March-April 2017.Pub
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
1. Introduction
1. INTRODUCTION 1.1 SUBJECT Three great mathematicians dominate the history of lunar theory in the middle of the 18th century: Leonhard Euler, Alexis Clairaut, and Jean le Rond d’Alembert. Each of them made a lasting contribution to the theory of celestial mechanics and their results had a broader impact than on lunar theory alone. To name but a few examples, Euler codified the trigonometric functions and pioneered the method of variation of orbital constants; Clairaut solved the arduous problem of the motion of the lunar apogee, thereby dealing a decisive blow to the sceptics of Newton’s law of gravitation; and d’Alembert worked out an accurate theory of precession and nutation. But during the second half of the 18th century, the most accurate tables of lunar motion were those of Tobias Mayer; not because he was better at solving the differ- ential equations of motion, but because he was eager to handle large and conflicting data sets in what could nowadays be called a statistical way. He was a true pioneer in the ‘combination of observations’, which comprises the handling of observational data in order to infer from them certain quantitative aspects of the physical reality. His tables of the moon’s motion had an important application in the determination of geographical longitude at sea, by the so-called method of lunar distances. What is known of Mayer’s work on lunar motion? Alfred Gautier, the 19th century astronomer, included a brief analysis of the contents of Mayer’s Theoria Lunae in his essay on the history of the three-body problem.1 Delambre, although full of admiration for Mayer, dedicated only a few lines to it.2 The 20th century research by Eric Forbes, culminating in a biography of Mayer, has brought about something of a Mayer revival.3 Forbes has constructed a unifying picture of the man Mayer and his work, after thorough investigation of correspondence, unpublished treatises and memoirs, and published sources as well. -
My Math Genealogy Graph
Nilos Kabasilas Elissaeus Judaeus Demetrios Kydones Georgios Plethon Gemistos Manuel Chrysoloras (1380) Basilios Bessarion Guarino da Verona Mystras (1436) (1408) Johannes Argyropoulos Università di Padova (1444) 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 Constantinople / Università di Mantova (1433) Università di Mantova Università di Firenze (1477) Heinrich von Langenstein Rudolf Agricola Demetrios Chalcocondyles Scipione Fortiguerra Leo Outers Thomas à Kempis Jacob ben Jehiel Loans Gaetano da Thiene Alessandro Sermoneta Moses Perez Université de Paris (1363) Università degli Studi di Ferrara (1478) Mystras / Accademia Romana (1452) Università di Firenze (1493) Université Catholique de Louvain (1485) Johannes von Gmunden Alexander Hegius Jan Standonck Janus Lascaris Johann (Johannes Kapnion) Reuchlin François Dubois Nicoletto Vernia Pietro Roccabonella Girolamo (Hieronymus Aleander) Aleandro Maarten (Martinus Dorpius) van Dorp Matthaeus Adrianus Jean Tagault Pelope Universität Wien (1406) (1474) Collège Sainte-Barbe / Collège de Montaigu (1474) Università di Padova (1472) Universität Basel / Université de Poitiers (1477) Université de Paris (1516) Università di Padova Università di Padova Università di Padova (1499) Université Catholique de Louvain (1504) Georg von Peuerbach Desiderius Erasmus Jacobus (Jacques Masson) Latomus Marco Musuro Jan (Johannes Campensis) van Campen Jacobus -
Leonhard Euler's Early Lunar Theories 1725–1752
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by RERO DOC Digital Library Arch. Hist. Exact Sci. (2013) 67:235–303 DOI 10.1007/s00407-012-0112-y Leonhard Euler’s early lunar theories 1725–1752 Part 1: first approaches, 1725–1730 Andreas Verdun Received: 9 October 2012 / Published online: 2 December 2012 © Springer-Verlag Berlin Heidelberg 2013 Abstract Leonhard Euler (1707–1783) published two lunar theories in 1753 and 1772. He also published lunar tables in 1745, 1746, and—anonymously—in 1750. There are notebook records, unpublished manuscripts, and manuscript fragments by Euler reflecting the development of his lunar