Painted Optics Symposium

Total Page:16

File Type:pdf, Size:1020Kb

Painted Optics Symposium FoNnazroNpGroncro RoNcHr ,r.@, Studio Art CentersInternational Palazzodei Cartelloni D. HOCKNEY,J.TSPIKE, S. GRUNDY, R. LAPUCCI, F.CAMEROTA, C.M. FALCO, C. PERNECHELE PaintedOptics Symposium Re-examiningtbe Hockney-Falcotbesis 7 yearson Florence, September7 -9, 2008 Via San Felice a Ema 20 501.25Firenze, Italia http://ronchi.isti.cnr.it Firenze 2009 Ibn al-Haytham'sContributions to Optics,Art, and Visual Literacy CHARLESI\4, FALCO, AIMEE L, \(EINTZ ALLEN C') Introduction In his book, Seuet Knowledge:rediscouering tbe lost tecbniquesof tbe old Masters(2001,2006), the artistDavid Hockney reported visual discoveries within someof the bestknown European paintings that affectlong-held understandings of the developmentof westemart overthe courseof the past600 years. Subse- quently,a collaborationcombining the visualskills of oneof the world'sgreatest artists(Childers, 1996; Langmuir & Lyrrton,2000) with the analyticalskills of an opticalphysicist (Charles M. Falco),resulted in Hockneyand Falcodeveloping the foundationsof a new methodologyfor extracdnginformation from complex, optics-basedimages (Hockney & Falco,2000,2004, 2005a, 2005b, 2005c). As will be discussedin this paper,this methodologyalso contributes to our burgeoning understandingof visualliteracy. Visualliteracy is not limited to the naffativeand symbolicqualities of pic- turesand images (Duncum,2001; Hockney, 1998), but it is alsorooted in the sci entificand culturalstudy of opticsand the visualsystem (Edgerton & Steinberg, 1987;Greenstein, 1997; Grootenboer, 2007). As we will discuss,the genesisof this conceptcan be tracedto the work of the 11'hcentury Arab polymath,Ibn al- Haltham (LatinizedAlhazen or Alhacen),rvhose scientific exploration of vision significantlyimpacted the studyand practice ofvisual art, as well asour cognitive capacityto interpretit. Historic Theoriesof Vsion During the first two centuriesofthe IslamicGolden Age (8th-1Jthcenturies), translationof ancientwritings on the scienceof opticsoffered contemporary in- tellectualswith variousphilosophical theories of vision.Euclid, Ptolemy, Galen (n) CollegeofOptical Sciences.University ofArizona, Tucson8J721 USA T 116 C.M. Falco,A.L. \N/etutzAllan and Aristotle, whose Greek texts were hanslated into Arabic dudng this period, provided disparateviervs on the way the organ of the eyereacts with light to aid in vision. Greek theorieswere largely appropdated by Islamic scholarsuntil the first quarter of the 11ihcentury, when a new method of inquiry rvasintroduced by Ibn 'scientific al-Haytham. Vith the method' he introduced to the rvodd, al-Haythanl used experimental evidence to develop a remarkably accurate theory of vision. His design and interpretation of elegantexperiments became the root sourcefor 'Westernunderstandings ofoptics up to the 17thcentury (Lindberg, 1967). Born in Basra in 965, Ibn al-Haytham primarily worked in Cairo's al-Azhar Mosque - an epicenter for academic inquiry - where he wrote prolifically on subjects as diverse as poetry and politics. He is primarily known however, for his writings on geometrical optics, astronomy, and mathematics.His landmark sevenvolume treatiseon the human visualsystem,Kitab al-Manazir lBook ol Oy> ticsJ,published sometime between 1028 [418 A.H.] and 1018 [429 A.H.], u.as incorporated throughout the core ofpost medieval\Western culture. This seminal work initiated an unbroken chain of continuous developmentof the modern un- derstanding of both optics (i.e. science),as rvell as understandingsrelated to two dimensional pictorial representationsof three dimensionalspace (i.e. art). FrG.1 lbn al Hattham's descriptionof the human visualsystem. From a copy othis Kitab al-Manaztu108i [175 A.H.] in the