A Reconstruction of the Tables of Rheticus' Canon Doctrinæ Triangulorum (1551)
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The Vienna University Observatory
The Vienna University Observatory THOMAS POSCH Abstract The Vienna University Observatory, housing what was once the world’s largest refracting telescope, still serves as a centre of astronomical research and teaching. In 1819, Johann Josef von Littrow (1781-1840) became Professor of Mathematics and Astronomy at the University of Vienna. He tried to move the University Observatory - which was at that time still located at the city centre - to the outskirts, but did not succeed. After his death, his son Carl Ludwig von Littrow (1811-1877) became director of the Observatory. The total solar eclipse which took place on July 8, 1842, in his first year as director, made astronomy very popular and helped promote new investment. In 1872, a large site was acquired for a new observatory on a hill called "Türkenschanze", near the village of Währing outside Vienna. Building began in 1874. The architects of the imposing new building were Ferdinand Fellner and Hermann Helmer, both specialists in theatre buildings. Their concept was to combine observatory and apartments on a cross-shaped plan, which was unusually large for its day; 101 m length and 73 m width. The big refractor telescope (with an aperture of 27 inches, or 68 cm and a focal length of 10.5 m) was then the largest refracting telescope in the world. The celebratory opening took place in 1883. The excellent instrumentation made possible numerous remarkable Fig. 1 - Georg von Peuerbach’s ‘Theoricae novae planetarum’, discoveries in the fields of binary stars, Nuremberg 1473 asteroids and comets. However, the Währing district quickly became attractive to the Viennese upper classes and the observatory was soon part of an illuminated urban area. -
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 -
Az Óvatos Copernicus. a De Revolutionibus Orbium Coelestium
IX. évf. $%&'/(. Vassányi Miklós Az óvatos Copernicus A De revolutionibus orbium coelestium polifón előszavai, elhallgatott bevezetése és korai egyházi kritikája1 1. Kérdésfelvetés Nicolaus Copernicus (Mikołaj Kopernik, 1473–1543)2 legismertebb műve, a De revolutionibus orbium coelestium (Az égi körpályák forgásairól)3 1543-as publikálását meg- előzte egyfelől a tőle magától származó, De hypothesibus motuum caelestium a se constitutis commentariolus (Rövid magyarázat az égi mozgásokról a szerző által felállított hipotézisek- 1 A tanulmány megírását a Hungarian-American Fulbright Commission 2017-es kutatói ösztöndíja tette lehetővé. A szerző ezúton is hálás köszönetét fejezi ki a Hungarian-American Fulbright Com- missionnek az ösztöndíjért; valamint Szénási Rékának a szakirodalom feldolgozásában nyújtott segít- ségéért. 2 Copernicus életrajzához ld. J. DoBrzyCki: „Nicolaus Copernicus – His Life and Work.” In B. BieńkoWska (szerk.): $e Scientific World of Copernicus. On the Occasion of the 500th Occasion of His Birth 1473–1973, Dordrecht (Holland)–Boston (USA), D. Reidel Publishing Company, 1973, 13–37; és a Nicolaus Copernicus Gesamtausgabe VI/1-2 (Documenta Copernicana) kötetében kiadott elsődleges, valamint a IX. (Die Copernicus-Biographien des 16. bis 18. Jahrhunderts) kötetében kiadott másodlagos forrásokat (Berlin, Akademie-Verlag, 2009 és 2004). 3 Editio princeps: Nicolai Copernici Torinensis de revolvtionibvs orbium coelestium, Libri VI. Norimbergae apud Ioh. Petreium, Anno MDXLIII. A címben szereplő orbis szó „körpálya”-ként való fordításáról ld. az alant közölt szemelvény lábjegyzetét, amely szerint ez a fogalom megkülönböztetendő a sphaera fogalmától (jóllehet hagyományosan azonosítani szokás azzal), illetve különösen F. Ross- mann magyarázatát: „Die orbes müßten sich auch, wenn sie als Sphären zu denken wären, wiederholt durchschneiden, was mit Starrheit schwer zu vereinbaren ist. -