theories between about 1725 until about 1752. These documents might be used to reconstruct Euler’s theory on which he based his calculations of those lunar tables and to analyze the development of his lunar theories within this time span. The results of this analysis will be published here in three parts representing three stages of Euler’s research on this topic: First approaches (about 1725–1730), developing the methods (about 1730–1744), and the breakthrough (about 1744–1752). In this part, I analyze Euler’s manuscripts and, predominantly, Euler’s records of his first two notebooks written between 1725 and 1730. I found that his early theoretical approach is coined by his development of analytical (rational) mechanics of punctiform bodies moved by central forces. He tried to describe the Moon’s motion in terms of two simultaneously acting centripetal forces, Huygens’ centrifugal theorem, and associated osculating radii. In memoriam Emil A. -
The Creation of Color in Eighteenth-Century Europe: Number, O
The Creation of Color in 18th-Century Europe Number, Order, Form Sarah Lowengard Number, Order, Form Color Systems and Systematization Assume that it is possible to determine the number of colors in the world. Ignore, for the moment, certain philosophical and physiological questions—for example, whether a color exists if it cannot be seen and if the number of colors must be different for each person because it is a unique product of the physics and biology of the eye. While these considerations are important in themselves, they are, for our purposes, tangential. If we can agree that the number of colors is finite and determinable, then what is that number, and how is it calculated? How do the answers to these questions aid the work of colorists, whether scientists, manufacturers, experimenters, or the unaffiliated curious? Assume also that there is some primordial physical form for colors, one that conveys critical information to the viewer at a glance. What should this be? What should it tell? How should it be created? How, exactly, will this critical information aid and reflect the development of the practices and theories of color? Finally, accept that the relationship among coloring materials is such that specific mixtures of certain colors yield specific other colors. There must be, then, some small number of colors from which all others are made. What is that number, and what are those colors? I have begun upon a great undertaking. The arrangement of my fossils and making a catalogue for them. As a Potter I make clays my first article, after which stones vitrifiable will follow, but I cannot draw the line betwixt clays and some of the stones. -
Milestones in the History of Thematic Cartography, Statistical Graphics, and Data Visualization∗
Milestones in the history of thematic cartography, statistical graphics, and data visualization∗ Michael Friendly October 16, 2008 1 Introduction The only new thing in the world is the history you don’t know. Harry S Truman, quoted by David McCulloch in Truman The graphic portrayal of quantitative information has deep roots. These roots reach into histories of thematic cartography, statistical graphics, and data visualization, which are intertwined with each other. They also connect with the rise of statistical thinking up through the 19th century, and developments in technology into the 20th century. From above ground, we can see the current fruit; we must look below to see its pedigree and germination. There certainly have been many new things in the world of visualization; but unless you know its history, everything might seem novel. A brief overview The earliest seeds arose in geometric diagrams and in the making of maps to aid in navigation and explo- ration. By the 16th century, techniques and instruments for precise observation and measurement of physical quantities were well-developed— the beginnings of the husbandry of visualization. The 17th century saw great new growth in theory and the dawn of practice— the rise of analytic geometry, theories of errors of measurement, the birth of probability theory, and the beginnings of demographic statistics and “political arithmetic”. Over the 18th and 19th centuries, numbers pertaining to people—social, moral, medical, and economic statistics began to be gathered in large and periodic series; moreover, the usefulness of these bod- ies of data for planning, for governmental response, and as a subject worth of study in its own right, began to be recognized. -