SiileyminiyeLibrary, Istinbul. Ib n al-Haltham's Cofttibutions. Ill Frc. 2 The anatomyof the eyeaccording to Ibn al-H^yrh^m, horn Ki/abal,ManziL MuseumVictoria. Prior to thework oflbn al-Ha1tham,theories ofvision could be broadly clas- sifiedinto oneofthree categories:extramission, intromission, or a combinationof the two. Extfamissiontheories require that somesort of illuminatingparticles be emittedby the eye.Euclid and Ptolemyare well-known scholars associated with this category(Linberg, 1981). Although there are obvious flaws with extramrssron theories,they do get the geomeryright, with a one-to-onecorrespondence be- tweenpoints on the objectand points on the eye.Intromission theories, with Ar, istotleas a prominentproponent, postulated that objectscontinuously sloughed off microscopicallythin replicasof themselvesthat then travelledto the eyeof the observerIntromission theories avoid some obvious problems of extramission theories,such as near and far objectssimultaneously being visible the momentthe eyeis opened.A third alternative,supported by Platoand Galen(and Aristode, to a lesserdegree), combines the trvotheories, proposing that light emittedby the eyeengages in someway with the interveningair and aforementionedreplicas, or species(Lindberg, 1,967 , 1981,). Like othersbefore him, Ibn al-Haltham also recognizedthat therewere problemswith all existingtheories of vision,but he viasuniquely successful in findinga solutionthat hadeluded the bestminds of antiquity.He proposeda type 118 C.M.Falco, A.L. \VeintzAllcn of intromission theory ofvision, and validatedhis cor.rclusionsby empirical under standing deduced from scientific experimentation, This methodology expanded his understanding beyond the theoretical,which resulted in the incorporation of psychology to explain vision, in combination with the behavior of light and the physiology of tl.reeye. tIG. ' l.rnunfr,k. ll, l. ll;.i \,1.t4l2.,l4t4,d,1d l 'hos insapproxim.r.c h z'"-ot rr. il.c.5o.7.nrL,jnrincr.Birru,ir.i\,r';rsol LrcrspcLri\L;nN. din en.i.'rrJlLrJc,:, specLFcinforri,,ti,'n .in be eLi.jtcd aboui the mannel in rvhich imagcs are produced. Ibr.r al Haytham also linked sight and vision with the properties of light throughout his studies.His experimentssubsequently verified scienti6cprinciples conmonly associatedwith what is known todayas optical'ray tacing'. Theseex' periments included using flat and curved mirrors to control and manipulate light, but primarily involved obseruing the effect of light pouring through aperturesof varioussizes into dalkenedspaces (i.e. camera obscura) (Smith,2001a, 2001b). Perhapsmost inrportantly, they provided him a theoreticalbasis for the existence of rays; a theoretical construct that he used as a meansfor describing and inter preting the visualsystem.These lays are subsequentlyrepresented by geometrical lines associatedon a point by point basisu'ith an object in space. Al Haytham did get one important aspectof vision l'rong: the fact that an image projected by a lens is upside down and flipped right-toJeft apparently rvas more than he could acceptin a theory olvision, eventhough it is containedrvithin his optical fornalism. Leonardo da Vinci also failed to accept this when he ap proached the problem much later (Kemp, 1977).Ultimately, it rvould take another live hundred yearsbefore Kepler would follow Ibn al Haytham's formalism to its inevitable and logical conclusionin developing the theory of the retir.ralimage. Smith (2005) poir.rtsout that such contasting theo es of vision in the pre ceding centuriesbefore Kepler had profound epistemologicalimplications on me- dieval culture. The Platonist perspectivistssupporting extromission,for exampie, suggestthat the eye has powers which extend outward as a meansfor engagrng reality rvhich, in a general sense,can be understood