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Cartography and the Geometry of Spoce Re-Imagining the Legacy of Claudius Rdemy

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Cartography and the Geometry of Spoce Re-Imagining the Legacy of Claudius Rdemy Cartography and the geometry of spoce Re-imagining the legacy of Claudius Rdemy Christine Elizabeth Eari, BSc. A thesis submitted to The Faculty of Graduate Shidies and Research in partial fulfilment of the requirements for the degree of Master of Arts Department of Geography Carleton University Ottawa, Ontario July, 1999 @ 1999, Christine E. Earl National Library Bibliothèque nationale 1*1 of Canada du Canada Acquisitions and Acquisitions et Bibliographic Services services bibliographiques 395 Wellington Street 395. rw, WdingtOn OnawaON K1AW OrtawaOIY K1A ûfU4 canada canada The author has granted a non- L'auteur a accordé une Licence non exclusive licence ailowing the exclusive permettant à la National Library of Canada to Biblioîhèque nationale du Canada de reproduce, loan, distri'bute or seii reproduire, prêter, distribuer ou copies of this thesis in microform, vendre des copies de cette thèse sous paper or electronîc formats. la forme de microfiche/film, de reproduction sur papier ou sur format électronique. The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantial extracts fiom it Ni la thèse ni des extraits substantiels may be prïnted or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation. It is generaily recognized that during the span of thefrom the mid-15" to mid-17" centuries, European cosmology undenivent a fundamental change. The new idea of the universe was theorized as substanceless extension, or space, infinite and homogeneous but divisible into any number of finite, absolute spaces by the imposition of an abstract grid. This action has been characterized as the 'geometrization of space,' and it resulted in a deep philosophical shift. This thesis develops a general chronology and context for the hypothesis that cartographic representation provided a perceptual pre-requisite for the new cosmological ideas. The key idea behind this proposition is that the mapping mode1 expticated in the Geographia by Claudius Ptolemy took Euclidean geometq as its basic principle, and that this Ied to the adoption of Euclidean geomeûy as the basis for what was eventuaily known as 'Newtonian' cosmology. The thesis therefore develops three paralleI thematic histories - cosmological ideas, geometry, and cartography - and explores and sumises connections between them. iii Acknowledgements This thesis would not have been written without the help and encouragement of many of my friends, farniiy, and colleagues, and without the institutional support of Carleton University where 1 have been employed for the past 22 years. It is with sincere gratitude and pleasure that 1 thank those individu& whose interest and advice have made it possible to complete this project, and who have made the thesis, as cornpleted, much better than it would otherwise have been. My supervisor, Simon Dalby, provided sure and patient guidance while 1 was engaged with this project. In addition to Simon, several people gave generously of their tirne to read the thesis in whole or in part and made valuable comments. They are Thomas Wilkinson, Bruce Richter, David Bennett, and MichaeI Phelan, and I am greatly appreciative of their efforts. 1 should also like to thank my colleagues in the Department of Geography for their personal support and for providing examples of academic integity and excellence. For their interest and help, thanks are also due to tain Taylor and David Woodward. FinalIy, 1 must express my deepest thanks to my mother for her love and momi support, and to Nessa, my faithhl hound. for hers. For my father. Thomas Desmond Earl(2 92 1 -1 993) Table of Contents Acceptance Il Abstract iii Acknowledgements iv Table of Contents vi Geneml Chronology vii Cartogmphic Chrono!ogy X Schernatic TirneIine xii Introduction Image The shift to the visual Image and cognition Mapping as represen tational practke Cosmology Aristotelian n atuml phihoph-v The waning of the Aristotelim philosophical he-vduy From Descartes to Newton Geometry Concepts of space in Greek ma thematics hfathematics in the Midàle Ages Euclidean geomeûy Maps and îhe geomee of space Cartograp h y Mapping in medieval Europe Ptolemy 's map The grid Mathematics and cartography - contextualizing links Ancient Greece to the Middle &es The Renaissance milieu Toscanelli. Renaissance man Nicholas of Cusa Mathema ticians and cartography in the 1 P and 17Lh centuries Reflections and extrapolations Reflections Extrapolations General Chronology Ptolemaic planetary systern available in Min &ansL of the Almagest Fibonacci Liber abau church in Paris fohids teachings of Aristode's works îranslation