Copernicus' First Friends: Physical Copernicanism
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SIMON STEVIN (1548 – 1620) by HEINZ KLAUS STRICK, Germany
SIMON STEVIN (1548 – 1620) by HEINZ KLAUS STRICK, Germany The Flemish mathematician, physicist and engineer SIMON STEVIN is one of the lesser-known personalities in the history of science. However, his work has left many traces. We do not even know his exact date of birth and death; his birthplace was Bruges; where he died is uncertain: either Leiden or the Hague. Raised in the Calvinist tradition, he grew up in Flanders, became an accountant and cashier for a trading firm in Antwerp, travelled for several years through Poland, Prussia and Norway until he took a job at the tax office in Bruges in 1577. Around this time, the 17 provinces of the Netherlands, which also include the area of present-day Belgium, Luxembourg and parts of northern France, belong to the Spanish dominion. Large parts of the population, especially in the northern provinces, converted to the Calvinist faith. In 1567 King PHILIP II OF SPAIN appointed the DUKE OF ALBA as governor. When ALBA carried out a punitive expedition against the Protestants, a war began which only ended in 1648 with the Peace Treaty of Münster (partial treaty of the Peace of Westphalia). In 1579 the Protestant provinces in the north of the Netherlands united to form the Union of Utrecht and declared their independence as the Republic of the United Netherlands; they elected WILLIAM THE SILENT or WILLIAM OF ORANGE as regent. As the political situation came to a head, SIMON STEVIN's life situation also changed: although he was already 33 years old, he still attended a Latin school and then took up studies at the newly founded University of Leiden. -
The Origins of the Ptolemaic Tradition and Its Adoption and Replacement in Colonial America
The Origins of the Ptolemaic Tradition and its Adoption and Replacement in Colonial America Master Thesis By Ben Baumann 11592583 June 2018 University of Amsterdam Graduate School of Humanities Master’s Program in Classics and Ancient Civilizations: Ancient Studies First Supervisor: Dr. Jan Willem van Henten Second Supervisor: Dr. Fred Spier Baumann 1 I. Introduction The mapping of the universe and the attempt to understand the cosmos through scholarly investigation has been a constant endeavor of the human race since ancient times. This investigation is known as cosmography. In this thesis, I will analyze how early Colonial American scholars made sense of ancient Greek understandings of cosmography. In particular, I will focus on the way these Greek ideas shaped American thinking not only about the cosmos itself, but also about the way cosmographic understanding became intertwined with views about God and theology. When they first arrived in North America, Colonial Americans generally had a cosmography that was based on the Ptolemaic tradition. But, once they became established in the new world, and especially after the founding of Harvard University, a cosmographic revolution taking place in Europe would begin to resonate in the so-called New World. Thus, some Colonial American scholars willingly engaged in contemplation of the new outlook and proved receptive to the ideas of Nicolas Copernicus. Not surprisingly, in a land where scientific and religious thought overlapped so extensively, this caused heated scholarly debate over the topic and even resulted in student protests at Harvard University. The record of these debates can be traced back to the 17th-century writings of Colonial America, such as several astronomical almanacs, that since have been preserved as vitally significant artifacts of intellectual life in the colonies. -
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 -
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. -
Geometry and Mathematical Symbolism of the 16Th Century Viewed Through a Construction Problem
THE TEACHING OF MATHEMATICS 2016, Vol. XIX, 1, pp. 32–40 GEOMETRY AND MATHEMATICAL SYMBOLISM OF THE 16TH CENTURY VIEWED THROUGH A CONSTRUCTION PROBLEM Milana Dabi´c Abstract. This paper represents a construction problem from Problematum geometricorum IV written by Simon Stevin from Bruges in 1583. The problem is used for illustrating the geometry practice and mathematical language in the 16th century. The large impact of Euclid and Archimedes can be noted. In one part of the construction, Stevin expressed the need for using numbers for greater clarity. Hence, the link with the work of Descartes and the further geometry development is pointed out. MathEduc Subject Classification: A35 MSC Subject Classification: 97A30 Key words and phrases: 16th century mathematics; mathematical symbolism; Simon Stevin; construction problems 1. Introduction From the times of Ancient Greece until the 16th century there was no signif- icant geometrical contribution that would expand the existing geometrical knowl- edge. Only in the second half of the 16th century we can find geometry works of Simon Stevin from Bruges (1548–1620). It is believed that his influence was neglected in the history of mathematics and that his name should be mentioned together with the name of his contemporary Galileo Galilei, from whom Stevin was a whole generation older (16 years) [8]. It is considered that Stevin, as a predecessor of Descartes, prepared a path for introducing correspondence between numbers and points on the line by studying the 10th book of Euclid’s Elements and translating it to numbers [9]. Besides his work on the Problematum geometricorum libri V, he wrote Tomus secundus de geometriae praxi (in 1605) which is: ::: different from the Problemata geometrica and inferior to it; it is also a collection of geometrical problems but it is not arranged as logically as the former; it was chiefly made to complete the Prince’s geometrical training [6, p. -
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. -
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 -
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) -
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 -
Johannes Kepler
PORTRAIT I FAMOUS OPTICIAN Johannes Kepler The German mathematician and astronomer MAIN DATES Johannes Kepler is above all famous for discovering the eponymous laws governing planetary motion. Born 27 December 1571, Weil der Stadt (Germany) Combining Tycho Brahe’s meticulous observations 1601 Mathematicus imperialis, Prague and his own theoretical predictions, his astronomical 1609 First two Kepler laws tables were some of the most enduringly accurate 1611 Dioptricae publication ever established. They provided a firm footing for 1619 The Harmony of the World's third law Copernican theory in the face of the then universally Deceased 15 November 1630, Regensburg (Germany) acknowledged model of a geocentric universe. Despite A portrait of Johannes Kepler poor eyesight that prevented him from carrying out original experimental research, he became a major figure in the field of optics, overhauling all introduce him to the heliocentric theory put forward by its fundamental concepts and developing a sound Nicolaus Copernicus [1473-1543]. In a world dominated by mathematical approach that supported Galileo’s first the Church and the geocentric model devised by Claudius telescopic observations. Ptolemy [ca. AD 90 – ca. 168], which placed the Earth at the centre of the universe, this act was nothing short of unlaw- Riad HAIDAR, [email protected] ful. However, his teacher’s arguments were so compelling and the reasoning so seductive that Kepler soon became a convinced Copernican. As this new stance was obviously ohannes Kepler was born on 27 December 1571 to a incompatible with the role of a pastor, Kepler abandoned his family of modest means in the town of Weil der Stadt.