This book provides a unique perspective on the history of European algebra up to the advent of Viète and Descartes. The standard version of this history is written on the basis of a narrow and misleading source basis: the Latin translations of al-Khwārizmī, Fibonacci's Liber abbaci, Luca Pacioli's Summa, Cardano's Ars magna -- with neither Fibonacci nor Pacioli being read in detail. The existence of the Italian abacus and German cossic algebra is at most taken note of but they are not read, leading to the idea that Viète's and Descartes' use of genuine symbolism (not only abbreviations), many unknowns, and abstract coefficients seem to be miraculous leaps. This book traces the meandering development of all these techniques along with the mostly ignored but very important parenthesis function, by means of detailed readings of all pertinent sources, including the abacus and cossic algebra and French algebra from Chuquet to Gosselin. It argues for a necessary distinction between abbreviating glyphs and genuine symbols serving within a symbolic syntax, which allows it to trace the emergence of symbolic calculation. Characterization of the mathematical practice of the environment within which Viète and Descartes moved allows for an explanation of how these two figures did not even need to invent abstract coefficients but rather received them as a gift.

Students of the Italian Renaissance who wish to go beyond the standard names and subjects will find in this text abundant information on the lives, customs, beliefs, and practices of those who lived during this exciting time period. The World of Renaissance Italy: A Daily Life Encyclopedia engages all of the Italian peninsula from the Black Death (1347–1352) to 1600. Unlike other encyclopedic works about the Renaissance era, this book deals exclusively with Italy, revealing the ways common Italian people lived and experienced the events and technological developments that marked the Renaissance era. The coverage specifically spotlights marginal or traditionally marginalized groups, including women, homosexuals, Jews, the elderly, and foreign communities in Italian cities. The entries in this two-volume set are organized into 10 sections of 25 alphabetically listed entries each. Among the broad sections are art, fashion, family and gender, food and drink, housing and community, politics, recreation and social customs, and war. The "See Also" sources for each article are listed by section for easy reference, a feature that students and researchers will greatly appreciate. The extensive collection of contemporary documents include selections from a diary, letters, a travel journal, a merchant's inventory, Inquisition testimony, a metallurgical handbook, and text by an artist that describes what the author feels constitutes great work. Each of the primary source documents accompanies a specific article and provides an added dimension and degree of insight to the material.

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.

Few eras took education so seriously or were so innovative in their approaches to schools and universities as the Renaissance. At the same time, religious and political concerns strongly influenced educational developments. This third volume of articles by Paul F. Grendler explores the close connections between education, religion, and politics at several levels and in different contexts. It combines detailed research into various kinds of schools with broad overviews of European and especially Italian education. The lead article compares Italian and German universities and assesses the impact of the Protestant Reformation on the latter. Even Erasmus, the great critic of university theologians, felt the need to acquire a doctorate in theology and did so. In Italy, the new schools of the Jesuits and the Piarists taught boys and young men gratis, but not without opposition. Two articles deal with students, the consumers of education. While teachers and students were most directly involved in schools and universities, ecclesiastical and political authorities, including the leaders of the Republic of Venice, the subject of the final study, kept a watchful eye on them.

In scope, this book matches The History of Cartography, vol. 1 (1987) edited by Brian Harley and David Woodward. Now, twenty years after the appearance of that seminal work, classicists and medievalists from Europe and North America highlight, distill and reflect on the remarkably productive progress made since in many different areas of the study of maps. The interaction between experts on antiquity and on the Middle Ages evident in the thirteen contributions offers a guide to the future and illustrates close relationships in the evolving practice of cartography over the first millennium and a half of the Christian era. Contributors are Emily Albu, Raymond Clemens, Lucy Donkin, Evelyn Edson, Tom Elliott, Patrick Gauthier Dalché, Benjamin Kedar, Maja Kominko, Natalia Lozovsky, Yossef Rapoport, Emilie Savage-Smith, Camille Serchuk, Richard Talbert, and Jennifer Trimble.

An epic cultural journey that reveals how Venetian ingenuity and inventions—from sunglasses and forks to bonds and currency—shaped modernity. How did a small, isolated city—with a population that never exceeded 100,000, even in its heyday—come to transform western civilization? Acclaimed anthropologist Meredith Small, the author of the groundbreaking Our Babies, Ourselves examines the the unique Venetian social structure that was key to their explosion of creativity and invention that ranged from the material to social. Whether it was boats or money, medicine or face cream, opera, semicolons, tiramisu or child-labor laws, these all originated in Venice and have shaped contemporary notions of institutions and conventions ever since. The foundation of how we now think about community, health care, money, consumerism, and globalization all sprung forth from the Laguna Veneta. But Venice is far from a historic relic or a life-sized museum. It is a living city that still embraces its innovative roots. As climate change effects sea-level rises, Venice is on the front lines of preserving its legacy and cultural history to inspire a new generation of innovators.

The legendary Renaissance math duel that ushered in the modern age of algebra The Secret Formula tells the story of two Renaissance mathematicians whose jealousies, intrigues, and contentious debates led to the discovery of a formula for the solution of the cubic equation. Niccolò Tartaglia was a talented and ambitious teacher who possessed a secret formula—the key to unlocking a seemingly unsolvable, two-thousand-year-old mathematical problem. He wrote it down in the form of a poem to prevent other mathematicians from stealing it. Gerolamo Cardano was a physician, gifted scholar, and notorious gambler who would not hesitate to use flattery and even trickery to learn Tartaglia's secret. Set against the backdrop of sixteenth-century Italy, The Secret Formula provides new and compelling insights into the peculiarities of Renaissance mathematics while bringing a turbulent and culturally vibrant age to life. It was an era when mathematicians challenged each other in intellectual duels held outdoors before enthusiastic crowds. Success not only enhanced the winner's reputation, but could result in prize money and professional acclaim. After hearing of Tartaglia's spectacular victory in one such contest in Venice, Cardano invited him to Milan, determined to obtain his secret by whatever means necessary. Cardano's intrigues paid off. In 1545, he was the first to publish a general solution of the cubic equation. Tartaglia, eager to take his revenge by establishing his superiority as the most brilliant mathematician of the age, challenged Cardano to the ultimate mathematical duel. A lively account of genius, betrayal, and all-too-human failings, The Secret Formula reveals the epic rivalry behind one of the fundamental ideas of modern algebra.

This book deals with one of the earliest surviving "abbacus" treatises, one that is by far more orderly than any of the extant predecessors and is also the first to contain a presentation of algebra. The book contains an edition and an English translation of a manuscript from c. 1450. In addition, it features an extensive discussion of the contents of the treatise and its location within early abbacus culture.