Was Valentinus Otho a Mathematics Professor at the University of Heidelberg?
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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 -
The Science of Astrology: Schreibkalender, Natural Philosophy, and Everyday Life in the Seventeenth-Century German Lands
The Science of Astrology: Schreibkalender, Natural Philosophy, and Everyday Life in the Seventeenth-Century German Lands A dissertation submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of History of the College of Arts and Sciences by Kelly Marie Smith M.A. University of Cincinnati, December 2003 B.S. Eastern Michigan University, December 2000 Committee Chair: Sigrun Haude, Ph.D. Abstract This dissertation explores the use of Schreibkalender, or writing-calendars, and their accompanying prognostica astrologica to evaluate how ideas about seventeenth-century natural philosophy – particularly the relationship between astronomy and astrology – changed throughout the period. These calendars contain a wealth of information that demonstrates the thirst early modern readers had for knowledge of the world around them. Because Schreibkalender and prognostica were written annually for the general populace and incorporated contemporary ideas regarding natural philosophy, they provide a means to assess the roles of both astronomical and astrological ideas during this period and how these changes were conveyed to the average person. Not only did authors present practical information related to the natural world, but they also explained basic philosophical principles and new discoveries to their audience. This research examines how changing ideas about the role of natural philosophy and its direct influence on everyday life developed over the course of the seventeenth century. An examination of the Schreibkalender and prognostica reveals a shift in emphasis throughout the period. Early calendars (approximately 1600-30) presented direct astronomical and astrological information related to the daily life of the average person, whereas those from the middle of the century (~1630-70) added helpful details explaining astronomical and astrological concepts. -
The Nova Stella and Its Observers
Running title: Nova stella 1572 AD The Nova Stella and its Observers P. Ruiz–Lapuente ∗,∗∗ 1. Introduction In 1572, physicists were still living with the concepts of mechanics inherited from Aris- totle and with the classification of the elements from the Greek philosopher. The growing criticism towards the Aristotelian views on the natural world could not turn very produc- tive, because the necessary elements of calculus and the empirical tools to move into a better frame were still lacking. However, in astronomy, observers had witnessed by that time the comet of 1556 and they would witness a new one in 1577. Moreover, since 1543 when De Revolutionibus Orbium Caelestium by Copernicus came to light, the apparent motion of the planets had a radically different explanation from the ortodox geocentrism. The new helio- centric view slowly won supporters among astronomers. The explanations concerning the planetary motions would depart from the “common sense” intuitions that had placed the earth sitting still at the center of the planetary system. Thus the “nova stella” in 1572 happened in the middle of the geocentric–versus–heliocentric debate. The other “nova”, the one that would be observed in 1604 by Kepler, came just shortly after the posthumous publication of Tycho Brahe’s Astronomiae Instauratae Progymnasmata1 which contains most of the debates in relation to the appearance of the “new star”2. arXiv:astro-ph/0502399v1 21 Feb 2005 The machinery moving the planetary spheres, i.e. the intrincate system of solid spheres rotating by the motion imparted to them as the wheels in a clock, was not directly affected by the new heliocentric proposal. -
The Academic Genealogy of Swapnil Haria