Method for Determining the Longitude of Places by Observing Occultations of Fixed Stars by the Moon*
Synopsis of Leonhard Euler's 1749 paper: METHOD FOR DETERMINING THE LONGITUDE OF PLACES BY OBSERVING OCCULTATIONS OF FIXED STARS BY THE MOON* By Jennifer Grabowski, Jeffrey Meyer, and Erik Tou Carthage College, June 2009 1. History of the problem Navigation has been important in traveling as well as safety. For example, in 1707, a British fleet made an error on their longitude findings that sent them in the wrong direction where four of the five ships were destroyed and nearly two thousand soldiers lost their lives. This problem may have been avoided if the sailors had an accurate method of finding longitude. In 1714, the British Parliament passed the Longitude Act, which offered £20,000 to anyone who could calculate longitude to within a half degree. Since one degree of longitude can be as much as 69 miles, even a fraction of a degree comes out to a significant distance. Therefore, the required method would need to be very accurate. In the late 1720s, a self-educated British watchmaker named John Harrison set out to construct a sea clock which could keep accurate enough time to calculate longitude. Harrison succeeded in constructing a sea clock in 1735 which was deserving of the £20,000 prize. However, he was very critical of his machine even though everyone else, including the royal board of longitude, was very impressed. The sextant was then invented by a couple of inventors during the same time period. A sextant had incorporated a longer measuring arc as well as a telescope. These additional pieces enabled the device to measure distances during the day from the moon to the sun and from the moon to the stars at night. -
Astronomers As Sketchers and Painters: the Eye – the Hand – the Understanding1
ПРИЛОЗИ, Одделение за природно-математички и биотехнички науки, МАНУ, том 39, бр. 1, стр. 5–14 (2018) CONTRIBUTIONS, Section of Natural, Mathematical and Biotechnical Sciences, MASA, Vol. 39, No. 1, pp. 5–14 (2018) Received: November 7, 2017 ISSN 1857–9027 Accepted: December 12, 2017 e-ISSN 1857–9949 UDC: 520-1:528.94]:75.05 DOI: 10.20903/csnmbs.masa.2018.39.1.115 Review ASTRONOMERS AS SKETCHERS AND PAINTERS: THE EYE – THE HAND – THE UNDERSTANDING1 Dieter B. Herrmann Leibniz-Sozietät der Wissenschaften zu Berlin, Berlin, Germany e-mail: [email protected] Today we are accustomed to seeing the objects of the universe in magnificent digital pictures vividly before our eyes. But before the invention of photography, the art of painting and drawing played an important role in scientific research. Those who were powerful astronomers of this art had the advantage. This article substantiates this thesis by means of selected examples. The drawings and the related discoveries of Galileo Galilei (1564–1642), Johannes Hevelius (1611–1687), Tobias Mayer (1723–1762), Johann Heinrich Mädler (1794–1874), Julius Schmidt (1825–1884), Giovanni Schiaparelli (1835–1910), Eugenios Antoniadi (1870–1944), William Parsons alias Lord Rosse (1800–1867), Ernst Wilhelm Leberecht Tempel (1821–1889), Etienne Trouvelot (1827–1895) and Walter Löbering (1895–1969) and showed their most important drawn observation documents. It can be seen that thanks to their art and the associated highly developed ability to perceive it, astronomers' drawings have made astounding discoveries that others have been denied. Finally, some thoughts on the role of drawn or painted astronomical motifs in the present are developed. -
Euler: Genius Blind Astronomer Mathematician