Academic Genealogy of the Oakland University Department Of
Basilios Bessarion Mystras 1436 Guarino da Verona Johannes Argyropoulos 1408 Università di Padova 1444 Academic Genealogy of the Oakland University Vittorino da Feltre Marsilio Ficino Cristoforo Landino Università di Padova 1416 Università di Firenze 1462 Theodoros Gazes Ognibene (Omnibonus Leonicenus) Bonisoli da Lonigo Angelo Poliziano Florens Florentius Radwyn Radewyns Geert Gerardus Magnus Groote Università di Mantova 1433 Università di Mantova Università di Firenze 1477 Constantinople 1433 DepartmentThe Mathematics Genealogy Project of is a serviceMathematics of North Dakota State University and and the American Statistics Mathematical Society. Demetrios Chalcocondyles http://www.mathgenealogy.org/ Heinrich von Langenstein Gaetano da Thiene Sigismondo Polcastro Leo Outers Moses Perez Scipione Fortiguerra Rudolf Agricola Thomas von Kempen à Kempis Jacob ben Jehiel Loans Accademia Romana 1452 Université de Paris 1363, 1375 Université Catholique de Louvain 1485 Università di Firenze 1493 Università degli Studi di Ferrara 1478 Mystras 1452 Jan Standonck Johann (Johannes Kapnion) Reuchlin Johannes von Gmunden Nicoletto Vernia Pietro Roccabonella Pelope Maarten (Martinus Dorpius) van Dorp Jean Tagault François Dubois Janus Lascaris Girolamo (Hieronymus Aleander) Aleandro Matthaeus Adrianus Alexander Hegius Johannes Stöffler Collège Sainte-Barbe 1474 Universität Basel 1477 Universität Wien 1406 Università di Padova Università di Padova Université Catholique de Louvain 1504, 1515 Université de Paris 1516 Università di Padova 1472 Università -
Simon Stevin
II THE PRINCIPAL WORKS OF SIMON STEVIN E D IT E D BY ERNST CRONE, E. J. DIJKSTERHUIS, R. J. FORBES M. G. J. MINNAERT, A. PANNEKOEK A M ST E R D A M C. V. SW ETS & Z E IT L IN G E R J m THE PRINCIPAL WORKS OF SIMON STEVIN VOLUME II MATHEMATICS E D IT E D BY D. J. STRUIK PROFESSOR AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE (MASS.) A M S T E R D A M C. V. SW ETS & Z E IT L IN G E R 1958 The edition of this volume II of the principal works of SIMON STEVIN devoted to his mathematical publications, has been rendered possible through the financial aid of the Koninklijke. Nederlandse Akademie van Wetenschappen (Royal Netherlands Academy of Science) Printed by Jan de Lange, Deventer, Holland The following edition of the Principal Works of SIMON STEVIN has been brought about at the initiative of the Physics Section of the Koninklijke Nederlandse Akademie van Weten schappen (Royal Netherlands Academy of Sciences) by a committee consisting of the following members: ERNST CRONE, Chairman of the Netherlands Maritime Museum, Amsterdam E. J. DIJKSTERHUIS, Professor of the History of Science at the Universities of Leiden and Utrecht R. J. FORBES, Professor of the History of Science at the Municipal University of Amsterdam M. G. J. M INNAERT, Professor of Astronomy at the University of Utrecht A. PANNEKOEK, Former Professor of Astronomy at the Municipal University of Amsterdam The Dutch texts of STEVIN as well as the introductions and notes have been translated into English or revised by Miss C. -
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. -
Napier's Ideal Construction of the Logarithms
Napier’s ideal construction of the logarithms Denis Roegel To cite this version: Denis Roegel. Napier’s ideal construction of the logarithms. [Research Report] 2010. inria-00543934 HAL Id: inria-00543934 https://hal.inria.fr/inria-00543934 Submitted on 6 Dec 2010 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Napier’s ideal construction of the logarithms∗ Denis Roegel 6 December 2010 1 Introduction Today John Napier (1550–1617) is most renowned as the inventor of loga- rithms.1 He had conceived the general principles of logarithms in 1594 or be- fore and he spent the next twenty years in