�� John Mauropus, ���-���� �� Johannes VIII Xiphilinus, ����-���� �� Nicetas Byzantius The Academic University of Constantinople University of Constantinople, ���� | Patriarch of Constantinople �� Michael Psellos, ����-���� University of Constantinople Genealogy of �� John Italus, ����-���� University of Constantinople �� Theodore of Smyrna Swapnil Haria University of Constantinople �� Michael Italikos, c. ���� �� Stephanos Skylitzes Philippolis Trebizond | Constantinople, ���� Academic ancestors include two saints, Copernicus, Erasmus, and Leibniz. This �� Theodoros Prodromos, ����-���� Patriarch school, Constantinople geneology almost certainly contains errors and omissions. Information compiled �� Demetrios Karykes Smyrna, ���� from/by Mathematics Genealogy Project, �� Theodorus Exapterigus �� Nicephorus Blemmydes, ����-���� Neurotree, Nikos Hardavellas, Mark D. Hill, Prusa, Nicea | Smyrna, Scamander | Monastery of Ephesus Timothy Sherwood, and Gio Wiederhold. �� Georgius Acropolitus, ����-���� Nicae �� Georgius Pachymeres, ����-���� Constantinople �� Manual Byrennius, ����-XXXX Constantinople �� Theodore Metochites, ����-���� Nicea �� Elder St. Nicodemus of Vatopedi �� Nicephorus Gregoras, ����-���� �� Manuel Holobolos Vatopedi Monastery, Mt. Athos, ��XX Constantinople Rhetor at the court of Nicae, ���� �� St. Gregory Palamas, ����-���� �� Simon of Constantinople, ����-���� Constantinople | Vatopedi Monastery, Mt. Athos | Thessaloniki Pera near Contantinople �� Nilus Cabasilas, ����-���� �� Philip of Pera (Philippo de Bindo Incontri) -
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. -
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. -
The Copernican System
The Copernican system Jan P. Hogendijk Dept of Mathematics, Utrecht University 8 june 2011 1 Prelude: the 15th century Copernicus: biography Copernicus’ new system: Main Points Copernicus’ new system: Dirty Details The reception of the new system 2 Renaissance Invention of Printing by Johannes Gutenberg (Mainz), ca. 1450: typesetting with movable type, printing press, paper. 3 Most important astronomer of the 15th century Johannes Muller¨ of K¨onigsberg (Bavaria), or Regiomontanus (1436-1476) 4 Biography of Regiomontanus (1436-1476) 1448: Entered University of Leipzig. 1460: Met cardinal Bessarion (from Trebizond), travelled with him to Italy. 1463: completed Epitome of the Almagest (of Ptolemy) [printed 1492]. ca. 1461: made observations of eclipses, etc. which diverged from the predictions by e.g. the Alfonsine tables. 5 Quotation from Regiomontanus (1464) “I cannot [but] wonder at the indolence of common astronomers of our age, who, just as credulous women, receive as something divine and immutable whatever they come upon in books, either of tables of their instructions, for they believe in writers and make no effort to find the truth.” Regiomontanus wanted to restore and “update” Ptolemaic astronomy in order to predict astronomical phenomena accurately. 1471: he founded printing press in Nurnberg,¨ producing mathematical and astronomical works with great accuracy. 6 Product of Regiomontanus’ Press (1472) Novae Theoricae Planetarum, Georg von Peuerbach (1423-1461) 7 Example of Regiomontanus’ own predictions solar and lunar eclipses, 1489, 1490 8 Nicolas Copernicus (1473-1543): biography 1473 Torun (Poland) - 1543 Frauenburg = Frombork (now in Poland, near coast and Russian border) Studied at the University of Krakow. Worked in service of the Catholic Church until his death. -
The (Likely) Last Edition of Copernicus's Libri Revolutionum
Variants The Journal of the European Society for Textual Scholarship 14 | 2019 Varia The (likely) Last Edition of Copernicus’s Libri revolutionum André Goddu Electronic version URL: http://journals.openedition.org/variants/908 DOI: 10.4000/variants.908 ISSN: 1879-6095 Publisher European Society for Textual Scholarship Printed version Number of pages: 159-178 ISSN: 1573-3084 Electronic reference André Goddu, « The (likely) Last Edition of Copernicus’s Libri revolutionum », Variants [Online], 14 | 2019, Online since 10 July 2019, connection on 12 July 2019. URL : http://journals.openedition.org/ variants/908 ; DOI : 10.4000/variants.908 The authors The (likely) Last Edition of Copernicus’ Libri revolutionum André Goddu Review essay of Nicolas Copernic, De revolutionibus orbium coelestium, Des revolu- tions des orbes célestes. 