A Commentary on the First Book of Euclid's Elements


Author: Proclus

Publisher: Princeton University Press

ISBN: 9780691020907

Category: Mathematics

Page: 355

View: 2609

In Proclus' penetrating exposition of Euclid's method's and principles, the only one of its kind extant, we are afforded a unique vantage point for understanding the structure and strenght of the Euclidean system. A primary source for the history and philosophy of mathematics, Proclus' treatise contains much priceless information about the mathematics and mathematicians of the previous seven or eight centuries that has not been preserved elsewhere.

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

With a Translation of that Portion of Book I Missing from Ms Leiden Or. 399.1 But Present in the Newly Discovered Qom Manuscript Edited by Rèudiger Arnzen


Author: Anaritius,Anthony Lo Bello

Publisher: BRILL

ISBN: 9004173897

Category: Philosophy

Page: 215

View: 9180

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 Books II-IV of Euclid's Elements of Geometry

With a Translation of That Portion of Book I Missing from MS Leiden Or. 399.1 but Present in the Newly Discovered Qom Manuscript Edited by Rüdiger Arnzen


Author: Anthony Lo Bello

Publisher: BRILL

ISBN: 9047444418

Category: Philosophy

Page: 248

View: 6938

The Commentary of al-Nayrizi (circa 920) on Euclid’s Elements occupies an important place in the history of mathematics and of philosophy. The present work presents an annotated English translation of Books II-IV and of a hitherto lost portion of Book I.

Cultural Foundations of Mathematics

The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16th C. CE


Author: C. K. Raju

Publisher: Pearson Education India

ISBN: 9788131708712

Category: Calculus

Page: 477

View: 4451

The Volume Examines, In Depth, The Implications Of Indian History And Philosophy For Contemporary Mathematics And Science. The Conclusions Challenge Current Formal Mathematics And Its Basis In The Western Dogma That Deduction Is Infallible (Or That It Is Less Fallible Than Induction). The Development Of The Calculus In India, Over A Thousand Years, Is Exhaustively Documented In This Volume, Along With Novel Insights, And Is Related To The Key Sources Of Wealth-Monsoon-Dependent Agriculture And Navigation Required For Overseas Trade - And The Corresponding Requirement Of Timekeeping. Refecting The Usual Double Standard Of Evidence Used To Construct Eurocentric History, A Single, New Standard Of Evidence For Transmissions Is Proposed. Using This, It Is Pointed Out That Jesuits In Cochin, Following The Toledo Model Of Translation, Had Long-Term Opportunity To Transmit Indian Calculus Texts To Europe. The European Navigational Problem Of Determining Latitude, Longitude, And Loxodromes, And The 1582 Gregorian Calendar-Reform, Provided Ample Motivation. The Mathematics In These Earlier Indian Texts Suddenly Starts Appearing In European Works From The Mid-16Th Century Onwards, Providing Compelling Circumstantial Evidence. While The Calculus In India Had Valid Pramana, This Differed From Western Notions Of Proof, And The Indian (Algorismus) Notion Of Number Differed From The European (Abacus) Notion. Hence, Like Their Earlier Difficulties With The Algorismus, Europeans Had Difficulties In Understanding The Calculus, Which, Like Computer Technology, Enhanced The Ability To Calculate, Albeit In A Way Regarded As Epistemologically Insecure. Present-Day Difficulties In Learning Mathematics Are Related, Via Phylogeny Is Ontogeny , To These Historical Difficulties In Assimilating Imported Mathematics. An Appendix Takes Up Further Contemporary Implications Of The New Philosophy Of Mathematics For The Extension Of The Calculus, Which Is Needed To Handle The Infinities Arising In The Study Of Shock Waves And The Renormalization Problem Of Quantum Field Theory.


Neo-platonic Philosophy and Science


Author: Lucas Siorvanes

Publisher: Yale University Press

ISBN: 9780300068061

Category: History

Page: 340

View: 9025

Proclus (410-485) was the last great Greek philosopher. In this study, Proclus expert Lucas Siorvantes sets out to strip away the complexities surrounding this traditionally difficult philosopher, with the intention of providing an accessible introduction to his work. Based on extensive study of the primary sources, he takes the reader through Proclus' metaphysics and epistemology, introducing the results of original research as well as explaining the more difficult passages. Sorivantes surveys the philosophical climate of Late Antiquity dominated by Aristotle and Plato, and points out the direct influence Proclus had on the subsequent work of Kepler and Copernicus.

