Gerard of Cremona’s Translation of the Commentary of al-Nayrizi on Book I of Euclid’s Elements of Geometry


Book Description

This book provides an annotated English translation of Gerard of Cremona’s Latin version of Book I of al-Nayrizi's Commentary on Euclid’s Elements. Lo Bello concludes with a critical analysis of the idiosyncrasies of Gerard’s method of translation.




The Commentary of Al-Nayrizi on Books II-IV of Euclid's Elements of Geometry


Book Description

The Commentary of al-Nayrizi (circa 920) on Euclid s "Elements of Geometry" occupies an important place both in the history of mathematics and of philosophy, particularly Islamic philosophy. It is a compilation of original work by al-Nayrizi and of translations and commentaries made by others, such as Heron. It is the most influential Arabic mathematical manuscript in existence and a principle vehicle whereby mathematics was reborn in the Latin West. Furthermore, the Commentary on Euclid by the Platonic philosopher Simplicius, entirely reproduced by al-Nayrizi, and nowhere else extant, is essential to the study of the attempt to prove Euclid s Fifth Postulate from the preceding four. Al-Nayrizi was one of the two main sources from which Albertus Magnus (1193-1280), the Doctor Universalis, learned mathematics. This work presents an annotated English translation of Books II-IV and of a hitherto lost portion of Book I.




The Commentary of al-Nayrizi on Book I of Euclid's Elements of Geometry


Book Description

For more than two millennia, the Elements of Geometry by the Greek mathematician Euclid of Alexandria (ca. 300 B.C.E. ) was held to be “the supreme example of the exercise of human reason” and “a paradigm of rational certainty” (from the preface, after Simon Blackburn). The Commentary of al-Nayrizi on Book I of Euclid’s Elements of Geometry introduces readers to the transmission of Euclid’s Elements from the Middle East to the Latin West in the medieval period and then offers the first English translation of al-Nayrizi’s (d. ca. 922) Arabic commentary on Book I. The Three Volumes are also available as set (ISBN 0 391 04197 5)




The Commentary of Albertus Magnus on Book I of Euclid's Elements of Geometry


Book Description

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.




Leibniz on the Parallel Postulate and the Foundations of Geometry


Book Description

This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz’s work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the seventeenth-century studies on the foundations of geometry. It also provides a detailed mathematical and philosophical commentary on his writings on the theory of parallels, and discusses how they were received in the eighteenth century as well as their relevance for the non-Euclidean revolution in mathematics. The second part offers a collection of Leibniz’s essays on the theory of parallels and an English translation of them. While a few of these papers have already been published (in Latin) in the standard Leibniz editions, most of them are transcribed from Leibniz’s manuscripts written in Hannover, and published here for the first time. The book provides new material on the history of non-Euclidean geometry, stressing the previously neglected role of Leibniz in these developments. This volume will be of interest to historians in mathematics, philosophy or logic, as well as mathematicians interested in non-Euclidean geometry.




The A to Z of Medieval Philosophy and Theology


Book Description

The Middle Ages is often viewed as a period of low intellectual achievement. The name itself refers to the time between the high philosophical and literary accomplishments of the Greco-Roman world and the technological advances that were achieved and philosophical and theological alternatives that were formulated in the modern world that followed. However, having produced such great philosophers as Anselm, Peter Abelard, John Duns Scotus, William of Ockham, Peter Lombard, and the towering Thomas Aquinas, it hardly seems fair to label the medieval period as such. Examining the influence of ancient Greek philosophy as well as of the Arabian and Hebrew scholars who transmitted it, The A to Z of Medieval Philosophy and Theology presents the philosophy of the Christian West from the 9th to the early 17th century. This is accomplished through a chronology, an introduction, appendixes, a bibliography, and hundreds of cross-referenced dictionary entries on the philosophers, concepts, issues, institutions, and events, making this an important reference for the study of the progression of human thought.




Historical Dictionary of Medieval Philosophy and Theology


Book Description

This second edition concentrates on various philosophers and theologians from the medieval Arabian, Jewish, and Christian worlds. It principally centers on authors such as Abumashar, Saadiah Gaon and Alcuin from the eighth century and follows the intellectual developments of the three traditions up to the fifteenth-century Ibn Khaldun, Hasdai Crescas and Marsilio Ficino. The spiritual journeys presuppose earlier human sources, such as the philosophy of Plato, Aristotle, Plotinus, and Porphyry and various Stoic authors, the revealed teachings of the Jewish Law, the Koran and the Christian Bible. The Fathers of the Church, such as St. Augustine and Gregory the Great, provided examples of theology in their attempts to reconcile revealed truth and man’s philosophical knowledge and deserve attention as pre-medieval contributors to medieval intellectual life. Avicenna and Averroes, Maimonides and Gersonides, St. Thomas Aquinas and St. Bonaventure, stand out in the three traditions as special medieval contributors who deserve more attention. This second edition of Historical Dictionary of Medieval Philosophy and Theology contains a chronology, an introduction, appendixes, and an extensive bibliography. The dictionary section has over 300 cross-referenced entries on important persons, events, and concepts that shaped medieval philosophy and theology. This book is an excellent resource for students, researchers, and anyone wanting to know more about medieval philosophy and theology.




Scripta Mediterranea


Book Description




From China to Paris


Book Description

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.




Ptolemy's Almagest


Book Description

Ptolemy's Almagest is one of the most influential scientific works in history. A masterpiece of technical exposition, it was the basic textbook of astronomy for more than a thousand years, and still is the main source for our knowledge of ancient astronomy. This translation, based on the standard Greek text of Heiberg, makes the work accessible to English readers in an intelligible and reliable form. It contains numerous corrections derived from medieval Arabic translations and extensive footnotes that take account of the great progress in understanding the work made in this century, due to the discovery of Babylonian records and other researches. It is designed to stand by itself as an interpretation of the original, but it will also be useful as an aid to reading the Greek text.