3 volumes. Science et Humanisme, Collection published under the patronage of the Association Guillaume Budé (Paris: Les Belles Lettres, 2015). Vol. I: Introduction by Michel-Pierre Lerner and Alain-Philippe Segonds with the collaboration of Concetta Luna, Isabelle Pantin, and Denis Savoie, xxviii + 859 pp. Vol. II: Critical Edition and translation by Lerner, Segonds, and Jean-Pierre Verdet with the collaboration of Concetta Luna, viii + 537 pp. with French and Latin on facing pages and with the same page numbers. Vol. III: Notes, appendices, iconographic dossier, and general index by Lerner, Segonds, and Verdet with the collaboration of Luna, Savoie, and Michel Toulmonde, xviii + 783 pp. and 34 plates. T C’ , probably the last for the foresee- able future, represents the culmination of efforts that can be traced back to 1973. The two fundamental sources of De revolutionibus are Copernicus’s auto- graph copy which survived by sheer luck and the first edition published in Nuremberg in 1543. -
How Researchers Make Valuable Chemicals from Green Electricity and CO2 → P. 10 Digital Gmbh: Getting Closer to the Customers
ELEMENTS Research. Knowledge. The future. Bring on the CO2 1/2018 How researchers make valuable chemicals from green electricity and CO2 → p. 10 Digital GmbH: Getting closer to the customers → p. 28 Implants: Intelligent healing for broken bones → p. 46 LEXICON Georg Joachim Rheticus Astronomer and mathematician Georg Joachim Rheticus (* February 16, 1514 in Feldkirch; † December 4, 1574 in Kaschau) was an astronomer and a mathematician. Rheticus was one of the first scholars to disseminate the heliocentric theory of Nicolaus Copernicus, according to which the sun—in contrast to the Christian doctrine of that era—does not orbit the Earth. He studied with Copernicus, an astronomer and physician, for two years as his sole student, encouraging him to complete his work and publish it. In 1551 Rheticus published the most significant of his own works, the Canon doctrinae triangulorum, which included many trigonometric tables. Feldkirch: city in Vorarlberg (Austria) Kaschau: now Košice (Slovakia) Nicolaus Copernicus: astronomer, 1473–1543 → You can read more about the Rheticus project on page 10 ff. 02 EDITORIAL DEAR READERS, In the new Evonik magazine ELEMENTS, we are conducting an experi- ment. We’ll present the same kind of science journalism you’re already familiar with from the old ELEMENTS, but now we’ll be putting it into a social, economic, and political context. We will continue to report on the latest research and innovation from Evonik—and we’ll also ask questions about its social relevance. What kind of impact will this innovation have on my life? Who will benefit from it? And where will it be used in the future? We won’t be the only ones answering these questions. -
Bulletin 26Iii Sonderegger
UNEXPECTED ASPECTS OF ANNIVERSARIES or: Early sundials, widely travelled HELMUT SONDEREGGER his year my hometown, Feldkirch in Germany, cel- Iserin was appointed town physician and all of his family ebrates the 500th anniversary of Rheticus. He was were accepted as citizens of Feldkirch. Georg, a man with T the man who published the first report on Coperni- widespread interests, owned a considerable number of cus’s new heliocentric view of the world. Subsequently, he books and a collection of alchemical and medical instru- helped Copernicus complete his manuscript for publication ments. Over the years, superstitious people suspected this and arranged its printing in Nürnberg. When I planned my extraordinary man of being a sorcerer in league with attendance at the BSS Conference 2014 at Greenwich, I sources of darkness. asked myself if there could be any connections between the A few weeks before his appointment as town physician, on th th 25 BSS anniversary and the 500 anniversary of Rheticus’ 16 Feb 1514, his only son Georg Joachim was born. When birth. And now in fact, I have found a really interesting the son was 14 his father was accused of betraying his story! patients and, additionally, of being a swindler and klepto- maniac. He was sentenced to death and subsequently Feldkirch 500 Years Ago beheaded by the sword. His name Iserin was officially Feldkirch, a small district capital of about 30,000 people, is erased by so-called ‘damnatio memoriae’. His wife and situated in the very west of Austria close to Switzerland children changed their name to the mother’s surname. -
