Sources and Studies in the History of Mathematics and Physical Sciences
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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. -
From the Edition of the Tractatus De Sphaera (1516) to the Cosmographia (1532)
Chapter 8 Oronce Fine and Sacrobosco: From the Edition of the Tractatus de sphaera (1516) to the Cosmographia (1532) Angela Axworthy Abstract This paper considers the contribution of the French mathematician Oronce Fine to the diffusion and transformation of Johannes de Sacrobosco’s Tractatus de sphaera by considering his 1516 edition of the Sphaera and his Cosmographia, sive sphaera mundi (in Protomathesis, 1532). The article first describes Fine’s life and career, as well as his work as editor of the Sphaera. In a second part, it considers what Fine, in the Cosmographia, has drawn and left aside from the Sphaera, revealing the consequent transformations to the teaching of Sacrobosco’s theory of the sphere and its adaptation to the cultural and intellectual environment in which Fine evolved. A last part considers the treatment, in the Cosmographia, of the cosmological representations transmitted by Sacrobosco and by subsequent interpreters of Ptolemaic astronomy concerning the number of celes- tial spheres and its relation to judicial astrology. A. Axworthy (*) Technische Universität Berlin, Berlin, Germany Max Planck Institute for the History of Science, Berlin, Germany e-mail: [email protected] © The Author(s) 2020 185 M. Valleriani (ed.), De sphaera of Johannes de Sacrobosco in the Early Modern Period, https://doi.org/10.1007/978-3-030-30833-9_8 186 A. Axworthy 1 Introduction1 Oronce Fine or Finé2 (1494–1555), a French mathematician from the Dauphiné, is chiefly known to historians of science for having been the first to -
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 -
Al-Kindi, a Ninth-Century Physician, Philosopher, And
AL-KINDI, A NINTH-CENTURY PHYSICIAN, PHILOSOPHER, AND SCHOLAR by SAMI HAMARNEH FROM 9-12 December, I962, the Ministry of Guidance in Iraq celebrated the thousandth anniversary of one of the greatest intellectual figures of ninth century Baghdad, Abui Yuisuf Ya'qiib ibn Ishaq al-Kind? (Latin Alkindus).1 However, in the aftermath ofthis commendable effort, no adequate coverage of al-Kindl as a physician-philosopher ofardent scholarship has, to my knowledge, been undertaken. This paper, therefore, is intended to shed light on his intel- lectual contributions within the framework of the environment and time in which he lived. My proposals and conclusions are mainly based upon a study of al-Kindi's extant scientific and philosophical writings, and on scattered information in the literature of the period. These historical records reveal that al-Kindi was the only man in medieval Islam to be called 'the philosopher of the Arabs'.2 This honorary title was apparently conferred upon him as early as the tenth century if not during his lifetime in the ninth. He lived in the Abbasids' capital during a time of high achievement. As one of the rare intellectual geniuses of the century, he con- tributed substantially to this great literary, philosophic, and scientific activity, which included all the then known branches of human knowledge. Very little is known for certain about the personal life of al-Kind?. Several references in the literary legacy ofIslam, however, have assisted in the attempt to speculate intelligently about the man. Most historians of the period confirm the fact that al-Kindl was of pure Arab stock and a rightful descendant of Kindah (or Kindat al-Muliuk), originally a royal south-Arabian tribe3. -
A Short Modern History of Studying Sacrobosco's De
STUDIA UBB. PHILOSOPHIA, Vol. 65 (2020), Special Issue, pp. 23-33 (RECOMMENDED CITATION) DOI:10.24193/subbphil.2020.spiss.02 A SHORT MODERN HISTORY OF STUDYING SACROBOSCO’S DE SPHAERA CORFU ALIN CONSTANTIN ABSTRACT. A Short Modern History of Studying Sacrobosco’s De sphaera. The treatise generally known as De sphaera offered at the beginning of the 13th century a general image of the structure of the cosmos. In this paper I’m first trying to present a triple stake with which this treaty of Johannes de Sacrobosco (c. 1195 - c. 1256). This effort is intended to draw a context upon the treaty on which I will present in the second part of this paper namely, a short modern history of studying this treaty starting from the beginning of the 20th century up to this day. The first stake consists in the well-known episode of translation of the XI-XII centuries in the Latin milieu of the Greek and Arabic treaties. The treatise De sphaera taking over, assimilating and