as a "r'isual finger reaching out to palpate things" (Smith, 2005, p. 223). Intromissiolr theories howeveq are uniquely Aristotlian. They ascribe to the idea that, "Knowledge is inductive... lbn al Haytham's Contribrtions. .. I19 Sensationand its representationsare therefore not to be deprecatedas the bearefs of falsehood(Platonism) but ratherto be prizedas the bearersof tuth" (Smith, 2001,p. cx). Perhapspredictably, as cultural understandings of visionard cognitionex pandedto includethese disparate theories, so too did evolvingcultural consid- erationsfof conceptsseemingly unrelated to the scienceof optics,the impactof whichwas not relegatedto the sciencecommunity alone but spreadout to include the humanitiesat large. 3. Interdisciplinary disseminationand appropriation of Kiffib al-Mdndzir Thereis little debatethat Ibn al-Haltham'sseminal work, Kitab al-Manazir, translatedinto Latin asDe Aspectibus In theearly to mid-1.1th century, is largelyre, sponsiblefor the widespreadappropriation of its contentsby \WesternEuropean intellectuals(Lindberg, 1967). Smith recognizesthat variationsexist among the Latin versionas compared with theArabic original, not simplyin its organizarion- al sructurebut in theinterpretation of specificterms (2001). From thebeginning, however,knowledge of the coreprinciples and experimentsdetai.led throughout the manuscriptby its originalauthor were not limited to lWesternreaders alone, or to scientificaudiences specifically. De Aspectibusis first referencedin Bartolomeo Anglicus'De proprietatibus rcrun,lOn thePrcpertyof Thingsl c1220-1T0(Smith.2001), a monumentaland earlyencyclopedia covering a widevariety of subjects.The text refersto the study ofoptics andIbn al'Haythamspecifically several times. It wasrequired reading at the Universityof P arisin 1296,avatlable in the universitylibrary of the Sorbonne by 1306,and usedwidely as referencematerial at Oxford, Cambridge,Canter- bury andMerton Collegeby the mid-fourteenthcentury (Holbrook, 1998). Specificproposals contained withn De Aspectibzzshowever,
Recommended publications
  • “Aesthetic in Alhazen's Kitāb Al-Manāẓir”
    International Journal of Arts 2014, 4(1): 1-7 DOI: 10.5923/j.arts.20140401.01 “Aesthetic in Alhazen’s Kitāb al-manāẓir” Hasan Bolkhari Ghehi Associate Professor of University of Tehran Abstract Abū ʿAlī al-Hasan ibn al-Haytham, also known in the West as Alhazen1 is one of the greatest researchers of Optic concept in all the centuries, according to George Sarton (Sarton, 1967:704). His greatest work, Kitāb al-manāẓir‖ (Treasury of Optics), had a major influence not only on 13th-century thinkers such as Roger Bacon but also on later scientists such as the astronomer Johannes Kepler (Britannica encyclopedia. Ibn al-Haytham). Furthermore, the definition of beauty which had come into spotlight in Greek philosophy by attempts of Plato (Such as Hippias Major & Phaedrus) was well and deeply reexamined in explorations of Alhazen in optic under his inductive and experimental method. His researches had a great influence on the attitudes of the Westerners toward beauty in late middle ages and renaissance. This paper has taken into consideration the comprehensive definition that Alhazen has given on beauty in his book ―Kitāb al-manāẓir”. His definition promised the foundation of a kind of Islamic aesthetics, but no thinker in Islamic civilization followed his way except Kamal al Din Farsi2 in ―Kitab Tanqih al-Manazir” (The Revision of Ibn al-Haytham's Optics), while the Western thinkers followed his way through translating ―Al-manāẓir‖ in 1272. In his studies, Umberto Eco has adequately explained such definition and although he attributes the researches to Witelo3 (not Alhazen) nowadays it has become clear that the main body of Witelo’s ―Perspectivae‖ was famous book of Alhazen.
