The Impact of Copernicanism on Judicial Astrology at the English Court, 1543-1660 ______

Total Page:16

File Type:pdf, Size:1020Kb

The Impact of Copernicanism on Judicial Astrology at the English Court, 1543-1660 ______ Clemson University TigerPrints All Theses Theses 1-2011 'In So Many Ways Do the Planets Bear Witness': The mpI act of Copernicanism on Judicial Astrology at the English Court, 1543-1660 Justin Dohoney Clemson University, [email protected] Follow this and additional works at: https://tigerprints.clemson.edu/all_theses Part of the History of Science, Technology, and Medicine Commons Recommended Citation Dohoney, Justin, "'In So Many Ways Do the Planets Bear Witness': The mpI act of Copernicanism on Judicial Astrology at the English Court, 1543-1660" (2011). All Theses. 1143. https://tigerprints.clemson.edu/all_theses/1143 This Thesis is brought to you for free and open access by the Theses at TigerPrints. It has been accepted for inclusion in All Theses by an authorized administrator of TigerPrints. For more information, please contact [email protected]. "IN SO MANY WAYS DO THE PLANETS BEAR WITNESS": THE IMPACT OF COPERNICANISM ON JUDICIAL ASTROLOGY AT THE ENGLISH COURT, 1543-1660 _____________________________________________________ A Thesis Presented to the Graduate School of Clemson University _______________________________________________________ In Partial Fulfillment of the Requirements for the Degree Master of Arts History _______________________________________________________ by Justin Robert Dohoney August 2011 _______________________________________________________ Accepted by: Pamela Mack, Committee Chair Alan Grubb Megan Taylor-Shockley Caroline Dunn ABSTRACT The traditional historiography of science from the late-nineteenth through the mid-twentieth centuries has broadly claimed that the Copernican revolution in astronomy irrevocably damaged the practice of judicial astrology. However, evidence to the contrary suggests that judicial astrology not only continued but actually expanded during the sixteenth and early seventeenth centuries. During this time period, judicial astrologers accomplished this by appropriating contemporary science and mathematics. Copernicus’s De revolutionibus , in particular, provided better mathematics for determining the positions of the planets than the prevailing Ptolemaic system and reformist astrologers interested in making astrology a precise, mathematical science embraced this new astronomy. This study evaluates the impact that Copernicus’s heliocentric theory of the cosmos had on the practice of judicial astrology, particularly within the English court patronage system between the publication of Copernicus’s De revolutionibus in 1543 and the Restoration of the monarchy and founding of the Royal Society in 1660. In England, while noble patrons defined the value of science in terms of its practical utility, many English judicial astrologers successfully argued for scientific legitimacy based on their ability to precisely predict planetary locations. Contrary to their European counterparts on the Continent, English patrons typically required tangible, practical results to justify their support of client-scientists. The heliocentric theory received a largely positive reaction in England, and many astrologers readily employed its mathematics to make more precise ii predictions of planetary locations, which would presumably lead to better prognostications of human events. As long as scientists and patrons defined science in these exclusively mathematical terms, astrology could comfortably exist within these scientific boundaries. However, throughout the mid-sixteenth century, multiple processes occurred that changed astrology from a science into a popular belief in England. Patrons began to lose interest in astrology and thus financed fewer astrologers, and with the instability of the Civil War, fewer patrons were in positions of power to provide this sort of support. Furthermore, as astrology enjoyed increased popularity among the lower and merchant classes of England through almanac and pamphlet publications, scientists saw it in their best professional interest to consciously distance themselves from astrology and redefine and re-categorize it beyond the reasonable margins of proper scientific practice. In short, while astrology declined as a scientific activity during the latter half of the seventeenth century, it found success as a popular activity beyond the confines of conventional science. iii DEDICATION To my mother, for teaching me the love of reading; to my father, for teaching me the love of the past; and to Kirsten, for teaching me to love. iv ACKNOWLEDGEMENTS First of all, I would like to thank my committee, without whom this thesis would not be possible. Dr. Pamela Mack spent almost as much time as I did editing the manuscript, and more importantly, challenged my conceptions of both history and science, which led to a much richer