The Irrationals

A Story of the Numbers You Can’t Count On


Author: Julian Havil

Publisher: Princeton University Press

ISBN: 1400841704

Category: Mathematics

Page: 312

View: 1957

The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define—and why so many questions still surround them. Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.

From Discrete to Continuous

The Broadening of Number Concepts in Early Modern England


Author: K. Neal

Publisher: Springer Science & Business Media

ISBN: 940170077X

Category: Mathematics

Page: 175

View: 2686

In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible. This traditional idea of discrete number versus continuous magnitude was challenged in the early modern period in several ways. This detailed study explores how the development of algebraic symbolism, logarithms, and the growing practical demands for an expanded number concept all contributed to a broadening of the number concept in early modern England. An interest in solving practical problems was not, in itself, enough to cause a generalisation of the number concept. It was the combined impact of novel practical applications together with the concomitant development of such mathematical advances as algebraic notation and logarithms that produced a broadened number concept.

New Perspectives on Galileo

Papers Deriving from and Related to a Workshop on Galileo held at Virginia Polytechnic Institute and State University, 1975


Author: Robert E. Butts,Joseph C. Pitt

Publisher: Springer Science & Business Media

ISBN: 940099799X

Category: Science

Page: 264

View: 358

The essays in this volume (except for the contribution of Dr. Le Grand) are extremely revised versions of papers originally delivered at a workshop on Galileo held in Blacksburg, Virginia in October, 1975. The meeting was organized by Professor Joseph Pitt and sponsored by the Department of Philosophy and Religion, The College of Arts and Sciences, and the Division of Research of Virginia Polytechnic Institute and State University. The papers that follow deal with problems OIf Galileo's philosophy of science, specific and general problems connected with his methodology, and with historical and conceptual questions concerning the relationship of his work to that of contemporaries and both earlier and later scientists. New perspectives take many forms. In this book the 'newness' has, for the most part, two forms. First, in the papers by Wisan, Shea, Le Grand and Wallace (the concerns will also appear in some of the other contributions), greatly enriched historical discoveries of how Galileo's science and its method ology developed are provided. It should be stressed that these papers are attempts to recapture a deep sense of the kind of science Galileo was creating. Other papers in the volume, for example, those by McMullin, Machamer, Butts and Pitt, underscore the importance of this historical venture by discussing various aspects of the philosophical background of Galileo's thought. The historical and philosophical evaluations and analyses compliment one another.

The Greek Qabalah

Alphabetical Mysticism and Numerology in the Ancient World


Author: Kieren Barry

Publisher: Weiser Books

ISBN: 1609252276

Category: Religion

Page: 312

View: 1324

This book will be of interest to a wide range of readers, from students of Ancient History and early Christianity, to Qabalists and modern magicians. Extensive notes and citations from original sources will make this authoritative work an essential reference for researchers and practitioners for years to come. Includes are appendices for tables of alphabetic symbolism, a list of authors, and a numeric dictionary of Greek words, which represents the largest collection of gematria in print.

Archiv Für Geschichte Der Philosophie


Author: N.A

Publisher: N.A


Category: Philosophy

Page: N.A

View: 7857

Vols. 1-23 (1888-1910) include "Jahresberichte über sämtliche Erscheinungen auf dem Gebiete der Geschichte der Philosophie"; v. 24-41 include section "Die neuesten Erscheinungen auf dem Gebiete der Geschichte der Philosophie" (varies slightly)

