The Astrolabe (Edited from Wikipedia)
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In the Wake of the Compendia Science, Technology, and Medicine in Ancient Cultures
In the Wake of the Compendia Science, Technology, and Medicine in Ancient Cultures Edited by Markus Asper Philip van der Eijk Markham J. Geller Heinrich von Staden Liba Taub Volume 3 In the Wake of the Compendia Infrastructural Contexts and the Licensing of Empiricism in Ancient and Medieval Mesopotamia Edited by J. Cale Johnson DE GRUYTER ISBN 978-1-5015-1076-2 e-ISBN (PDF) 978-1-5015-0250-7 e-ISBN (EPUB) 978-1-5015-0252-1 ISSN 2194-976X Library of Congress Cataloging-in-Publication Data A CIP catalog record for this book has been applied for at the Library of Congress. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2015 Walter de Gruyter Inc., Boston/Berlin Typesetting: Meta Systems Publishing & Printservices GmbH, Wustermark Printing and binding: Hubert & Co. GmbH & Co. KG, Göttingen ♾ Printed on acid-free paper Printed in Germany www.degruyter.com Notes on Contributors Florentina Badalanova Geller is Professor at the Topoi Excellence Cluster at the Freie Universität Berlin. She previously taught at the University of Sofia and University College London, and is currently on secondment from the Royal Anthropological Institute (London). She has published numerous papers and is also the author of ‘The Bible in the Making’ in Imagining Creation (2008), Qurʾān in Vernacular: Folk Islam in the Balkans (2008), and 2 (Slavonic Apocalypse of) Enoch: Text and Context (2010). Siam Bhayro was appointed Senior Lecturer in Early Jewish Studies in the Department of Theology and Religion, University of Exeter, in 2012, having previously been Lecturer in Early Jewish Studies since 2007. -
Babylonian Astral Science in the Hellenistic World: Reception and Transmission
CAS® e SERIES Nummer 4 / 2010 Francesca Rochberg (Berkeley) Babylonian Astral Science in the Hellenistic World: Reception and Transmission Herausgegeben von Ludwig-Maximilians-Universität München Center for Advanced Studies®, Seestr. 13, 80802 München www.cas.lmu.de/publikationen/eseries Nummer 4 / 2010 Babylonian Astral Science in the Hellenistic World: Reception and Transmission Francesca Rochberg (Berkeley) In his astrological work the Tetrabiblos, the astronomer such as in Strabo’s Geography, as well as in an astrono- Ptolemy describes the effects of geography on ethnic mical text from Oxyrhynchus in the second century of character, claiming, for example, that due to their specific our era roughly contemporary with Ptolemy [P.Oxy. geographical location „The ...Chaldeans and Orchinians 4139:8; see Jones 1999, I 97-99 and II 22-23]. This have familiarity with Leo and the sun, so that they are astronomical papyrus fragment refers to the Orchenoi, simpler, kindly, addicted to astrology.” [Tetr. 2.3] or Urukeans, in direct connection with a lunar parameter Ptolemy was correct in putting the Chaldeans and identifiable as a Babylonian period for lunar anomaly Orchinians together geographically, as the Chaldeans, or preserved on cuneiform tablets from Uruk. The Kaldayu, were once West Semitic tribal groups located Babylonian, or Chaldean, literati, including those from in the parts of southern and western Babylonia known Uruk were rightly famed for astronomy and astrology, as Kaldu, and the Orchinians, or Urukayu, were the „addicted,” as Ptolemy put it, and eventually, in Greco- inhabitants of the southern Babylonian city of Uruk. He Roman works, the term Chaldean came to be interchan- was also correct in that he was transmitting a tradition geable with „astrologer.” from the Babylonians themselves, which, according to a Hellenistic Greek writers seeking to claim an authorita- Hellenistic tablet from Uruk [VAT 7847 obv. -
Models for Earth and Maps
Earth Models and Maps James R. Clynch, Naval Postgraduate School, 2002 I. Earth Models Maps are just a model of the world, or a small part of it. This is true if the model is a globe of the entire world, a paper chart of a harbor or a digital database of streets in San Francisco. A model of the earth is needed to convert measurements made on the curved earth to maps or databases. Each model has advantages and disadvantages. Each is usually in error at some level of accuracy. Some of these error are due to the nature of the model, not the measurements used to make the model. Three are three common models of the earth, the spherical (or globe) model, the ellipsoidal model, and the real earth model. The spherical model is the form encountered in elementary discussions. It is quite good for some approximations. The world is approximately a sphere. The sphere is the shape that minimizes the potential energy of the gravitational attraction of all the little mass elements for each other. The direction of gravity is toward the center of the earth. This is how we define down. It is the direction that a string takes when a weight is at one end - that is a plumb bob. A spirit level will define the horizontal which is perpendicular to up-down. The ellipsoidal model is a better representation of the earth because the earth rotates. This generates other forces on the mass elements and distorts the shape. The minimum energy form is now an ellipse rotated about the polar axis. -