and more interesting and multifaceted work than I would have written without her tutelage. My coursework with Dr. Alan Grubb formed the backbone of my graduate education, and his advice, particularly regarding historiography, has been indispensable. Dr. Megan Taylor-Shockley held many discussions with me about all manner of popular beliefs during the early modern era, and this contributed a great deal to my historical approach to astrology. Finally, Dr. Caroline Dunn supplemented my own meager knowledge of Latin to ensure that my translations were correct. Many others facilitated the completion of this study. Dr. Jeremiah Hackett of the University of South Carolina read an early prospectus version of my thesis and provided some conceptual suggestions as well as encouragement that the idea was worth pursuing, and Dr. Rienk Vermij of the University of Oklahoma also read an early draft and offered a great deal of insight into the patron-scientist relationship in northern Europe for some very useful comparisons in my own research. I would also like to thank my colleague, friend, and fellow graduate student here at Clemson University Matt Henderson for suggesting a provocative title and for our many, many discussions and debates about the history and philosophy of science in general and Copernicus in particular. Cathy Felten v generously granted me access to the Early English Books online database through the University of Louisville library system, without which I would not have been able to conduct the majority of my primary source research. Finally, I would like to thank all of those who read drafts of my thesis at various stages, especially Kirsten Mull, Carly Niermeier, Jeremy Weston, and Adam Zucconi, all of whom provided valuable suggestions. vi TABLE OF CONTENTS Page TITLE PAGE .................................................................................................................... i ABSTRACT ..................................................................................................................... ii DEDICATION ................................................................................................................ iv ACKNOWLEDGEMENTS ............................................................................................. v INTRODUCTION ........................................................................................................... 1 CHAPTER 1. FROM PTOLEMY TO COPERNICUS: A BRIEF HISTORY OF ANCIENT AND MEDIEVAL ASTROLOGY ............................................ 16 2. COPERNICANS, SEMI-COPERNICANS, AND MATHEMATICAL COPERNICANS: THE ENGLISH REACTION TO HELIOCENTRISM ................................................................................ 40 3. COPERNICANISM AND ASTROLOGY IN SIXTEENTH-CENTURY ENGLAND: PATRONAGE AND PRACTICALITY ................................. 63 4. REDEFINING ASTROLOGY IN THE SEVENTEENTH-CENTURY: UNIVERSITIES, ALMANACS, AND JACOBEAN PATRONAGE .............................................................................................. 96 CONCLUSIONS.......................................................................................................... 118 BIBLIOGRAPHY ........................................................................................................ 122 vii INTRODUCTION When Copernicus wrote in his seminal astronomical treatise De revolutionibus orbium coelestium that “in so many…ways do the planets bear witness,” he was referring to how their observed motions provided evidence for the earth’s mobility.1 But for most of the scientifically-educated elite in sixteenth-century Europe, the planets bore witness in quite another way and provided evidence of a very different kind—that of their astrological influence over human events.2 Copernicus’s epoch-making work, of course, displaced the earth from the center of the cosmos and replaced it with the sun, but it also provided more precise calculations for the prediction of planetary positions than the Ptolemaic system. Among astrologers interested in applying this new astronomical data to the prognostication of human events, a great reform movement flourished throughout much of the sixteenth and early seventeenth centuries. Eventually, however, the reform movement foundered, scientists and their patrons lost interest, and astrology relocated to other more receptive venues. The narrative of astrology’s scientific decline in the latter half of the seventeenth century is less a story about the elimination of a superstition and more a story about how science was defined, who defined it, and what values determined its definition. Most scientists accepted astrology in the early sixteenth century and most 1 Nicolaus Copernicus, De revolutionibus orbium coelestium [1543] ,trans. Edward Rosen (Baltimore:
Recommended publications
  • University of California, San Diego
