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 Liège 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.

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 is a path-breaking contribution to the study of medieval metalwork and to the broader re-evaluation of medieval art.

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 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. 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.

An element common to all the articles collected here is the attempt to make parallel use of sources from different cultures - Biblical and Talmudic Hebrew, Greek and Latin, Arabic and Judaeo-Arabic - comparing these different but complementary sources in the investigation of topics in Jewish and Arabic history. In the first studies Professor Gil deals primarily with the Roman and Byzantine periods, elucidating how a Biblical term was understood, the historical significance of passages from the Mishna, and the origins of the Book of Enoch. The next group is concerned with the history of early Islam, during the years in which the Prophet Muhammad lived and worked, and later traditions of this period. The final studies are based specifically on sources from the Cairo Geniza, and examine a term of Greek origin and questions of taxation and commerce.

This volume, the third by Charles Burnett in the Variorum series, brings together articles on the different numeral forms used in the Middle Ages, and their use in mathematical and other contexts. Some pieces study the introduction of Hindu-Arabic numerals into Western Europe, documenting, in more detail than anywhere else, the different forms in which they are found, before they acquired the standard shapes with which we are familiar today. Others deal with experiments with other forms of numeration within Latin script: e.g., using the first nine Roman numerals as symbols with place value, abbreviating the Roman numerals, and using the Latin letters as numerals. The author discusses how different types of numerals are used for different purposes, and the application of numerals to the abacus, and to calculation with pen and ink. The studies include the critical edition of several Latin texts.

This volume complements the previous collection of articles by Menso Folkerts, Essays on Early Medieval Mathematics. It deals with the development of mathematics in Europe from the 12th century to about 1500.