    [Show full text]
  • Light in a Socio- Cultural Perspective
    Light in a Socio- Cultural Perspective Edited by Ruth Lubashevsky and Ronit Milano Light in a Socio-Cultural Perspective Edited by Ruth Lubashevsky and Ronit Milano This book first published 2017 Cambridge Scholars Publishing Lady Stephenson Library, Newcastle upon Tyne, NE6 2PA, UK British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Copyright © 2017 by Ruth Lubashevsky, Ronit Milano and contributors All rights for this book reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. ISBN (10): 1-4438-7907-X ISBN (13): 978-1-4438-7907-1 CONTENTS List of Figures............................................................................................ vii Introduction ................................................................................................ ix Part 1: Between Image and Truth Chapter One ................................................................................................. 3 From the Overview Effect to the Data Sublime: Stargazing in the Twenty- First Century Romi Mikulinsky Chapter Two .............................................................................................. 19 Cartesian Illuminations: Transfers of Light between the Physics and Philosophy of Descartes Stephan Gregory Part 2: Exposing Reality Chapter Three ...........................................................................................
    [Show full text]
  • Deep Time of the Media ELECTRONIC CULTURE: HISTORY, THEORY, and PRACTICE
    Deep Time of the Media ELECTRONIC CULTURE: HISTORY, THEORY, AND PRACTICE Ars Electronica: Facing the Future: A Survey of Two Decades edited by Timothy Druckrey net_condition: art and global media edited by Peter Weibel and Timothy Druckrey Dark Fiber: Tracking Critical Internet Culture by Geert Lovink Future Cinema: The Cinematic Imaginary after Film edited by Jeffrey Shaw and Peter Weibel Stelarc: The Monograph edited by Marquard Smith Deep Time of the Media: Toward an Archaeology of Hearing and Seeing by Technical Means by Siegfried Zielinski Deep Time of the Media Toward an Archaeology of Hearing and Seeing by Technical Means Siegfried Zielinski translated by Gloria Custance The MIT Press Cambridge, Massachusetts London, England © 2006 Massachusetts Institute of Technology Originally published as Archäologie der Medien: Zur Tiefenzeit des technischen Hörens und Sehens, © Rowohlt Taschenbuch Verlag, Reinbek bei Hamburg, 2002 The publication of this work was supported by a grant from the Goethe-Institut. All rights reserved. No part of this book may be reproduced in any form by any elec- tronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. I have made every effort to provide proper credits and trace the copyright holders of images and texts included in this work, but if I have inadvertently overlooked any, I would be happy to make the necessary adjustments at the first opportunity.—The author MIT Press books may be purchased at special quantity discounts for business or sales promotional use. For information, please e-mail [email protected] or write to Special Sales Department, The MIT Press, 55 Hayward Street, Cambridge, MA 02142.
    [Show full text]
  • Technology and Sustainable Development Edited by Roshdi Rashdi, Azzedineboudrioua and Vasudevan Lakshminarayanan (CRC Press, to Be Published April 2017)
    1 Chapter in Light-Based Science: Technology and Sustainable Development edited by Roshdi Rashdi, AzzedineBoudrioua and Vasudevan Lakshminarayanan (CRC Press, to be published April 2017) Ibn al-Haytham and His Influence on Post-Medieval Western Culture Charles M. Falco College of Optical Sciences University of Arizona, Tucson 85721 USA Abstract As described in this chapter, Ibn al-Haytham (Alhazen) made intellectual contributions that were subsequently incorporated throughout the core of post-Medieval Western culture. The noted science historian, David Lindberg, wrote that "Alhazen was undoubtedly the most significant figure in the history of optics between antiquity and the seventeenth century." Impressive and accurate as that characterization is, the examples in this chapter show that it significantly understates the impact that al-Haytham's work on optics had on areas as wide-ranging as the science, literature, art and even the theology of Europe. Introduction Ibn al-Haytham (Latinized as Alhazen or Alhacen) wrote nearly one hundred works on topics as diverse as astronomy, poetry and politics. Although today he is largely known for his writings on geometrical optics, astronomy, and mathematics, with his landmark seven-volume Kitāb al-Manāzir [Book of Optics], published sometime between 1028 and 1038, he made intellectual contributions that subsequently were incorporated throughout Western culture. The Kitāb al-Manāzir was translated into Latin as de Aspectibus sometime prior to 1230 where it profoundly influence on European intellectuals as diverse as the writer Geoffrey Chaucer, the theologian John Wyclif, and the scientific work on optics of Bacon, Pecham, and Witelo. The noted science historian, David Lindberg, wrote that "Alhazen was undoubtedly the most significant figure in the history of optics between antiquity and the seventeenth century." However, accurate as that characterization is, it significantly understates the impact that al-Haytham had on areas as wide-ranging as the art, science, theology, and literature of Europe.