    UNIVERSITY OF CALIFORNIA, SAN DIEGO THE SCIENCE OF THE STARS IN DANZIG FROM RHETICUS TO HEVELIUS A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in History (Science Studies) by Derek Jensen Committee in charge: Professor Robert S. Westman, Chair Professor Luce Giard Professor John Marino Professor Naomi Oreskes Professor Donald Rutherford 2006 The dissertation of Derek Jensen is approved, and it is acceptable in quality and form for publication on microfilm: _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ Chair University of California, San Diego 2006 iii FOR SARA iv TABLE OF CONTENTS Signature Page........................................................................................................... iii Dedication ................................................................................................................. iv Table of Contents ...................................................................................................... v List of Figures ........................................................................................................... vi Acknowledgments..................................................................................................... vii Vita, Publications and Fields of Study...................................................................... x A Note on Dating
    [Show full text]
  • Dissertation Title Page
    “Singing by Course” and the Politics of Worship in the Church of England, c1560–1640 By James Campbell Nelson Apgar A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Music in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Davitt Moroney, Chair Professor James Davies Professor Diego Pirillo Spring 2018 Abstract “Singing by Course” and the Politics of Worship in the Church of England, c1560–1640 by James Campbell Nelson Apgar Doctor of Philosophy in Music University of California, Berkeley Professor Davitt Moroney, Chair “Singing by course” was both a product of and a rhetorical tool within the religious discourses of post-Reformation England. Attached to a variety of ostensibly distinct practices, from choirs singing alternatim to congregations praying responsively, it was used to advance a variety of partisan agendas regarding performance and sound within the services of the English Church. This dissertation examines discourses of public worship that were conducted around and through “singing by course,” treating it as a linguistic and conceptual node within broader networks of contemporary religious debate. I thus attend less to the history of the vocal practices to which “by course” and similar descriptions were applied than to the polemical dynamics of these applications. Discussions of these terms and practices slipped both horizontally, to other matters of ritual practice, and vertically, to larger topics or frameworks such as the nature of the Christian Church, the production of piety, and the roles of sound and performance in corporate prayer. Through consideration of these issues, “singing by course” emerges as a rhetorical, political, and theological construction, one that circulated according to changing historical conditions and to the interests of various ecclesiastical constituencies.
    [Show full text]
  • 1577-1580) Y Thomas Cavendish (1586-1588
    Apropiaciones simbólicas y ejercicio de la violencia en los viajes de circunnavegación de Francis Drake (1577-1580) y Thomas Cavendish (1586-1588) [Malena López Palmero] prohistoria año XXIII, núm. 34 - dic. 2020 Prohistoria, Año XXIII, núm. 34, dic. 2020, ISSN 1851-9504 Apropiaciones simbólicas y ejercicio de la violencia en los viajes de circunnavegación de Francis Drake (1577-1580) y Thomas Cavendish (1586-1588)* Symbolic Appropriations and use of Violence in the Circumnavigation Voyages of Francis Drake (1577-1580) and Thomas Cavendish (1586-1588) MALENA LÓPEZ PALMERO Resumen Abstract A cinco siglos del primer cruce del Estrecho de Five centuries after the first crossing of the Magellan Magallanes, se analizan las experiencias inglesas de Strait, the English experiences of Francis Drake (1577- Francis Drake (1577-1580) y Thomas Cavendish (1586- 1580) and Thomas Cavendish (1586-1588) are analyzed 1588) con el propósito de reconstruir las apropiaciones with the aim of reconstructing the symbolic simbólicas que los navegantes hicieron de la región appropriations that the navigators made on the Tierra fueguina y sus habitantes. Impresos, manuscritos, del Fuego region and its inhabitants. Printed books, imágenes y mapas evocan a la alteridad americana manuscripts, images and maps evoke the más austral en tanto dispositivo de la competencia southernmost American otherness as a device of the ultramarina entre Inglaterra y España. Asimismo, dan overseas competition between England and Spain. cuenta de las hostilidades con los nativos desatadas Besides, they show the hostilities with the Natives durante el cruce, interpretadas en función de los unleashed during the crossing, which were seen objetivos de los viajeros y su validación autoral.