Anaximander and the Problem of the Earth's Immobility
Binghamton University The Open Repository @ Binghamton (The ORB) The Society for Ancient Greek Philosophy Newsletter 12-28-1953 Anaximander and the Problem of the Earth's Immobility John Robinson Windham College Follow this and additional works at: https://orb.binghamton.edu/sagp Recommended Citation Robinson, John, "Anaximander and the Problem of the Earth's Immobility" (1953). The Society for Ancient Greek Philosophy Newsletter. 263. https://orb.binghamton.edu/sagp/263 This Article is brought to you for free and open access by The Open Repository @ Binghamton (The ORB). It has been accepted for inclusion in The Society for Ancient Greek Philosophy Newsletter by an authorized administrator of The Open Repository @ Binghamton (The ORB). For more information, please contact [email protected]. JOHN ROBINSON Windham College Anaximander and the Problem of the Earth’s Immobility* N the course of his review of the reasons given by his predecessors for the earth’s immobility, Aristotle states that “some” attribute it I neither to the action of the whirl nor to the air beneath’s hindering its falling : These are the causes with which most thinkers busy themselves. But there are some who say, like Anaximander among the ancients, that it stays where it is because of its “indifference” (όμοιότητα). For what is stationed at the center, and is equably related to the extremes, has no reason to go one way rather than another—either up or down or sideways. And since it is impossible for it to move simultaneously in opposite directions, it necessarily stays where it is.1 The ascription of this curious view to Anaximander appears to have occasioned little uneasiness among modern commentators. -
On the Origin of the Lunar and Solar Periods in Babylonian Lunar Theory De Jong, T
UvA-DARE (Digital Academic Repository) On the Origin of the Lunar and Solar Periods in Babylonian Lunar Theory de Jong, T. DOI 10.17171/3-44-6 Publication date 2017 Document Version Final published version Published in Studies on the Ancient Exact Sciences in Honour of Lis Brack-Bernsen License CC BY-NC Link to publication Citation for published version (APA): de Jong, T. (2017). On the Origin of the Lunar and Solar Periods in Babylonian Lunar Theory. In J. M. Steele, & M. Ossendrijver (Eds.), Studies on the Ancient Exact Sciences in Honour of Lis Brack-Bernsen (pp. 105-126). Berlin: Edition Topoi. https://doi.org/10.17171/3-44-6 General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl) Download date:28 Sep 2021 Teije de Jong On the Origin of the Lunar and Solar Periods in Babylonian Lunar Theory Summary In this investigation, I sketch the way in which Babylonian astronomers may have derived the basic parameters of their lunar theory. -
You Can Only Use a Planar Surface So Far, Before the Equidistance Assumption Creates Large Errors
You can only use a planar surface so far, before the equidistance assumption creates large errors Distance error from Kiester to Warroad is greater than two football fields in length So we assume a spherical Earth P. Wormer, wikimedia commons Longitudes are great circles, latitudes are small circles (except the Equator, which is a GC) Spherical Geometry Longitude Spherical Geometry Note: The Greek letter l (lambda) is almost always used to specify longitude while f, a, w and c, and other symbols are used to specify latitude Great and Small Circles Great circles splits the Small circles splits the earth into equal halves earth into unequal halves wikipedia geography.name All lines of equal longitude are great circles Equator is the only line of equal latitude that’s a great circle Surface distance measurements should all be along a great circle Caliper Corporation Note that great circle distances appear curved on projected or flat maps Smithsonian In GIS Fundamentals book, Chapter 2 Latitude - angle to a parallel circle, a small circle parallel to the Equatorial great circle Spherical Geometry Three measures: Latitude, Longitude, and Earth Radius + height above/ below the sphere (hp) How do we measure latitude/longitude? Well, now, GNSS, but originally, astronomic measurements: latitude by north star or solar noon angles, at equinox Longitude Measurement Method 1: The Earth rotates 360 degrees in a day, or 15 degrees per hour. If we know the time difference between 2 points, and the longitude of the first point (Greenwich), we can determine the longitude at our current location. Method 2: Create a table of moon-star distances for each day/time of the year at a reference location (Greenwich observatory) Measure the same moon-star distance somewhere else at a standard or known time. -