    [Show full text]
  • HINDSIGHT Journal of Optometry History
    HINDSIGHT Journal of Optometry History October, 2007 Volume 38, Number 4 Official Publication of the Optometric Historical Society Hindsight: Journal of Optometry History publishes material on the history of optometry and related topics. As the official publication of the Optometric Historical Society, Hindsight: Journal of Optometry History supports the purposes and functions of the Optometric Historical Society. The purposes of the Optometric Historical Society, according to its by-laws, are: • to encourage the collection and preservation of materials relating to the history of optometry, • to assist in securing and documenting the recollections of those who participated in the development of optometry, • to encourage and assist in the care of archives of optometric interest, • to identify and mark sites, landmarks, monuments, and structures of significance in optometric development, and • to shed honor and recognition on persons, groups, and agencies making notable contributions toward the goals of the society. Officers and Board of Trustees of the Optometric Historical Society for 2007: President: Melvin Wolfberg, 3095 Buckinghammock Trl., Vero Beach FL 32960-4968, [email protected] Vice-President: Jerome J. Abrams Secretary-Treasurer: Bridget Kowalczyk, International Library, Archives, and Museum of Optometry, 243 North Lindbergh Boulevard, St. Louis, MO 63141; [email protected] Trustees: Walter W. Chase Jay M. Enoch Chuck Haine Douglas K. Penisten The official publication of the Optometric Historical Society was previously titled: Newsletter of the Optometric Historical Society, 1970-1991 (volumes 1-22), and Hindsight: Newsletter of the Optometric Historical Society, 1992-2006 (volumes 23-37). Hindsight: Journal of Optometry History began in 2007 with volume 38, number 1.
    [Show full text]
  • Some Secret Involuntary Encounters: a Quarter Century After Downcast Eyes
    Some secret involuntary encounters 63 Some secret involuntary encounters: A quarter century after Downcast Eyes Yuichi Sato * Introduction The true problem is to understand why such different cultures become involved in the same search and have the same task in view(and when the opportunity arises, encounter the same modes of expression). We must understand why what one culture produces has meaning for another culture, even if it is not its original meaning(Signes, 84, PM, 111) This question appears in an article written by Maurice Merleau-Ponty about André Malraux’s imaginary museum. In this article Merleau-Ponty discusses the institution of a painter’s work, or of a style in the history of painting. Institution can be understood as “the events which deposit a sense in me, not just as something surviving or as a residue, but as the call to follow, the demand of a future”(IP, 124), that is, the “internal circulation between the past and the future”(IP, 125). The efforts and the interests of the painter are prospective, but there are the “resumption(s)[reprise(s)]”(Cf., Signes, 73) of his own past works or those of other painters. Works that were created in the past seem to shut out the future, but in actuality, they wish to continue into the future. Martin Jay’s Downcast Eyes also has its resumptions, and still call for them. As Jay mentioned, there have * Associate Professor, National Institute of Technology, Fukui College 64 立命館大学人文科学研究所紀要(118号) been numerous responses to this book in the quarter century since it appeared, 1) but beneath the direct responses there is growing silence.