    [Show full text]
  • The Persian-Toledan Astronomical Connection and the European Renaissance
    Academia Europaea 19th Annual Conference in cooperation with: Sociedad Estatal de Conmemoraciones Culturales, Ministerio de Cultura (Spain) “The Dialogue of Three Cultures and our European Heritage” (Toledo Crucible of the Culture and the Dawn of the Renaissance) 2 - 5 September 2007, Toledo, Spain Chair, Organizing Committee: Prof. Manuel G. Velarde The Persian-Toledan Astronomical Connection and the European Renaissance M. Heydari-Malayeri Paris Observatory Summary This paper aims at presenting a brief overview of astronomical exchanges between the Eastern and Western parts of the Islamic world from the 8th to 14th century. These cultural interactions were in fact vaster involving Persian, Indian, Greek, and Chinese traditions. I will particularly focus on some interesting relations between the Persian astronomical heritage and the Andalusian (Spanish) achievements in that period. After a brief introduction dealing mainly with a couple of terminological remarks, I will present a glimpse of the historical context in which Muslim science developed. In Section 3, the origins of Muslim astronomy will be briefly examined. Section 4 will be concerned with Khwârizmi, the Persian astronomer/mathematician who wrote the first major astronomical work in the Muslim world. His influence on later Andalusian astronomy will be looked into in Section 5. Andalusian astronomy flourished in the 11th century, as will be studied in Section 6. Among its major achievements were the Toledan Tables and the Alfonsine Tables, which will be presented in Section 7. The Tables had a major position in European astronomy until the advent of Copernicus in the 16th century. Since Ptolemy’s models were not satisfactory, Muslim astronomers tried to improve them, as we will see in Section 8.
    [Show full text]
  • The Adventures of Captain John Smith, Pocahontas, and a Sundial Sara J
    The Adventures of Captain John Smith, Pocahontas, and a Sundial Sara J. Schechner (Cambridge MA) Let me tell you a tale of intrigue and ingenuity, savagery and foreign shores, sex and scientific instruments. No, it is not “Desperate Housewives,” or “CSI,” but the “Adventures of Captain John Smith, Pocahontas, and a Sundial.”1 As our story opens in 1607, we find Captain John Smith paddling upstream through the Virginia wilderness, when he is ambushed by Indians, held prisoner, and repeatedly threatened with death. His life is spared first by the intervention of his magnetic compass, whose spinning needle fascinates his captors, and then by Pocahontas, the chief’s sexy daughter. At least that is how recent movies and popular writing tell the story.2 But in fact the most famous compass in American history was more than a compass – it was a pocket sundial – and the Indian princess was no seductress, but a mere child of nine or ten years, playing her part in a shaming ritual. So let us look again at the legend, as told by John Smith himself, in order to understand what his instrument meant to him. Who was John Smith?3 When Smith (1580-1631) arrived on American shores at the age of twenty-seven, he was a seasoned adventurer who had served Lord Willoughby in Europe, had sailed the Mediterranean in a merchant vessel, and had fought for the Dutch against Spain and the Austrians against the Turks. In Transylvania, he had been captured and sold as a slave to a Turk. The Turk had sent Smith as a gift to his girlfriend in Istanbul, but Smith escaped and fled through Russia and Poland.