Paths Between Points on Earth: Great Circles, Geodesics, and Useful Projections
Paths Between Points on Earth: Great Circles, Geodesics, and Useful Projections I. Historical and Common Navigation Methods There are an infinite number of paths between two points on the earth. For navigation purposes there are only a few historically common choices. 1. Sailing a latitude. Prior to a good method of finding longitude at sea, you sailed north or south until you cane to the latitude of your destination then you sailed due east or west until you reached your goal. Of course if you choose the wrong direction, you can get in big trouble. (This happened in 1707 to a British fleet that sunk when it hit rocks. This started the major British program for a longitude method useful at sea.) In this method the route follows the legs of a right triangle on the sphere. Just as in right triangles on the plane, the hypotenuse is always shorter than the sum of the other two sides. This method is very inefficient, but it was all that worked for open ocean sailing before 1770. 2. Rhumb Line A rhumb line is a line of constant bearing or azimuth. This is not the shortest distance on a long trip, but it is very easy to follow. You just have to know the correct azimuth to use to get between two sites, such as New York and London. You can get this from a straight line on a Mercator projection. This is the reason the Mercator projection was invented. On other projections straight lines are not rhumb lines. 3. Great Circle On a spherical earth, a great circle is the shortest distance between two locations. -
The Shape of the Earth
The Shape of the Earth Produced for the Cosmology and Cultures Project of the OBU Planetarium by Kerry Magruder August, 2005 2 Credits Written & Produced by: Kerry Magruder Nicole Oresme: Kerry Magruder Students: Rachel Magruder, Hannah Magruder, Kevin Kemp, Chris Kemp, Kara Kemp Idiot Professor: Phil Kemp Andrew Dickson White: Phil Kemp Cicero, Aquinas: J Harvey NASA writer: Sylvia Patterson Jeffrey Burton Russell: Candace Magruder Images courtesy: History of Science Collections, University of Oklahoma Libraries Digital photography and processing by: Hannah Magruder Soundtrack composed and produced by: Eric Barfield Special thanks to... Jeffrey Burton Russell, 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_______________________________________6 3. Before the Show_________________________________________ 7 A. Video: A Private Universe______________________________ 7 B. Pre-Test_____________________________________________ 8 4. Production Script_________________________________________9 A. Production Notes______________________________________9 B. Theater Preparation___________________________________10 C. Script______________________________________________ -
307 Lesson 21: Eratosthenes' Measurement of the Earth the Most
307 Lesson 21: Eratosthenes’ Measurement of the Earth The most important parallel of latitude is the equator; it is the only parallel of latitude that is a great circle. However, in the previous lesson we learned about four other parallels of latitude which are of great importance because of the relative geometry of the Earth and the Sun. These are the Tropics of Cancer and Capricorn and the Arctic and Antarctic Circles. We briefly review the basic facts about these four parallels. At each moment on the day of the summer solstice, there is a single point on the surface of the Earth that is closet to the Sun. As the Earth rotates through the day of the summer solstice, this closest point to the Sun moves around the surface of the Earth and traces a parallel of latitude called the Tropic of Cancer. Another description of the Tropic of Cancer is that it is the set of all points on the Earth’s surface where the Sun is directly overhead at solar noon on the day of the summer solstice. The latitude coordinate of the Tropic of Cancer equals the measure of the angle that the Earth’s axis makes with the perpendicular to the ecliptic plane: approximately 23.5º N. On the day of the summer solstice, as the Earth rotates about its axis, the terminator (the division between daytime and nighttime) moves, and its northernmost point traces out a parallel of latitude called the Arctic Circle. Similarly, as the Earth rotates, the southernmost point of the terminator traces out a parallel of latitude called the Antarctic Circle. -
Astronomy Through the Ages 1 Early History and Greek Astronomy