developing their theory [108, p. 63], [33, pp. 103–104]. His description of logarithms, Mirifici Logarithmorum Ca- nonis Descriptio, was published in Latin in Edinburgh in 1614 [131, 161] and was considered “one of the very greatest scientific discoveries that the world has seen” [83]. Several mathematicians had anticipated properties of the correspondence between an arithmetic and a geometric progression, but only Napier and Jost Bürgi (1552–1632) constructed tables for the purpose of simplifying the calculations. Bürgi’s work was however only published in incomplete form in 1620, six years after Napier published the Descriptio [26].2 Napier’s work was quickly translated in English by the mathematician and cartographer Edward Wright3 (1561–1615) [145, 179] and published posthu- mously in 1616 [132, 162]. -
Beginnings of Trigonometry
Beginnings of Trigonometry Trigonometry is an area of mathematics used for determining geometric quantities. Its name, first published in 1595 by B. Pitiscus, means "the study of trigons (triangles)" in Latin. Ancient Greek Mathematicians first used trigonometric functions with the chords of a circle. The first to publish these chords in 140 BC was Hipparchus, who is now called the founder of trigonometry. In AD 100, Menelaus, another Greek mathematician, published six lost books of tables of chords. Ptolemy, a Babylonian, also wrote a book of chords. Using chords, Ptolemy knew that sin(xy+= ) sin x cos y + cos x sin y and abc = = sinABC sin sin In his great astronomical handbook, The Almagest, Ptolemy provided a table of chords for steps of °, from 0° to 180°, that is accurate to 1/3600 of a unit. Ptolemy's degree of accuracy is due in part because the Hellenistic Greeks had adopted the Babylonian base- 60 (sexagesimal) numeration system. He also explained his method for constructing his table of chords, and in the course of the book he gave many examples of how to use the table to find unknown parts of triangles from known parts. Ptolemy provided what is now known as Menelaus's theorem for solving spherical triangles, as well, and for several centuries his trigonometry was the primary introduction to the subject for any astronomer. Sine first appeared in the work of Aryabhata, a Hindu. He used the word jya for sine. He also published the first sine tables. Brahmagupta, in 628, also published a table of sines for any angle. -
Copernicus and His Revolutions
Copernicus and his Revolutions Produced for the Cosmology and Cultures Project of the OBU Planetarium by Kerry Magruder August, 2005 2 Credits Written & Produced by: Kerry Magruder Narrator: Candace Magruder Copernicus: Kerry Magruder Cardinal Schönberg: Phil Kemp Andreas Osiander: J Harvey C. S. Lewis: Phil Kemp Johann Kepler: J Harvey Book Images courtesy: History of Science Collections, University of Oklahoma Libraries Photographs and travel slides courtesy: Duane H.D. Roller Archive, History of Science Collections, University of Oklahoma Libraries Digital photography by: Hannah Magruder Soundtrack composed and produced by: Eric Barfield Special thanks to... Peter Barker, Bernie Goldstein, Katherine Tredwell, Dennis Danielson, Mike Keas, JoAnn Palmeri, Hannah Magruder, Rachel Magruder, Susanna Magruder, Candace Magruder Produced with a grant from the American Council of Learned Societies 3 1. Contents 1. Contents________________________________________________3 2. Introduction _____________________________________________4 A. Summary ____________________________________________4 B. Synopsis ____________________________________________5 C. Instructor Notes_______________________________________7 3. Before the Show _________________________________________9 A. Vocabulary and Definitions _____________________________9 B. Pre-Test ____________________________________________10 4. Production Script________________________________________11 A. Production Notes_____________________________________11 B. Theater Preparation___________________________________13 -