    [Show full text]
  • Colonial Failure in the Anglo-North Atlantic World, 1570-1640 (2015)
    FINDLEY JR, JAMES WALTER, Ph.D. “Went to Build Castles in the Aire:” Colonial Failure in the Anglo-North Atlantic World, 1570-1640 (2015). Directed by Dr. Phyllis Whitman Hunter. 266pp. This study examines the early phases of Anglo-North American colonization from 1570 to 1640 by employing the lenses of imagination and failure. I argue that English colonial projectors envisioned a North America that existed primarily in their minds – a place filled with marketable and profitable commodities waiting to be extracted. I historicize the imagined profitability of commodities like fish and sassafras, and use the extreme example of the unicorn to highlight and contextualize the unlimited potential that America held in the minds of early-modern projectors. My research on colonial failure encompasses the failure of not just physical colonies, but also the failure to pursue profitable commodities, and the failure to develop successful theories of colonization. After roughly seventy years of experience in America, Anglo projectors reevaluated their modus operandi by studying and drawing lessons from past colonial failure. Projectors learned slowly and marginally, and in some cases, did not seem to learn anything at all. However, the lack of learning the right lessons did not diminish the importance of this early phase of colonization. By exploring the variety, impracticability, and failure of plans for early settlement, this study investigates the persistent search for usefulness of America by Anglo colonial projectors in the face of high rate of
    [Show full text]
  • Nicolaus Copernicus: the Loss of Centrality
    I Nicolaus Copernicus: The Loss of Centrality The mathematician who studies the motions of the stars is surely like a blind man who, with only a staff to guide him, must make a great, endless, hazardous journey that winds through innumerable desolate places. [Rheticus, Narratio Prima (1540), 163] 1 Ptolemy and Copernicus The German playwright Bertold Brecht wrote his play Life of Galileo in exile in 1938–9. It was first performed in Zurich in 1943. In Brecht’s play two worldviews collide. There is the geocentric worldview, which holds that the Earth is at the center of a closed universe. Among its many proponents were Aristotle (384–322 BC), Ptolemy (AD 85–165), and Martin Luther (1483–1546). Opposed to geocentrism is the heliocentric worldview. Heliocentrism teaches that the sun occupies the center of an open universe. Among its many proponents were Copernicus (1473–1543), Kepler (1571–1630), Galileo (1564–1642), and Newton (1643–1727). In Act One the Italian mathematician and physicist Galileo Galilei shows his assistant Andrea a model of the Ptolemaic system. In the middle sits the Earth, sur- rounded by eight rings. The rings represent the crystal spheres, which carry the planets and the fixed stars. Galileo scowls at this model. “Yes, walls and spheres and immobility,” he complains. “For two thousand years people have believed that the sun and all the stars of heaven rotate around mankind.” And everybody believed that “they were sitting motionless inside this crystal sphere.” The Earth was motionless, everything else rotated around it. “But now we are breaking out of it,” Galileo assures his assistant.
    [Show full text]
  • A History of Astronomy, Astrophysics and Cosmology - Malcolm Longair
    ASTRONOMY AND ASTROPHYSICS - A History of Astronomy, Astrophysics and Cosmology - Malcolm Longair A HISTORY OF ASTRONOMY, ASTROPHYSICS AND COSMOLOGY Malcolm Longair Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE Keywords: History, Astronomy, Astrophysics, Cosmology, Telescopes, Astronomical Technology, Electromagnetic Spectrum, Ancient Astronomy, Copernican Revolution, Stars and Stellar Evolution, Interstellar Medium, Galaxies, Clusters of Galaxies, Large- scale Structure of the Universe, Active Galaxies, General Relativity, Black Holes, Classical Cosmology, Cosmological Models, Cosmological Evolution, Origin of Galaxies, Very Early Universe Contents 1. Introduction 2. Prehistoric, Ancient and Mediaeval Astronomy up to the Time of Copernicus 3. The Copernican, Galilean and Newtonian Revolutions 4. From Astronomy to Astrophysics – the Development of Astronomical Techniques in the 19th Century 5. The Classification of the Stars – the Harvard Spectral Sequence 6. Stellar Structure and Evolution to 1939 7. The Galaxy and the Nature of the Spiral Nebulae 8. The Origins of Astrophysical Cosmology – Einstein, Friedman, Hubble, Lemaître, Eddington 9. The Opening Up of the Electromagnetic Spectrum and the New Astronomies 10. Stellar Evolution after 1945 11. The Interstellar Medium 12. Galaxies, Clusters Of Galaxies and the Large Scale Structure of the Universe 13. Active Galaxies, General Relativity and Black Holes 14. Classical Cosmology since 1945 15. The Evolution of Galaxies and Active Galaxies with Cosmic Epoch 16. The Origin of Galaxies and the Large-Scale Structure of The Universe 17. The VeryUNESCO Early Universe – EOLSS Acknowledgements Glossary Bibliography Biographical SketchSAMPLE CHAPTERS Summary This chapter describes the history of the development of astronomy, astrophysics and cosmology from the earliest times to the first decade of the 21st century.