of Liber astronorniae conûasîs Ptolemaic and ANtotelian planetary systems Robert Grwseteste optia - lux (Engiish) Fibonaui Pmdica Ge~rne~ae(Ital). Eudidean geomeûy and trigonometxy stereogmphic projection descriid (French} Sacrobosco De sphaem (John of Holywood) Robert Grosseteste on scientific methodology Pope Gregoiy IX rescinds ban on study of physics Robert Grosseteste optics Albertus Magnus botanical dassikation (German) panus us translation of Eudid's Elernents hom Arabic to Latin (fint printed in 1482) Roger Bacon Opus Maius: mathematics. optia. experirnental geogmphical CO-or& Peregrinus magneth (celestial poles) (French) translation of many of the works of Archimedes and Asistode from Greek into Latin Witelo optia. mirrors. refraction (Silesian) St. Thomzç Aquinas 'Christianiition' of Aristotle (substitution of God for Prime Mover) William of Moerùeke translation of Archimedes Alfonsine Tables: predictions of celestial motion based on Ptolemaic syçtern. used for 3 c.'s Etienne Ternpier Bishop of Paris. condernns 219 propositions of Aristotle John Pecham Penpediva communis. standard work on optics for 3 centuries (Enqiiih) major work on planeûuy systern. cosrnography. geodesy. geogniphy. mechania (Persian) Wdiiar;. ' St. Cloud latitude of Paris (English-French) iclarco Polo descriptions of travel in Far east Giotto begins work on hescws at Padua, new way to represent relationship between visual space and 2D surface popular treatise on farm methods T. Bradwardine mathernatia of motion (English) Wdiarn of Odrham motion. logic (ûckharn's razor) (Englih) mathematical concept of infmity (ftalii) Jean Buridan irnpetus theory: no need for continual intervention of God in universe. only initial push (Fr) Nicole Orme 2D gmphs: 'latitude of fom' (French) Chaucer treatise on the astrolabe (Engliih) Henry the Navigator estabüshes school for navigation. astronomy. geography. norage of maps (Portuguese) voyages add to geogmphical icnowledge Brunelieschi demonstrates linear perspeaive Aiberti pubiiihes book on Linear perspective. Della piîtura Nicholas of Cusa On Leumed Ignorance (Dedoda ignomntia):universe indeterminate. no centre Gutenburg moveable type Ghiberti Third Commentuy: survey of mathematical tradition in optics and perspective theory Nicolas of Cusa Idiota Papal Jubilee celebrations in Rome. Nicolas of Cusa hosts visitoa fall of Byzantium Gutenburg Bible pubüshed. first pnnted book in Western wodd Regiomontanus ttigonorneky. Law of Sines death of Nichoias of Cusa Peuhach New Theory of the Planets Michelangelo Sktine Chape1 atomic theories of Democrinis. Epicurus. Lucretius inboduced into Europe sets up pruiting press (England). by end 15th c.: 9 million books in Europe Elernents pnnted (Campanus' ûanslation of 1255) 1482-1515 translations and printing of ciassical tex% 1489 algebraic syrnbolism. + and - signs 1491 long division 1492 Columbus saiis the ocean blue. discovery of America 1494 Luca Pacioli Summa de arithmeh'cu 1500 Leonardo da Vici speculations 1502 Amerigo Vespucci condudes South Arnenca not part of Asii but separate continent 1505 Viator three-point peqective 1509 Luca Paüoli De diuina propottione 1514 Copemicus writes fit version of treatise on planetaxy system. not publiçhed und 1543 1518 Fmncesco Feliciano Scola GrimddelIa Libm darimetka 1522 Waidseemder theodolite MagellanlElcano roundness of the earth wrified. round-the-world voyage completed 1531 Juan Lui. Vives condemns dogmatic #ceptance of Aristotelianism. advocates experimental evidence (Spanish) 1533 Gemrna FNius triangulation 1x3 Copemicus publication of De reuolutionibus. cenûe of universe moved from earth ro near the Sun (Polish) Tartaglia Italian transhtion of Eudid publication of Mwrkke's Archimedes 1544 S. Munster Cosnogrophia. &vol compendium of wodd geogmphy (Geman) 1545 Cardano initiates midy of probability ttieory (Itaiian) 1% Georgius Agricola mineralagical classification system 1551 Reinhold tables of planetay motions based on Copemican system 1553 Srwehis theory on circulation of blood. theology in book leads to Inquisition and death 1570 Euciid Eiements tmnslated into English 1572 Tycho Brahe new star 1576 Georgian calendar replaces Julian (adopted in 1582) Thomas Digges stehdistances variable. univeme infinite (English} 1577-78 Brahe/Masdin obsenration of amek, acceptance of Copemican theoiy 1584 Giordano Bruno defends Copemican îheoty. postulates infinite universe and non-existence of absolute huth 1591 Vieta algebra. generalities. symbolism (French) 160 Bruno bumed at the stike for heretical theories Gilbert magnetically-based concept of solar system 1602 Tycho Brahe posthurnous publication of observations 1604 Kepler mathematics (postulate re pdellines) and optics 16û5 Franck Bacon The Aduancernent of Lming encourages uses
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