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.

This book presents a broad selection of articles mainly published during the last two decades on a variety of topics within the history of mathematics, mostly focusing on particular aspects of mathematical practice. This book is of interest to, and provides methodological inspiration for, historians of science or mathematics and students of these disciplines.

For the affluent merchant class of fifteenth-century Florence, the education of future generations was a fundamental matter. Together with texts, images played an important role in the development of the young into adult citizens. In this book, Federico Botana demonstrates how illustrated manuscripts of vernacular texts read by the Florentine youth facilitated understanding and memorisation of basic principles and knowledge. They were an important means of acquiring skills then considered necessary to gain the respect of others, to prosper as merchants, and to participate in civic life. Botana focuses on illustrated texts that were widely read in Quattrocento Florence: the Fior di virtù (a moral treatise including a bestiary), the Esopo volgarizzato (Aesop's Fables in Tuscan), the Sfera by Goro Dati (a poem on cosmology and geography), and mathematical manuals known as libri d'abbaco. He elucidates, in light of original sources and medieval and modern cognitive theory, the mechanisms that empowered illustrations to transmit knowledge in the Italian Renaissance.

Silvestre François Lacroix was not a prominent mathematical researcher, but he was certainly a most influential mathematical book author. His most famous work is the three-volume Traité du calcul différentiel et du calcul intégral, which is an encyclopedic appraisal of 18th-century calculus that remained the standard reference on the subject through much of the 19th century. This book provides the first global and detailed study of Lacroix's Traité Traité du calcul.

This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics. It contains a well-balanced mixture of contributions by internationally established experts, such as Jeremy Gray and Jens Hoyrup; upcoming scholars, such as Erich Reck and Dirk Schlimm; and young, promising researchers at the beginning of their careers. The book is situated within a relatively new and broadly naturalistic tradition in the philosophy of mathematics. In this alternative philosophical current, which has been dramatically growing in importance in the last few decades, unlike in the traditional schools, proper attention is paid to scientific practices as informing for philosophical accounts.

Gives accurate and reliable summaries of the current state of research. It includes entries on philosophers, problems, terms, historical periods, subjects and the cultural context of Renaissance Philosophy. Furthermore, it covers Latin, Arabic, Jewish, Byzantine and vernacular philosophy, and includes entries on the cross-fertilization of these philosophical traditions. A unique feature of this encyclopedia is that it does not aim to define what Renaissance philosophy is, rather simply to cover the philosophy of the period between 1300 and 1650.

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.

This two-volume work, Latin-into-Hebrew: Texts and Studies sheds new light on an under-investigated phenomenon of European medieval intellectual history: the transmission of knowledge and texts from Latin into Hebrew between the twelfth and the fifteenth century. Because medieval Jewish philosophy and science in Christian Europe drew mostly on Hebrew translations from Arabic, the significance of the input from the Christian majority culture has been neglected. Latin-into-Hebrew: Texts and Studies redresses the balance. It highlights the various phases of Latin-into-Hebrew translations and considers their disparity in time, place, and motivations. Special emphasis is put on the singular role of the translations of Latin medical and philosophical literature. Volume One: Studies, offers 18 studies and Volume Two: Texts in Contexts, includes editions and analyses of hitherto unpublished texts of medieval Latin-into-Hebrew translations. Both volumes are available separately or together as a set. This groundbreaking work is indispensable for any scholar interested in the history of medieval philosophic and scientific thought in Hebrew, Latin, and Arabic in relationship to the vicissitudes of Jewish-Christian relations.