    [Show full text]
  • PERSPECTIVES on Science and Christian Faith
    PERSPECTIVES on Science and Christian Faith JOURNAL OF THE AMERICAN SCIENTIFIC AFFILIATION In This Issue … Pharaoh’s Gift: Was Ancient Nubia the Land of Milk and Camels? The Role of Psychology in Advancing Dialogue between Science and Christianity Newton Deified and Defied: The Many “Newtons” of the Enlightenment Reformed Theology and Evolutionary Theory: A Critical Review “The fear of the Lord is the beginning of Wisdom.” Psalm 111:10 VOLUME 72, NUMBER 4 DECEMBER 2020 (US ISSN 0892-2675) (CPM #40927506) Perspectives on Science and Christian Faith Manuscript Guidelines © 2020 by the American Scientific Affiliation The pages of Perspectives on Science and Christian Faith (PSCF) are open Editor-in-Chief to original, unpublished contributions that interact with science and Christian James C. Peterson (Roanoke College and faith in a manner consistent with scientific and theological integrity. A brief Virginia Tech) description of standards for publication in PSCF can be found in the lead 221 College Lane editorial of the December 2013 issue. This is available at www.asa3.org Salem, VA 24153 PUBLICATIONS PSCF Academic Journal. Published papers do not reflect [email protected] any official position of the American Scientific Affiliation. 1. Submit all manuscripts to: James C. Peterson, Editor, Roanoke College, Book Reviews 221 College Lane, Salem, VA 24153. E-mail: [email protected]. Stephen Contakes (Westmont College) Submissions are typically acknowledged within 10 days of their receipt. Book Review Editor 2. Authors must submit an electronic copy of the manuscript formatted 912 Westmont Road in Word as an email attachment. Typically 2–3 anonymous reviewers Santa Barbara, CA 93108-1035 critique each manuscript considered for publication.
    [Show full text]
  • Copernicus and Tycho Brahe
    THE NEWTONIAN REVOLUTION – Part One Philosophy 167: Science Before Newton’s Principia Class 2 16th Century Astronomy: Copernicus and Tycho Brahe September 9, 2014 TABLE OF CONTENTS I. The Copernican Revolution .................................................................................................................. 1 A. Ptolemaic Astronomy: e.g. Longitudes of Mars ................................................................... 1 B. A Problem Raised for Philosophy of Science ....................................................................... 2 C. Background: 13 Centuries of Ptolemaic Astronomy ............................................................. 4 D. 15th Century Planetary Astronomy: Regiomantanus ............................................................. 5 E. Nicolaus Copernicus: A Brief Biography .............................................................................. 6 F. Copernicus and Ibn al-Shāţir (d. 1375) ……………………………………………………. 7 G. The Many Different Copernican Revolutions ........................................................................ 9 H. Some Comments on Kuhn’s View of Science ……………………………………………... 10 II. De Revolutionibus Orbium Coelstium (1543) ..................................................................................... 11 A. From Basic Ptolemaic to Basic Copernican ........................................................................... 11 B. A New Result: Relative Orbital Radii ................................................................................... 12 C. Orbital
    [Show full text]