    [Show full text]
  • Ed 288 74; Se 048 756
    DOCUMENT RESUME ED 288 74; SE 048 756 AUTHOR Bruno, Leonard C. TITLE The Tradition of Science: Landmarks of Western Science in the Collections of the Library of Congress. INSTITUTION Library of Congress, Washington, D.C. REPORT NO ISBN-0-8444-0528-0 PUB DATE 87 NOTE 359p.; Some color photographs may not reproduce well. AVAILABLE FROMSuperintendent of Documents, Government Printing Office, Washington, DC 20402 ($30.00). PUB TYPE Books (010) -- Reference Aaterials - Bibliographies (131) -- Historical Materials (060) EDRS PRICE MFO1 Plus Postage. PC Not Available from EDRS. DESCRIPTORS Astronomy; Botany; Chemistry; *College Mathematics; *College Science; Geology; Higher Education; Mathematics Education; Medicine; Physics; *Science and Society; Science Education; *Science History; *Scientific and Technical Information; Zoology ABSTRACT Any real understanding of where we stand scientifically today and where we are headed depends to a great extent on an awareness of how we reached those scientific achievements. The increased impact of science and technology on our lives makes such an understanding even more important. For this reason, this book is intended to provide information about the major works of science in the collections of the Library of Congress. These selected works are organized here by traditional scientific discipline and are treated in historical and, generally, chronological order. The contents contain chapters on: (1) astronomy; (2) botany; (3) zoology; (4) medicine; (5) chemistry; (6) geology; (7) mathematics; and (8) physics. A bibliography provides information about particular Library of Congress collections to which a book or manuscript may belong, as well as specific bibliographic information. Title translations are also included. (TW) *********************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document.
    [Show full text]
  • Historical Writing and Community Among the Orti Oricellari
    HISTORICAL WRITING AND COMMUNITY AMONG THE ORTI ORICELLARI by Heather Stein A dissertation submitted to Johns Hopkins University in conformity with the requirements for the degree of Doctor of Philosophy Baltimore, Maryland September 14, 2015 Abstract My research interprets the specific context in which Florentine humanist historians of the late-fifteenth and early-sixteenth century wrote: the social, political and intellectual world that informed authors’ conceptions of history and how historical texts functioned in that world. Historical writing is the crucial link between Renaissance humanism and statescraft. In response to recent calls for a more actor-centred approach to problems of the state by scholars such as Pieroangelo Schiera, I demonstrate that by the early sixteenth century, the ten Florentine humanists and governors (Bernardo Rucellai, Giovanni Corsi, Pietro Crinito, Francesco da Diacceto, Francesco Vettori, Piero Martelli, Giovanni Canacci, Bartolomeo Fontius, Cosimo Pazzi and Bindaccio Ricasoli) who met regularly in Bernardo Rucellai’s eponymous gardens to discuss matters of politics and culture adopted a new philosophy of history that steered away from divine intervention in the secular world. Their historical philosophy focused instead on the human experience and emotional response to the spilling out of the violence of the battlefield into the population. My study situates the historical writing of the late-fifteenth and early- sixteenth century in the context of the Italian Wars and the developments in political thought leading up to the landmark publication of Machiavelli’s Il principe. Readers: Dr. Gabrielle M. Spiegel, Dr. Christopher S. Celenza, Dr. Walter Stephens, Dr. Eugenio Refini. ii Acknowledgements All dissertations are struggles, or so I have been told, but mine has been made much easier by a group of passionate, caring scholars who have encouraged my work on this project over the course of the past seven years.
    [Show full text]
  • Canterbury Tales Sub Title 『カンタベリー物語』のフラグメント5における科学と魔術 Author 浅川, 順子(Asakawa, Junko) Publisher 慶應義塾大学日吉紀要刊行委員会 Publication Year 2017 Jtitle 慶應義塾大学日吉紀要
    Title Science and magic in fragment V of the Canterbury Tales Sub Title 『カンタベリー物語』のフラグメント5における科学と魔術 Author 浅川, 順子(Asakawa, Junko) Publisher 慶應義塾大学日吉紀要刊行委員会 Publication year 2017 Jtitle 慶應義塾大学日吉紀要. 英語英米文学 (The Hiyoshi review of English studies). No.70 (2017. 12) ,p.1- 16 Abstract Notes Genre Departmental Bulletin Paper URL https://koara.lib.keio.ac.jp/xoonips/modules/xoonips/detail.php?koara_id=AN10030060-2017123 1-0001 慶應義塾大学学術情報リポジトリ(KOARA)に掲載されているコンテンツの著作権は、それぞれの著作者、学会または出版社/発行者に帰属し、その権利は著作権法によって 保護されています。引用にあたっては、著作権法を遵守してご利用ください。 The copyrights of content available on the KeiO Associated Repository of Academic resources (KOARA) belong to the respective authors, academic societies, or publishers/issuers, and these rights are protected by the Japanese Copyright Act. When quoting the content, please follow the Japanese copyright act. Powered by TCPDF (www.tcpdf.org) Science and Magic in Fragment V of the Canterbury Tales Junko Asakawa The Squire’s Tale is incomplete, but it is followed by the Franklin’s complimentary words to the Squire as if it is successfully finished and the Franklin is impressed and even inspired by the story and its teller; the Franklin markedly praises the Squire for not only his wit and eloquence but also his gentle behavior, confessing his yearning for “gentillesse,” which he introduces in his tale as a theme. Even if, as a critic argued,1) the Franklin interrupts the Squire as the Host does about Sir Thopas, his aim is to express admiration for the young nobleman’s tale. This development seems to indicate that Chaucer needs to create a strong connection between the two tales for some purpose. As Brian S.