Copernicus' First Friends: Physical Copernicanism
Filozofski vestnik Volume/Letnik XXV • Number/Številka 2 • 2004 • 143–166 COPERNICUS’ FIRST FRIENDS: PHYSICAL COPERNICANISM FROM 1543 TO 1610 Katherine A. Tredwell and Peter Barker Early assessments of the Copernican Revolution were hampered by the failure to understand the nature of astronomy in the sixteenth century, as scholars took statements made in praise of Copernicus to be implicit endorsements of his heliocentric cosmology. Gradually this view has been supplanted by the ac- knowledgement that many supposed partisans of Copernicus only endorsed the use of his astronomical models for the calculation of apparent planetary positions, while rejecting or remaining silent on the reality of heliocentrism. A classic example of this shift in historiography concerns Erasmus Reinhold (1511–1553), a professor of mathematics at the University of Wittenberg. Re- inhold’s use of Copernican models in his Prutenic Tables (Tabulae prutenicae, 1551) has led to the mistaken belief that he sanctioned a Sun-centered cos- mology as well. Careful reassessment of his published writings has revealed that he commended certain aspects of Copernicus’ work, such as the elimi- nation of the equant, but showed no interest in heliocentrism (Westman, 1975: pp. 174–178). Other supposed Copernicans, such as Robert Recorde (c. 1510–1558), expressed some openness to the Earth’s motion but left no clear indication of what they thought to be the true system of the world (Rus- sell, 1972: pp. 189–191). Between the publication of Copernicus’ epoch-making book On the Revo- lutions of the Celestial Orbs (De revolutionibus orbium coelestium) in 1543 and the year 1610, only a handful of individuals can be identified with certainty as Copernicans, in the sense that they considered heliocentrism to be physically real and not merely a calculational convenience. -
Homo Heidelbergensis Mathematicus
Digitale Bibliothek Mathematik Homo Heidelbergensis mathematicus Eine Materialsammlung zu bekannten Heidelberger Mathematikern zusammengestellt von Gabriele D¨orflinger Stand: 20. Mai 2014 Bekannte Mathematiker mit Bezug zu Heidelberg, d.h. Mathematiker, die in Heidelberg lebten, studierten oder lehrten oder Mitglieder der Heidelberger Akademie der Wissenschaften waren. LATEX-Dokumentation der Web-Seite http://ub-fachinfo.uni-hd.de/homoheid.htm und der direkt davon auf- gerufenen Unterseiten der Universit¨atsbibliothek Heidelberg. Nach allgemeinen Dokumenten zur Heidelberger Mathematikgeschichte folgen Einzelportraits von knapp 60 Mathematikern. Zwar gibt es noch viele Mathematiker, die die Auswahlbedingungen • Mathematiker • bekannt (nicht unbedingt als Mathematiker), • Aufenthalt in Heidelberg (mit Ausnahme von Kongressbesuchen) oder aktives Mitglied der Heidelberger Akademie der Wissenschaften erfullen,¨ aber der Aufwand ist zu hoch, um noch weitere Personen in die Sammlung zu integrieren. Die Informationen zu den einzelnen Personen sind immer in gleicher Weise gegliedert. • Bezug zu Heidelberg • Lexika • Biographische Informationen – im Internet – gedruckte Biographien • Werk – im Internet – in Heidelberg vorhandene Schriften – Literatur uber¨ das Werk • Bibliographien S¨amtliche Links werden als Fußnoten abgebildet. Die Fußnote wird durch den Text Link:“ eingeleitet. Web- ” Formulare erhalten die Kennung Formular:“ in der Fußnote. Es wird nur das aufrufende Programm ohne ” Parameter angegeben. Bilder erhalten die Kennung Bild:“ in der Fußnote und werden durch [BILD]“ im ” ” Text markiert. Am Ende jedes Unterdokuments ist die URL angegeben. Externe Links sind durch @⇒ und interne durch I gekennzeichnet. Die farbigen Symbole der Webseite wurden auf schwarz-weiße Zeichen umgesetzt. 2 Inhaltsverzeichnis Allgemeine Bemerkungen 4 Zur Geschichte des Mathematischen Instituts der Universit¨at Heidelberg. 6 Mathematiker im Heidelberger Gelehrtenlexikon . 8 Jakob Christmann, Valentin Otho, Bartholom¨aus Pitiscus .