  • Contents Humanities Notes
    Humanities Notes Humanities Seminar Notes - this draft dated 24 May 2021 - more recent drafts will be found online Contents 1 2007 11 1.1 October . 11 1.1.1 Thucydides (2007-10-01 12:29) ........................ 11 1.1.2 Aristotle’s Politics (2007-10-16 14:36) ..................... 11 1.2 November . 12 1.2.1 Polybius (2007-11-03 09:23) .......................... 12 1.2.2 Cicero and Natural Rights (2007-11-05 14:30) . 12 1.2.3 Pliny and Trajan (2007-11-20 16:30) ...................... 12 1.2.4 Variety is the Spice of Life! (2007-11-21 14:27) . 12 1.2.5 Marcus - or Not (2007-11-25 06:18) ...................... 13 1.2.6 Semitic? (2007-11-26 20:29) .......................... 13 1.2.7 The Empire’s Last Chance (2007-11-26 20:45) . 14 1.3 December . 15 1.3.1 The Effect of the Crusades on European Civilization (2007-12-04 12:21) 15 1.3.2 The Plague (2007-12-04 14:25) ......................... 15 2 2008 17 2.1 January . 17 2.1.1 The Greatest Goth (2008-01-06 19:39) .................... 17 2.1.2 Just Justinian (2008-01-06 19:59) ........................ 17 2.2 February . 18 2.2.1 How Faith Contributes to Society (2008-02-05 09:46) . 18 2.3 March . 18 2.3.1 Adam Smith - Then and Now (2008-03-03 20:04) . 18 2.3.2 William Blake and the Doors (2008-03-27 08:50) . 19 2.3.3 It Must Be True - I Saw It On The History Channel! (2008-03-27 09:33) .
    [Show full text]
  • Inquiry Question Can I Create a Timeline to Show How Trigonometry Developed?
    Math: Trigonometry Inquiry Question Can I create a timeline to show how Trigonometry developed? Name: ___________________________ Date: ____________ General Instructions Your task is to draw a timeline that shows the development of trigonometry through the ages. Project submission: • Submit your timeline and the answers to the questions below. 2021-08-04 Page 1 of 3 Math: Trigonometry You will find that there is a lot of information about the history of trigonometry available. Below are some concepts, formulae and Mathematicians that should be on your timeline. You need to show when the following concepts first became recognized: • Measuring angles • 360 degrees in a circle • Observing ratios/lengths using chords in circles • First trigonometric tables • Plimpton 322 • sine and cosine (versine) • tangent • Using the words sine and cosine • Treating trigonometry as a separate discipline of Mathematics • Defining trigonometric ratios in terms of triangles and not circles • Modern abbreviations for sin, cos and tan You need to show when the following formulae were found. • hypotenuse2=side2+side2 or c2=a2+b2 • sin2(x)+cos2(x)=1 • sin(x)=cos(90∘−x) • 1−sin2(x)=cos2(x)=sin(90∘−x) • tan(x)=sin(x)/cos(x) • sin(2x)=2sin(x)cos(x) sin 퐴 sin 퐵 sin 퐶 • = = 푎 푏 푐 Some names that should be mentioned are listed below. Include why these people are important – you may find that they discovered a concept or formulae listed above. It has been shown that there were different cultural contributions to trig, Indicate which group of people these mathematicians belonged to (e.g. Babylonian, Egyptian, Greek/Hellenistic, Indian, Islamic, Chinese, European) • Abu al-Wafa al-Buzjani • Ahmes • Aryabhata • Brahmagupta • Euler • Georg Joachim Rheticus • Hipparchus of Nicea • Muhammad ibn Jabir al-Battini (Albatenius) • Muhammad ibn Musa al-Khwaritmi • Ptolemy • Regiomontanus 2021-08-04 Page 2 of 3 Math: Trigonometry • Varahamihira Section B Answer all of the following questions.
    [Show full text]