Euler: Genius Blind Astronomer Mathematician Dora E. Musielak University of Texas at Arlington [email protected] Résumé. Leonhard Euler, the most prolific mathematician in history, contributed to advance a wide spectrum of topics in celestial mechanics. At the St. Petersburg Observatory, Euler observed sunspots and tracked the movements of the Moon. Combining astronomical observations with his own mathematical genius, he determined the orbits of planets and comets. Euler laid the foundations of the methods of planetary perturbations and solved many of the Newtonian mechanics problems of the eighteenth century that are relevant today. In his study of the three-body problem, Euler discovered two of five equilibrium points so-called the Lagrangian points. His pioneering work in astronomy was recognized with six of the twelve prizes he won from the Paris Academy of Sciences. In this article, we review some of Euler’s most interesting work in astronomy. Résumé. Leonard Euler, el matemático más prolífico de la historia, contribuyó al avance de una amplia gama de temas en la mecánica celeste. En el Observatorio de San Petersburgo, Euler observó las manchas solares e hizo observaciones de los movimientos de la Luna. Combinando las observaciones astronómicas con su propio genio matemático, él determinó las órbitas de los planetas y los cometas. Euler sentó las bases de los métodos de perturbaciones planetarias y resolvió muchos de los problemas de la mecánica newtoniana del siglo XVIII que aun hoy en día son relevantes. En su estudio sobre el problema de los tres cuerpos Euler descubrió dos de los puntos de equilibrio también llamados puntos de LaGrange. -
Museum „Physicalisches Cabinet“
MUSE UM „PH Y SIC A LIS C H E S C A B I N E T “ 19 Museum „Physicalisches Cabinet“ One of three collections of historic instruments in the faculty of physics is located at the foyer in front of the lecture halls. It showcases the history of physics in Göttingen, from the beginnings of systematic research in the 18th century to its most famous period as the world-leading center for physics and mathematics in the first half of the 20th century. Physics in the early years of the university 18th century: Lichtenberg The witnesses of more than 275 years of the physics tradition When Georg Christoph Lichtenberg (1742-1799) came from in Göttingen give us unique insight in the university teaching Darmstadt as a student in 1763 for three years, the lectures he and research in the 18th and 19th century. The first physics listened to were mainly devoted to mathematics, but he was lectures were given by the philosopher Samuel Christian also introduced into astronomy. In 1778 Lichtenberg assumed Hollmann (1696-1787) in 1734, preceding the official founding the lectures on physics from his colleague, the natural scientist of the university in 1737. He came as a well-known critical mind Johann Polycarp Erxleben (1744–1777), and gave his famous from the University of Wittenberg to teach ethics, psychology, experimental physics lectures from 1778 to 1799. A novelty at logic and metaphysics and established the tradition of well- that time, he put the experiments in focus, giving the first visited lectures on natural sciences. Due to the approach of the experimental physics lectures. -
Academic Genealogy of Gareth James Ludwig Bieberbach C
Nasir al-Din al-Tusi Shams ad-Din Al-Bukhari Maragheh Observatory Gregory Chioniadis Manuel Bryennios Theodore Metochites 1315 Gregory Palamas Nilos Kabasilas 1363 Elissaeus Judaeus Demetrios Kydones Georgios Plethon Gemistos Manuel Chrysoloras 1380, 1393 Basilios Bessarion Guarino da Verona 1436 Mystras 1408 Johannes Argyropoulos 1444 Università degli Studi di Padova Marsilio Ficino Cristoforo Landino Vittorino da Feltre 1462 Università degli Studi di Firenze 1416 Università degli Studi di Padova Theodoros Gazes Nicole Oresme Florens Florentius Radwyn Radewyns Geert Gerardus Magnus Groote Angelo Poliziano Ognibene (Omnibonus Leonicenus) Bonisoli da Lonigo 1433 Università di Mantova 1477 Università degli Studi di Firenze Università di Mantova 1433 Constantinople Heinrich von Langenstein Demetrios Chalcocondyles Thomas von Kempen à Kempis Jacob ben Jehiel Loans Rudolf Agricola Leo Outers Scipione Fortiguerra Moses Perez Sigismondo Polcastro Gaetano da Thiene 1363 Université de Paris 1452 Accademia Romana 1478 Università degli Studi di Ferrara 1485 Université Catholique de Louvain 1493 Università degli Studi di Firenze 1375 Université de Paris 1452 Mystras Johann (Johannes Kapnion) Reuchlin Jan Standonck Johannes von Gmunden Johannes Stöffler Alexander Hegius Matthaeus Adrianus Janus Lascaris François Dubois Jean Tagault Maarten (Martinus Dorpius) van Dorp Girolamo (Hieronymus Aleander) Aleandro Pelope Pietro Roccabonella Nicoletto Vernia 1477 Universität Basel 1474 Collège Sainte-Barbe 1406 Universität Wien 1476 Universität Ingolstadt -