    [Show full text]
  • Merzbach U C Boyer C B a Hi
    A History of Mathematics THIRD EDITION Uta C. Merzbach and Carl B. Boyer John Wiley & Sons, Inc. Copyright r 1968, 1989, 1991, 2011 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or trans mitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Pub lisher, or authorization through payment of the appropriate per copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750 8400, fax (978) 646 8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748 6011, fax (201) 748 6008, or online at http://www.wiley.com/go/permissions. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or war ranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a par ticular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suit able for your situation. You should consult with a professional where appropriate.
    [Show full text]
  • Antimetaphysics As Analytical Method in Croce's Conception of History
    _________________________________________________________________________Swansea University E-Theses Antimetaphysics as analytical method in Croce's conception of history. Paci, Luca How to cite: _________________________________________________________________________ Paci, Luca (2004) Antimetaphysics as analytical method in Croce's conception of history.. thesis, Swansea University. http://cronfa.swan.ac.uk/Record/cronfa42480 Use policy: _________________________________________________________________________ This item is brought to you by Swansea University. Any person downloading material is agreeing to abide by the terms of the repository licence: copies of full text items may be used or reproduced in any format or medium, without prior permission for personal research or study, educational or non-commercial purposes only. The copyright for any work remains with the original author unless otherwise specified. The full-text must not be sold in any format or medium without the formal permission of the copyright holder. Permission for multiple reproductions should be obtained from the original author. Authors are personally responsible for adhering to copyright and publisher restrictions when uploading content to the repository. Please link to the metadata record in the Swansea University repository, Cronfa (link given in the citation reference above.) http://www.swansea.ac.uk/library/researchsupport/ris-support/ Antimetaphysics as analytical method in Croce’s conception of history Luca Paci University of Wales Swansea Thesis submitted for the degree of PhD September 2004 ProQuest Number: 10801710 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a com plete manuscript and there are missing pages, these will be noted.
    [Show full text]
  • Thedatabook.Pdf
    THE DATA BOOK OF ASTRONOMY Also available from Institute of Physics Publishing The Wandering Astronomer Patrick Moore The Photographic Atlas of the Stars H. J. P. Arnold, Paul Doherty and Patrick Moore THE DATA BOOK OF ASTRONOMY P ATRICK M OORE I NSTITUTE O F P HYSICS P UBLISHING B RISTOL A ND P HILADELPHIA c IOP Publishing Ltd 2000 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher. Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency under the terms of its agreement with the Committee of Vice-Chancellors and Principals. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ISBN 0 7503 0620 3 Library of Congress Cataloging-in-Publication Data are available Publisher: Nicki Dennis Production Editor: Simon Laurenson Production Control: Sarah Plenty Cover Design: Kevin Lowry Marketing Executive: Colin Fenton Published by Institute of Physics Publishing, wholly owned by The Institute of Physics, London Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK US Office: Institute of Physics Publishing, The Public Ledger Building, Suite 1035, 150 South Independence Mall West, Philadelphia, PA 19106, USA Printed in the UK by Bookcraft, Midsomer Norton, Somerset CONTENTS FOREWORD vii 1 THE SOLAR SYSTEM 1
    [Show full text]