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. -
Preprint N°494
2019 Preprint N°494 The Reception of Cosmography in Vienna: Georg von Peuerbach, Johannes Regiomontanus, and Sebastian Binderlius Thomas Horst Published in the context of the project “The Sphere—Knowledge System Evolution and the Shared Scientific Identity of Europe” https://sphaera.mpiwg-berlin.mpg.de The Reception of Cosmography in Vienna: Georg von Peuerbach, Johannes Regiomontanus, and Sebastian Binderlius1 Abstract In this paper, the importance of the cosmographical activities of the Vienna astronomical “school” for the reception of the Tractatus de Sphaera is analyzed. First, the biographies of two main representatives of the Vienna mathematical/astronomical circle are presented: the Austrian astronomers, mathematicians, and instrument makers Georg von Peuerbach (1423– 1461) and his student Johannes Müller von Königsberg (Regiomontanus, 1436–1476). Their studies influenced the cosmographical teaching at the University of Vienna enormously for the next century and are relevant to understanding what followed; therefore, the prosopo- graphical introductions of these Vienna scholars have been included here, even if neither can be considered a real author of the Sphaera. Moreover, taking the examples of an impressive sixteenth-century miscellany (Austrian Na- tional Library, Cod. ser. nov. 4265, including the recently rediscovered cosmography by Sebastian Binderlius, compiled around 1518), the diversity of different cosmographical studies in the capital of the Habsburg Empire at the turning point between the Middle Ages and the early modern period is demonstrated. Handwritten comments in the Vienna edition of De sphaera (1518) also show how big the influence of Sacrobosco’s work remained as a didactical tool at the universities in the first decades of the sixteenth century—and how cosmographical knowledge was transformed and structured in early modern Europe by the editors and readers of the Sphaera. -
The Scientific Revolution
13/01/2017 the Scientific Revolution: the Cosmos Mechanized • 1543 Nicolaus Copernicus ‐ publishes heliocentric universe in De Revolutionibus Orbium Coelestium ‐ implicit introduction Copernican principle: Earth/Sun is not special • 1609‐1632 Galileo Galilei ‐ by means of (telescopic) observations, proves the validity of the heliocentric Universe. • 1609/1619 Johannes Kepler ‐ the 3 Kepler laws, describing the elliptical orbits of the planets around the Sun • 1687 Isaac Newton ‐ discovers Gravitational Force as agent behind cosmic motions ‐ publishes his Principia (Philosophiae Naturalis Principia Mathematica), which establishes the natural laws of motion and gravity (the latter only to be replaced by Einstein’s theory of GR) • 1755 Immanuel Kant ‐ asserts that nebulae are really galaxies separate from and outside from the Milky Way, ‐ calling these Island Universes • 1785 William Herschel ‐ proposes theory that our Sun is at or near the center of ou Galaxy (Milky Way) 1 13/01/2017 Birthhouse Copernicus, Nicolaus Copernicus Torun 1473 –born in Torun (Poland) 1491‐1495 ‐ study Univ. Krakow 1496‐1501 ‐ 3 years Univ. Bologna ‐ canon law 1503‐‐Warmia 1514 ‐ Frombork Languages: Latin , German 1514 ‐ Commentariolus Nicolai Copernici de hypothesibus motuum coelestium a se constitutis commentariolus + theoretical treatise on heliocentric mechanism + 40 pages, 7 basic assumptions Tower (living) Copernicus, Frombork Frombork Cathedral 2 13/01/2017 1. There is no one center of all the celestial circles or spheres. 2. The center of the earth is not the center of the universe, but only of gravity and of the lunar sphere. 3. All the spheres revolve about the sun as their midpoint, and therefore the sun is the center of the universe.