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.

Medieval English sermons teem with examples of quantitative reasoning, ranging from the arithmetical to the numerological, and regularly engage with numerical concepts. Examining sermons written in Middle English and Latin, this book reveals that popular English-speaking audiences were encouraged to engage in a wide range of numerate operations in their daily religious practices. Medieval sermonists promoted numeracy as a way for audiences to appreciate divine truth. Their sermons educated audiences in a hybrid form of numerate practice—one that relied on individuals’ pragmatic quantitative reasoning, which, when combined with spiritual interpretations of numbers provided by the preacher, created a deep and rich sense in which number was the best way to approach the sacred mysteries of the world as well as to learn how one could best live as a Christian. Analyzing both published and previously unpublished sermons and sermon cycles, Christine Cooper-Rompato explores the use of numbers, arithmetic, and other mathematical operations to better understand how medieval laypeople used math as a means to connect with God. Spiritual Calculations enhances our understanding of medieval sermons and sheds new light on how receptive audiences were to this sophisticated rhetorical form. It will be welcomed by scholars of Middle English literature, medieval sermon studies, religious experience, and the history of mathematics.

In 1202, a 32-year old Italian finished one of the most influential books of all time, which introduced modern arithmetic to Western Europe. Devised in India in the seventh and eighth centuries and brought to North Africa by Muslim traders, the Hindu-Arabic system helped transform the West into the dominant force in science, technology, and commerce, leaving behind Muslim cultures which had long known it but had failed to see its potential. The young Italian, Leonardo of Pisa (better known today as Fibonacci), had learned the Hindu number system when he traveled to North Africa with his father, a customs agent. The book he created was Liber abbaci, the 'Book of Calculation', and the revolution that followed its publication was enormous. Arithmetic made it possible for ordinary people to buy and sell goods, convert currencies, and keep accurate records of possessions more readily than ever before. Liber abbaci's publication led directly to large-scale international commerce and the scientific revolution of the Renaissance. Yet despite the ubiquity of his discoveries, Leonardo of Pisa remains an enigma. His name is best known today in association with an exercise in Liber abbaci whose solution gives rise to a sequence of numbers - the Fibonacci sequence - used by some to predict the rise and fall of financial markets, and evident in myriad biological structures. In The Man of Numbers, Keith Devlin recreates the life and enduring legacy of an overlooked genius, and in the process makes clear how central numbers and mathematics are to our daily lives.

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 indexes and concordances, numbering sermons and the like, and outside the scriptoria - for marking the scales on an astronomical instrument, writing year-numbers in astronomical tables, and for incising volumes on wine-barrels. Related notations were used in medieval and Renaissance shorthands and coded scripts. This richly-illustrated book surveys the medieval manuscripts and Renaissance books in which the ciphers occur, and takes a close look at an intriguing astrolabe from 14th-century Picardy marked with ciphers. With Indices. "Mit Kings luzider Beschreibung und Bewertung der einzelnen Funde und ihrer Beziehungen wird zugleich die Forschungsgeschichte - die bis dato durch Widerspruechlichkeit und Diskontinuit�t gepr�gt ist - umfassend aufgearbeitet." Zeitschrift fuer Germanistik.

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.

Named a Best Book of 2020 by The Telegraph, The Times, and BBC History Magazine An illuminating guide to the scientific and technological achievements of the Middle Ages through the life of a crusading astronomer-monk. "Falk’s bubbling curiosity and strong sense of storytelling always swept me along. By the end, The Light Ages didn’t just broaden my conception of science; even as I scrolled away on my Kindle, it felt like I was sitting alongside Westwyk at St. Albans abbey, leafing through dusty manuscripts by candlelight." —Alex Orlando, Discover Soaring Gothic cathedrals, violent crusades, the Black Death: these are the dramatic forces that shaped the medieval era. But the so-called Dark Ages also gave us the first universities, eyeglasses, and mechanical clocks. As medieval thinkers sought to understand the world around them, from the passing of the seasons to the stars in the sky, they came to develop a vibrant scientific culture. In The Light Ages, Cambridge science historian Seb Falk takes us on a tour of medieval science through the eyes of one fourteenth-century monk, John of Westwyk. Born in a rural manor, educated in England’s grandest monastery, and then exiled to a clifftop priory, Westwyk was an intrepid crusader, inventor, and astrologer. From multiplying Roman numerals to navigating by the stars, curing disease, and telling time with an ancient astrolabe, we learn emerging science alongside Westwyk and travel with him through the length and breadth of England and beyond its shores. On our way, we encounter a remarkable cast of characters: the clock-building English abbot with leprosy, the French craftsman-turned-spy, and the Persian polymath who founded the world’s most advanced observatory. The Light Ages offers a gripping story of the struggles and successes of an ordinary man in a precarious world and conjures a vivid picture of medieval life as we have never seen it before. An enlightening history that argues that these times weren’t so dark after all, The Light Ages shows how medieval ideas continue to color how we see the world today.

First published in 1202, Fibonacci’s Liber Abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe. This is the first translation into a modern European language, of interest not only to historians of science but also to all mathematicians and mathematics teachers interested in the origins of their methods.

This book zeroes in on hidden writing and alternative systems of graphic notation, exploring writings that deflect attention from language.

A biography of Leonardo Fibonacci, the 12th century mathematician who discovered the numerical sequence named for him.