Astronomy and Anthropologie in the Eighteenth Century
NÚMERO 42 MICHAEL J. SAUTER Germans in Space: Astronomy and Anthropologie in the Eighteenth Century MAYO 2007 www.cide.edu Las colecciones de Documentos de Trabajo del CIDE representan un medio para difundir los avances de la labor de investigación, y para permitir que los autores reciban comentarios antes de su publicación definitiva. Se agradecerá que los comentarios se hagan llegar directamente al (los) autor(es). • D.R. ® 2006. Centro de Investigación y Docencia Económicas, carretera México-Toluca 3655 (km. 16.5), Lomas de Santa Fe, 01210, México, D.F. Fax: 5727•9800 ext.6314 Correo electrónico: [email protected] www.cide.edu Producción a cargo del (los) autor(es), por lo que tanto el contenido así como el estilo y la redacción son su responsabilidad. Abstract Physical orientation was a central philosophical problem for German thinkers in the late eighteenth century. Moses Mendelssohn, for instance, pondered in Morgenstunden, o Vorlesungen uber das Daseyn Gotten (1785) whether one can orient oneself in the metaphysical realm with the human senses. Immanuel Kant took up the same question in “What is Orientation in Thinking?” (1786). In both works the authors struggled to understand how one can apply physical concepts —left, right, up, down— to places where the human body is not, or cannot be. These two thinkers’ ideas —and many of their German contemporaries— were a response to the eighteenth century’s discovery of “outer space”. The astronomical contemplation of an infinite universe, populated by multiple worlds and, perhaps, intelligences raised a series of cosmological and metaphysical questions that could only be answered through a complete reassessment of the human being’s physical relationship to “space”. -
How Is the Reference Axis for Precession and Nutation Defined ?
Apparent Places of Fundamental Stars (APFS) Past and present status Preview: Early astronomical ephemerides Predecessors of APFS (1776 – 1959) The "early years" of APFS (1960 – 1983): FK3 and FK4 A time of change (1984 – 1988): IAU 1976 System of Astronomical Constants, 1980 Theory of Nutation, FK5, Celestial Ephemeris Pole (CEP) New theories and concepts in astrometry (2000 – 2006): Adoption of the ICRS instead of FK5-System, IAU 2000/2006 nutation theory, Celestial Intermediate Pole (CIP) and Celestial Intermediate Origin (CIO) APFS today Early astronomical ephemerides "Connaissance des temps ou des mouvements celestes", 1679, published by Jean Picard, France "Astronomische Ephemeriden", 1757, published by Maximilian Hell, Austria "Nautical Almanac",1767, published by the Astronomer Royal Nevil Maskelyne, U.K. "Berliner Astronomisches Jahrbuch", 1776, more details subsequently "Almanaque Nautico" ,1792, San Fernando (Cadiz), Spain Predecessors of APFS Berliner Astronomisches Jahrbuch (1776 – 1959). First Volume: "Astronomisches Jahrbuch oder Ephemeriden für das Jahr 1776". Edited 1774 in Berlin by Johann Elert Bode (1747 – 1826), who became 1786 director of the "Berliner Sternwarte" Berliner Astronomisches Jahrbuch BAJ 1776 From preface BAJ 1776: "Es erscheinet hiermit der erste Jahrgang der Ephemeriden welche nach dem von der Königl. Preussischen Akademie der Wissenschaften gefassten Beschlusse und unter ihrer Aufsicht jährlich herauskommen sollen. Die Veranlassung dazu war vielfach und ungezwungen." Attempt of a translation: "Hereby appears the first volume of ephemerides which shall be published annually according to the decision of (and supervised by) the Royal Prussion Academy of Sciences. The motive was manifold and informal." BAJ 1776 The first volume contained the ephemerides of 280 stars for January 1, 1776.