comparing some of the new translations of the texts dedicated to astronomy. The second Consists in the fact that Sacrobosco`s work can be considered a response to a need of renewal of the curriculum dedicated to astronomy at the University of Paris. And the third consists in the novelty and the need to use the De sphaera treatise in the Parisian University’s curriculum of the 13th century. Keywords: astronomy, translation, university, 13th Century, Sacrobosco, Paris, curriculum The context. The De sphaera treaty of Master Johannes de Sacrobosco in the Curriculum of the University of Paris of the 13th Century In this first part of the research I aim to present the place of the treatise De sphaera, written by Johannes de Sacrobosco, at the beginning of the 13th century at the Parisian University in the curriculum of the liberal arts and the content of the treatise. -
A Lathe and the Material Sphaera
Edinburgh Research Explorer A lathe and the material sphaera Citation for published version: Oosterhoff, R 2020, A lathe and the material sphaera: Astronomical technique at the origins of the cosmographical handbook. in M Valleriani (ed.), De Sphaera of Johannes de Sacrobosco in the Early Modern Period: The Authors of the Commentaries. Springer, pp. 25-52. https://doi.org/10.1007/978-3-030- 30833-9_2 Digital Object Identifier (DOI): 10.1007/978-3-030-30833-9_2 Link: Link to publication record in Edinburgh Research Explorer Document Version: Publisher's PDF, also known as Version of record Published In: De Sphaera of Johannes de Sacrobosco in the Early Modern Period General rights Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 03. Oct. 2021 Chapter 2 A Lathe and the Material Sphaera: Astronomical Technique at the Origins of the Cosmographical Handbook Richard J. Oosterhoff Abstract Even though cosmographers loved to drape their discipline in the ancient dignity of Ptolemy, actual manuals of cosmography often depended on Johannes de Sacrobosco’s medieval introduction to spherical astronomy. -
Introduction
Cambridge University Press 978-0-521-51484-2 - Discovering the Expanding Universe Harry Nussbaumer and Lydia Bieri Excerpt More information 1 Introduction The discovery of the expanding universe in the first half of the twentieth century is one of the most exciting exploits in the history of astronomy; it is the main theme of this book. An intense and occasionally even fierce controversy divided the astronomical world at the beginning of the twentieth century: does the Milky Way represent the whole Universe, or is our Cosmos composed of an enormous or even infinite number of island universes, each of them similar to our own Milky Way? The question was definitely settled in 1925 in favour of island universes, a concept that had been proposed by Immanuel Kant in 1755. Yet, even before the debate was closed, that grand silent Universe had become the playground of theoreti- cians, who tried to fathom its structure with their abstract mathematics. Modern cosmology began in 1917 when Albert Einstein published his ‘Kosmologische Betrachtungen zur allgemeinen Relativita¨tstheorie’ (Cosmological considerations on the general theory of relativity). In his theory, space and time form a unity: spacetime. They are no longer absolute and independent concepts, the structure of spacetime is intrinsically related to the material and energetic content of the Universe: spacetime is structured by gravitation. More than two thousand years of astronomical observations showed the Universe to be stable and practically immutable in space as well as in time. Thus, when Einstein merged relativity with cosmology, he quite naturally wanted to accommodate a static universe that did not change with time. -
How Ptolemy's Geocentric Astronomy Helped Build the Modern World
How the Discredited Geocentric Cosmos Was a Critical Component of the Scientific Revolution by Rick Doble Copyright © 2015 Rick Doble From Doble's blog, DeconstructingTime, deconstructingtime.blogspot.com All pictures and photos are from commons.wikimedia.org How Ptolemy's Geocentric Astronomy Helped Build the Modern World If you took the standard required western history course in college as I did, you learned that about 400 years ago astronomers Copernicus, Galileo and Kepler along with Isaac Newton were key players in the scientific revolution that overturned the cumbersome system of geocentric astronomy. In this outdated system the Sun, moon and stars went around the stationary Earth. Instead these early scientists proved that the Earth and the planets went around the Sun. Known as the Copernican Revolution, it is considered the beginning of the scientific