Astronomy Through the Ages 1 Early History and Greek Astronomy ASTR 101 9/26/2018 1 Early History • Astronomy is often described as the oldest of the natural sciences. – Humans attempts to understand and make sense of the sky predates antiquity. – Religious, mythological and astrological beliefs and practices of pre-historical societies related to celestial objects and events can be seen from many artifacts that have survived to date. The Blanchard Bone, depicting a series of moon phases (France. 25,000 - 32,000 BCE) Stonehenge The Mayan observatory at Chichen Itza, seemed to have built to observe Venus and the Sun. The pyramid is aligned to solar equinox 2 Babylonian and ancient Egyptian astronomy (left) Mul Apin tablet(1100 BCE): Describing the appearance of different constellations and stars: Astronomical ceiling. 1470BCE Egyptian tomb (right) Babylonian clay tablets listing observation of Venus painting with constellations, planets, lunar th c. 7 century BCE. www.mesopotamia.co.uk/astronomer/explore/mulapin1.html cycle and stars depicted. • Astronomy and mathematics were in an advance state in the Babylonian civilization: • They kept records of position of the stars and planets and eclipses Many constellations visible from the northern hemisphere, and the zodiac are of Babylonian/Sumerian origin. • They used a number system with base 60 (sexadesimal), and a year of 360 days. • Circle 360 degrees, 60 minutes and 60 seconds descend from the Babylonian sexadesimal number system. • Egyptian astronomy mostly carried out by priest astronomers was largely concerned with time reckoning. Its main lasting contribution was the civil calendar of 365 days, with 12 months 3 • Unable to comprehend their underlying causes, early cultures resort to mysticism and religion for answers. -
Studies on the Ancient Exact Sciences in Honor of Lis Brack-Bernsen
44 Studies on the Ancient Exact Sciences in Honor of Lis Brack-Bernsen John M. Steele Mathieu Ossendrijver (eds.) EDITION TOPOI EDITION BERLIN STUDIES OF THE ANCIENT WORLD are the main subject in this collection of papers, o ered in honor of Lis Brack-Bernsen by her colleagues and friends. The topics of the articles are linked by the themes that have been at the center of much of Lis’s own work: the Babylo- nian observational record, and the relationship between observation and theory; the gnomon, sundials, and time measurement; and the relationship between di er- ent scientifi c activities in the ancient world, especially the connections between mathematics and astronomy. Lis Brack-Bernsen has been a key fi gure in transform- ing the study of Babylonian astronomy from an almost exclusive focus on the mathematical astronomy of the late period to embracing a much broader consideration of all aspects of the subject, both early and late, math- ematical and observational, astronomical and astrolog- ical, and their relationships between one another. The papers demonstrate the wide variety of questions asked and approaches used by historians of ancient science. 44 · 44 Studies on the Ancient Exact Sciences in Honor of Lis Brack-Bernsen John M. Steele Mathieu Ossendrijver Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliographie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de. © Edition Topoi / Exzellenzcluster Topoi der Freien Universität Berlin und der Humboldt-Universität zu Berlin Cover image: Sector of TU 11, hand copy of a tablet also known by its museum number AO , reverse side, lines –. -
A Concise History of Mathematics the Beginnings 3
A CONCISE HISTORY OF A CONCISE HISTORY MATHEMATICS STRUIK OF MATHEMATICS DIRK J. STRUIK Professor Mathematics, BELL of Massachussetts Institute of Technology i Professor Struik has achieved the seemingly impossible task of compress- ing the history of mathematics into less than three hundred pages. By stressing the unfolding of a few main ideas and by minimizing references to other develop- ments, the author has been able to fol- low Egyptian, Babylonian, Chinese, Indian, Greek, Arabian, and Western mathematics from the earliest records to the beginning of the present century. He has based his account of nineteenth cen- tury advances on persons and schools rather than on subjects as the treatment by subjects has already been used in existing books. Important mathema- ticians whose work is analysed in detail are Euclid, Archimedes, Diophantos, Hammurabi, Bernoulli, Fermat, Euler, Newton, Leibniz, Laplace, Lagrange, Gauss, Jacobi, Riemann, Cremona, Betti, and others. Among the 47 illustra- tions arc portraits of many of these great figures. Each chapter is followed by a select bibliography. CHARLES WILSON A CONCISE HISTORY OF MATHEMATICS by DIRK. J. STRUIK Professor of Mathematics at the Massachusetts Institute of Technology LONDON G. BELL AND SONS LTD '954 Copyright by Dover Publications, Inc., U.S.A. FOR RUTH Printed in Great Britain by Butler & Tanner Ltd., Frame and London CONTENTS Introduction xi The Beginnings 1 The Ancient Orient 13 Greece 39 The Orient after the Decline of Greek Society 83 The Beginnings in Western Europe 98 The