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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 proving results on the conchoid—a curve previously unknown in medieval Eur...
Historiography of the History of Science in Islamicate Societies
This book presents eight papers about important historiographical issues as debated in the history of science in Islamicate societies, the history of science and philosophy of medieval Latin Europe and the history of mathematics as an academic discipline. Six papers deal with themes about the sciences in Islamicate societies from the ninth to the seventeenth centuries, among them novelty, context and decline. Two other papers discuss the historiographical practices of historians of mathematics and other disciplines in the nineteenth and twentieth centuries. The central argument of the collected papers is that in addition and beyond the study of scientific texts and instruments historians of ...
Robert of Chester’s Redaction of Euclid’s Elements, the so-called Adelard II Version
The Latin "Version II", till now attributed to Adelard of Bath, is edited here for the first time. It was the most influential Euclid text in the Latin West in the 12th and 13th centuries. As the large number of manuscripts and the numerous quotations in other scientific and philosophical texts show, it was far better known than the three Euclid translations made from the Arabic in the 12th century (Adelard of Bath, version I; Hermann of Carinthia; Gerard of Cremona). Version II became the basis of later reworkings, in which the enunciations were taken over, but new proofs supplied; the most important text of this kind is the redaction made by Campanus in the late 1250s, which became the sta...
The Doctrine of Triangles
An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentieth The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the ma...
From China to Paris
The reports of a conference of 11 scholars who began the task of examing together primary sources that might shed som elight on exactly how and in what fomrs mathematical problems, concepts, and techniques may have been transmitted between various civilizations, from antiquity down to the European Renaissance following more or less the legendary silk routes between China and Western Europe.
The Ciphers of the Monks
This is the first comprehensive study of an ingenious number-notation from the Middle Ages that was devised by monks and mainly used in monasteries. A simple notation for representing any number up to 99 by a single cipher, somehow related to an ancient Greek shorthand, first appeared in early-13th-century England, brought from Athens by an English monk. A second, more useful version, due to Cistercian monks, is first attested in the late 13th century in what is today the border country between Belgium and France: with this any number up to 9999 can be represented by a single cipher. The ciphers were used in scriptoria - for the foliation of manuscripts, for writing year-numbers, preparing i...
A Companion to Twelfth-Century Schools
This Companion to Twelfth-Century Schools provides a comprehensive update and new synthesis of the last three decades of research. The fruit of a contemporary renewal of cultural history among international scholars of medieval studies, this collection draws on the discovery of new texts, the progress made in critical attribution, the growing attention given to the conditions surrounding the oral and written dissemination of works, the use of the notion of a “community of learning”, the reinterpretation of the relations between the cloister and the urban school, and links between institutional history and social history. Contributors are: Alexander Andrée, Irene Caiazzo, Cédric Giraud, Frédéric Goubier, Danielle Jacquart, Thierry Kouamé, Constant J. Mews, Ken Pennington, Dominique Poirel, Irène Rosier-Catach, Sita Steckel, Jacques Verger, and Olga Weijers. See inside the book.
Regiomontanus: His Life and Work
The 500th anniversary of Regiomontanus's birth has occasioned this depiction of his life and work. It is the first English translation of Ernst Zinner's monumental biography, plus a number of specially-written supplementary articles which help paint a more comprehensive picture of the current state of knowledge about Regiomontanus. The articles show the high regard in which the biography is still held by the community of scholars doing work on the mathematics of the Renaissance.Zinner's biography is a mine of information about early printing, astrolabes, tables of eclipses and the world of Henry of Langenstein, Johann of Gmunden, Georg Peuerbach, Cardinal Bessarion, Nicholas of Cusa and the extraordinary itinerant scholar, Johannes Müller of Königsberg — Regiomontanus. His contributions to mathematics are discussed (for example, he may have discovered the fifth and sixth perfect numbers) as well as the mysteries surrounding his life and death.
The Commentary of Albertus Magnus on Book I of Euclid's Elements of Geometry
This book provides an annotated English translation of the Commentary of Albertus Magnus on Book I of Euclid's Elements of Geometry. It includes a translation and a critical examination of the mathematical content of the commentary and of its sources.
The Forgotten Revolution
The period from the late fourth to the late second century B. C. witnessed, in Greek-speaking countries, an explosion of objective knowledge about the external world. WhileGreek culture had reached great heights in art, literature and philosophyalreadyin the earlier classical era, it is in the so-called Hellenistic period that we see for the ?rst time — anywhere in the world — the appearance of science as we understand it now: not an accumulation of facts or philosophically based speculations, but an or- nized effort to model nature and apply such models, or scienti?ctheories in a sense we will make precise, to the solution of practical problems and to a growing understanding of nature. ...