revolution, a new way of thinking which continues to this day and has created our modern world and our modern hi-tech marvels. Well, that story is sort of true, but in hindsight it greatly simplifies the complex path that the scientific revolution took, the path that ultimately led to today's scientific and technological wonders. Specifically it leaves out the fact that the geometry of a geocentric universe and its foremost astronomer, Ptolemy, who perfected the geocentric system, were key players in this new scientific outlook. In fact the discredited geocentric theory was, oddly, essential for building our new scientific/technological world. Doble, Rick How the Discredited Geocentric Cosmos Was a Critical Component of the Scientific Revolution Page 1 of 11 BACKGROUND OF THE GEOCENTRIC/PTOLEMAIC SYSTEM Over hundreds of years the early ancient Greeks put together a concept of the Solar System as a coherent system of concentric circles -- which was a major advance for Western thought. -
The Arabic-Latin Translators – Natural Science and Philosophy
CHARLES BURNETT List of Publications Books, and articles over 100 pages long Articles and pamphlets, arranged thematically, and in chronological order within each topic The Arabic-Latin Translators – Natural Science and Philosophy – Astronomy and Astrology - Medicine and Psychology – Magic and Divination – Arithmetic and Geometry – Anglo- Norman Science and Learning in the Twelfth Century – Peter Abelard and the French Schools – Music – Contacts between the West and the Far East – Miscellaneous – Reviews (selection) List of editions of Latin texts in books and articles above (Please note that some diacritical markings are missing) Books, and articles over 100 pages long: 1. Hermann of Carinthia, De essentiis, critical edition, translation and commentary, Leiden, 1982, 385 pp. (reviews in Speculum, 1984, pp. 911–3, Cahiers de civilisation médiévale, 28, 1985, p. 685, Mittellateinisches Jahrbuch, 20, 1985, pp. 287–90, Deutsches Archiv, 41, 1985, p. 255, Rivista di storia della filosofia, 2, 1984, pp. 349–51, Bulletin de théologie ancienne et médiévale, 14, 1989, p. 695). 2. ‘A Checklist of the Manuscripts Containing Writings of Peter Abelard and Heloise and Other Works Closely Associated with Abelard and his School’, Revue d’histoire des textes, 14–15, 1984–5, pp. 183–302 (with David Luscombe and Julia Barrow). 3. Pseudo-Bede, De mundi celestis terrestrisque constitutione: a Treatise on the Universe and the Soul, edition, translation and commentary, Warburg Institute Surveys and Texts 10, London, 1985. 88 pp. (reviews in Isis, 77, 1986, pp. 182–3, Revue d’histoire ecclésiastique, 81, 1986, p. 742, Ambix, 33, 1986, p. 155, Journal of the History of Astronomy, 19, 1988, pp. -
Vernacular Translations of Sacrobosco's Sphere in the Sixteenth Century
JHA0010.1177/0021828614567419Journal for the History of AstronomyCrowther et al. 567419research-article2015 Article JHA Journal for the History of Astronomy 2015, Vol. 46(1) 4 –28 The Book Everybody Read: © The Author(s) 2015 Reprints and permissions: Vernacular Translations of sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0021828614567419 Sacrobosco’s Sphere in the jha.sagepub.com Sixteenth Century Kathleen Crowther University of Oklahoma, Department of the History of Science, USA Ashley Nicole McCray University of Oklahoma, Department of the History of Science, USA Leila McNeill Independent scholar, Texas, USA Amy Rodgers University of Oklahoma, Department of the History of Science, USA Blair Stein University of Oklahoma, Department of the History of Science, USA Abstract This article presents four detailed case studies of sixteenth-century vernacular translations of Sacrobosco’s De sphaera. Previous scholarship has highlighted the important role of Sacrobosco’s Sphere in medieval and early modern universities, where it served as an introductory astronomy text. We argue that the Sphere was more than a university teaching text. It was translated many times and was accessible to a wide range of people. The popularity of the Sphere suggests widespread interest in cosmological questions. We suggest that the text was a profitable one for early modern printers, who strove to identify books that would be reliable sellers. We also argue that the Sphere was not a static text. Rather, translators and editors added commentaries and other supplemental material that corrected and updated Sacrobosco’s original text and Corresponding author: Kathleen Crowther, Department of the History of Science, University of Oklahoma, 601 Elm Avenue, Room 625, Norman, OK 73019, USA. -
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.