Alexander Raymond Jones Publications. Books and Monographs
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General Disclaimer One Or More of the Following Statements May Affect
https://ntrs.nasa.gov/search.jsp?R=19710025504 2020-03-11T22:36:49+00:00Z View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by NASA Technical Reports Server General Disclaimer One or more of the Following Statements may affect this Document This document has been reproduced from the best copy furnished by the organizational source. It is being released in the interest of making available as much information as possible. This document may contain data, which exceeds the sheet parameters. It was furnished in this condition by the organizational source and is the best copy available. This document may contain tone-on-tone or color graphs, charts and/or pictures, which have been reproduced in black and white. This document is paginated as submitted by the original source. Portions of this document are not fully legible due to the historical nature of some of the material. However, it is the best reproduction available from the original submission. Produced by the NASA Center for Aerospace Information (CASI) 6 X t B ICC"m date: July 16, 1971 955 L'Enfant Plaza North, S. W Washington, D. C. 20024 to Distribution B71 07023 from. J. W. Head suhiecf Derivation of Topographic Feature Names in the Apollo 15 Landing Region - Case 340 ABSTRACT The topographic features in the region of the Apollo 15 landing site (Figure 1) are named for a number of philosophers, explorers and scientists (astronomers in particular) representing periods throughout recorded history. It is of particular interest that several of the individuals were responsible for specific discoveries, observations, or inventions which considerably advanced the study and under- standing of the moon (for instance, Hadley designed the first large reflecting telescope; Beer published classic maps and explanations of the moon's surface). -
A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Scholarship@Claremont Journal of Humanistic Mathematics Volume 7 | Issue 2 July 2017 A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time John B. Little College of the Holy Cross Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the Ancient History, Greek and Roman through Late Antiquity Commons, and the Mathematics Commons Recommended Citation Little, J. B. "A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time," Journal of Humanistic Mathematics, Volume 7 Issue 2 (July 2017), pages 269-293. DOI: 10.5642/ jhummath.201702.13 . Available at: https://scholarship.claremont.edu/jhm/vol7/iss2/13 ©2017 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time Cover Page Footnote This essay originated as an assignment for Professor Thomas Martin's Plutarch seminar at Holy Cross in Fall 2016. -
A Short History of Greek Mathematics
Cambridge Library Co ll e C t i o n Books of enduring scholarly value Classics From the Renaissance to the nineteenth century, Latin and Greek were compulsory subjects in almost all European universities, and most early modern scholars published their research and conducted international correspondence in Latin. Latin had continued in use in Western Europe long after the fall of the Roman empire as the lingua franca of the educated classes and of law, diplomacy, religion and university teaching. The flight of Greek scholars to the West after the fall of Constantinople in 1453 gave impetus to the study of ancient Greek literature and the Greek New Testament. Eventually, just as nineteenth-century reforms of university curricula were beginning to erode this ascendancy, developments in textual criticism and linguistic analysis, and new ways of studying ancient societies, especially archaeology, led to renewed enthusiasm for the Classics. This collection offers works of criticism, interpretation and synthesis by the outstanding scholars of the nineteenth century. A Short History of Greek Mathematics James Gow’s Short History of Greek Mathematics (1884) provided the first full account of the subject available in English, and it today remains a clear and thorough guide to early arithmetic and geometry. Beginning with the origins of the numerical system and proceeding through the theorems of Pythagoras, Euclid, Archimedes and many others, the Short History offers in-depth analysis and useful translations of individual texts as well as a broad historical overview of the development of mathematics. Parts I and II concern Greek arithmetic, including the origin of alphabetic numerals and the nomenclature for operations; Part III constitutes a complete history of Greek geometry, from its earliest precursors in Egypt and Babylon through to the innovations of the Ionic, Sophistic, and Academic schools and their followers. -
Alexandria in Egypt, the Native Town of the Natural Sciences
Alexandria in Egypt, the Native Town of the Natural Sciences Dieter LELGEMANN, Germany (dedicated to B.L. van der Waerden) Key words: Alexandrians, Aristarchos, Archimedes, Eratosthenes, Apollonios, Ptolemy, heliocentric hypothesis, epicycle and mobile eccentric, distance earth/sun, Equant and Keplerian motion SUMMARY Looking at Alexandria as the native town of natural sciences the most interesting question will be: What happened to the heliocentric idea of Aristarchos of Samos? Has the group of the famous Alexandrian scientists, Aristarchos of Samos, Archimedes of Syracuse, Eratosthenes of Kyrene and Apollonius of Perge, be able to develop this idea further to a complete methodology of celestial mechanics? Did they at least have had the mathematical tools at hand? Did some Greeks use the heliocentric concept? The paper will give a possible answer to those questions: It was not only possible for them, it is also likely that they did it and that this methodology was used by all “other astronomers” at the time of Hipparch. WSHS 1 – History of Technology 1/15 Dieter Lelgemann WSHS1.3 Alexandria in Egypt, the Native Town of the Natural Sciences From Pharaohs to Geoinformatics FIG Working Week 2005 and GSDI-8 Cairo, Egypt April 16-21, 2005 Alexandria in Egypt, the Native Town of the Natural Sciences Dieter LELGEMANN, Germany (dedicated to B.L. van der Waerden) 1. INTRODUCTION Natural sciences in the modern sense started in Alexandria in the third century b.c. with the foundation of the Museion by king Ptolemy I and probably by the first “experimental physicist” Straton of Lampsakos (330-270/68 b.c.), later elected as third leader (after Aristoteles and Theophrastus) of the Lyceum, the philosophical school founded by Aristoteles. -