A Roman miscellany

essays in honour of Anthony R. Birley on his seventieth birthday


Author: Hans Michael Schellenberg,Vera Elisabeth Hirschmann,Andreas Krieckhaus

Publisher: Akanthina

ISBN: 9788375311464

Category: History

Page: 236

View: 8743

Anthony R. Birley, a leading authority in the field of Roman prosopography and well known for his biographies of the emperors Hadrian, Marcus Aurelius and Septimius Severus, was Professor of Ancient History at the University of Manchester from 1974-1990 and at the Heinrich Heine University, Dusseldorf from 1990 until his retirement in 2002. This Festschrift covers a variety of topics relating to the Roman Empire. Eight contributions are in English, one - an excerpt from a historical novel - is in French, the rest are in German. The book is edited by Birley's last three Dusseldorf pupils. After a short introduction by Hirschmann and Krieckhaus ('Statt eines Vorwortes') and a 'Postscript' by Birley himself, there follow the contributions by Bruno Bleckmann ('Kritische Passagen zu Konstantin in der Vita Constantini des Eusebios'), Lukas de Blois ('Soldiers and Leaders in Plutarch's Galba and Otho'), Hannah M. Cotton ('In Lieu of an Article: Reflexions on Hadrian, Antiochus Epiphanes and the Jews'), Werner Eck and Andreas Pangerl ('Neue Diplome fur die Hilfstruppen von Britannia'), Mark Hassall ('Footnotes to The Fasti'), Vera E. Hirschmann ('Die phrygische Opposition. Zu Novatianern und Montanisten im westlichen Kleinasien'), Peter Lampe ('Paulinos Mystes'), David Mattingly ('Urbanism, epigraphy and identity in the towns of Britain under Roman Rule'), Francois Paschoud ('Sulpicii Alexandri ex agente in rebus De uita sua'), Olli Salomies ('Choosing a Cognomen in Rome. Some Aspects'), Hans M. Schellenberg ('Anmerkungen zu Heron von Alexandria und seinem Werk uber den Geschutzbau'), Stefan Sommer ('Vereinigungen in Tarsos'), Richard Talbert ('A Forgotten Masterpiece of Cartography for Roman Historians: Pierre Lapie's Orbis Romanus ad Illustranda Itineraria (1845)'), Konrad Vossing ('Sallust und das 'Massaker von Cirta' 112 v.Chr. (Sall. Iug. 26)'), Klaus Wachtel ('Fragment einer Bauinschrift aus Sexaginta Prista (Moesia inferior)'), Everett L. Wheeler ('Pullarii, Marsi, Haruspices, and Sacerdotes in the Roman Imperial Army'), David Whitehead ('Apollodorus' Poliorketika: Author, Date, Dedicatee'), Ruprecht Ziegler ('Zur Munzemission in Anemurion (Kilikien) unter Kaiser Maximinus Thrax'), Hans M. Schellenberg ('Danksagungen mit einer Anmerkung zum Vorhandensein der Vielzahl personlicher Fotografien'), and Birley's 'Bibliography from 1961 to 2007'. The CD-Rom included with the book contains maps illustrating Talbert's paper.

Alhacen's Theory of Visual Perception

A Critical Edition, with English Translation and Commentary, of the First Three Books of Alhacen's De Aspectibus, the Medieval Latin Version of Ibn Al-Haytham's Kitab Al-Manazir


Author: Alhazen,A. Mark Smith

Publisher: N.A

ISBN: 9780871699145

Category: Optics

Page: 819

View: 3633

The Reader's Adviser


Author: Jack A. Clarke

Publisher: N.A

ISBN: 9780835208536

Category: Language Arts & Disciplines

Page: 1034

View: 2364

A History of Mathematics


Author: Jeff Suzuki

Publisher: Pearson College Division


Category: Mathematics

Page: 815

View: 5900

Blending relevant mathematics and history, this book immerses readers in the full, rich detail of mathematics. It provides a description of mathematics and shows how mathematics was actually practiced throughout the millennia by past civilizations and great mathematicians alike. As a result, readers gain a better understanding of why mathematics developed the way it did. Chapter topics include Egyptian Mathematics, Babylonian Mathematics, Greek Arithmetic, Pre-Euclidean Geometry, Euclid, Archimedes and Apollonius, Roman Era, China and India, The Arab World, Medieval Europe, Renaissance, The Era of Descartes and Fermat, The Era of Newton and Leibniz, Probability and Statistics, Analysis, Algebra, Number Theory, the Revolutionary Era, The Age of Gauss, Analysis to Mid-Century, Geometry, Analysis After Mid-Century, Algebras, and the Twentieth Century. For teachers of mathematics.