen uber Entstehung und Einfluss der betreffenden Sammlung zu machen. Gerade in den letzten Jahrzehnten sind hier neue Untersuchungen erschienen. So hat K.

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 proving results on the conchoid--a curve previously unknown in medieval Europe; Levi ben Gershon's use of mathematical induction in combinatorial proofs; Al-Mu'taman Ibn H?d's extensive survey of mathematics, which included proofs of Heron's Theorem and Ceva's Theorem; and Muhy? al-D?n al-Maghrib?'s interesting proof of Euclid's parallel postulate. The 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.

The contributors and their methods are diverse. Their papers deal with subjects such as anamorphic art, the geometry of Durer, musical works of Mozart and Beethoven, the history of negative numbers, the development of mathematical notation, and efforts to bring mathematics to bear on problems in commerce and engineering. All papers have English summaries.
This book provides historians of mathematics or mathematicians with an interest in history with an overview of the methods, concerns, and results of research in the history of mathematics as it stands today.

This book deals with the mathematics of the medieval West between ca. 500 and 1100, the period before the translations from Arabic and Greek had their impact. Four of the studies appear for the first time in English. Among the topics treated are: the Roman surveyors (agrimensores); recreational mathematics in the period of Bede and Alcuin; geometrical texts compiled in Corbie and Lorraine from Latin sources from late antiquity; the abacus at the time of Gerbert (pope Sylvester II.); and a board-game invented in the first half of the 11th century (the 'Rithmimachia') to help people to learn mathematics. Included in the volume are critical editions of several texts, e.g. that of Franco of Liege on squaring the circle, Bede and Alcuin on recreational mathematics, and part of Pseudo-Boethius' Geometry I. The book opens with a survey of mathematics in the Middle Ages, and ends with a history of Rithmimachia up to the 17th century, when the game fell into disuse.