Boethius the Demiurge
BOETHIUS THE DEMIURGE: TIMAEAN DOUBLE-CIRCLE SPIRAL STRUCTURE IN THE CONSOLATIO by Cristalle N. Watson Submitted in partial fulfilment of the requirements for the degree of Master of Arts at Dalhousie University Halifax, Nova Scotia April 2020 © Copyright by Cristalle N. Watson, 2020 For my Opa, Karl Heinz Hiob 1926-1999 Vir doctissimus & lover of words, who first introduced me to Latin Ars longa, vita brevis ii TABLE OF CONTENTS LIST OF TABLES..............................................................................................................vi LIST OF FIGURES...........................................................................................................vii ABSTRACT.....................................................................................................................viii ACKNOWLEDGEMENTS................................................................................................ix CHAPTER 1: INTRODUCTION........................................................................................1 CHAPTER 2: POETRY AND THE CIRCLE IN THE CONSOLATIO: AN OVERVIEW….............................................................................................................3 2.1 A "MULTIFACETED" CONSOLATIO AND AUTHOR.............................................3 2.2 THE METERS OF THE CONSOLATIO: A NEGLECTED STUDY............................11 2.3 IIIM9: CENTRAL PIVOT, TIMAEAN PARAPHRASE, PRAYER...........................17 2.4 THE CIRCLE IN THE CONSOLATIO AND IN IIIM9.............................................22 -
Aristarchus of Samos and Graeco-Babylonian Astronomy George Huxley
Arfstarchus of Samos and Graeco-Babylonian Astronomy Huxley, George Greek, Roman and Byzantine Studies; Summer 1964; 5, 2; ProQuest pg. 123 Aristarchus of Samos and Graeco-Babylonian Astronomy George Huxley N THE HALF CENTURY following the death of Alexander the Great the I history of astronomy amongst the Greeks is dominated by Aris tarchus the Samian, who is best known for his theory of the earth's revolution about the sun. His life cannot be dated exactly, but it is clear that he was already of mature age by 280 B.C., for Ptolemy states that "the men around Aristarchus," that is to say his pupils, observed the summer solstice in that year, the 50th of the first Callippic period [Ptolemy, Almagest 3.1]. He was a pupil of Strato the Lampsacene, who succeeded Theophrastus as head of the Lyceum in ca. 288/7 B.C. [Apollodorus 244 F 40] and remained in that post for eighteen years till his death not later than 269 B.C. [Apollodorus 244 F 350]. The date of the publication of Aristarchus's heliocentric theory is not known, but the doctrine was attacked by Cleanthes the Stoic land so must have been well known by 232 B.C., when Cleanthes died; but the helio centric hypothesis may have been formulated much earlier than that. Vitruvius spoke highly of the versatility of Aristarchus in geometry, astronomy, and music [De Architectura 1.1.16], and ascribes to him the invention of two kinds of sundial-the hemispherical uKac/>T} and the disc in the plane [9.8.1].2 He perhaps made use of these improved instruments in his observations of the solstices. -
5. Hipparchus 6. Ptolemy
introduction | 15 catalogue included into his oeuvre? Our answer is in Hipparchus. The catalogue itself has not survived. the positive. We have developed a method to serve However, it is believed that the ecliptic longitude and this end, tested it on several veraciously dated cata- latitude of each star was indicated there, as well as the logues, and then applied it to the Almagest. The reader magnitude. It is believed that Hipparchus localised the shall find out about our results in the present book. stars using the same terms as the Almagest: “the star Let us now cite some brief biographical data con- on the right shoulder of Perseus”,“the star over the cerning the astronomers whose activities are imme- head of Aquarius” etc ([395], page 52). diately associated with the problem as described above. One invariably ponders the extreme vagueness of These data are published in Scaligerian textbooks. One this star localization method. Not only does it imply must treat them critically, seeing as how the Scaligerian a canonical system of drawing the constellations and version of history is based on an erroneous chronol- indicating the stars they include – another stipulation ogy (see Chron1 and Chron2). We shall consider is that there are enough identical copies of a single star other facts that confirm it in the present book. chart in existence. This is the only way to make the verbal descriptions of stars such as the above work 5. and help a researcher with the actual identification of HIPPARCHUS stars. However, in this case the epoch of the cata- logue’s propagation must postdate the invention of Scaligerian history is of the opinion that astron- the printing press and the engraving technique, since omy became a natural science owing to the works of no multiple identical copies of a single work could be Hipparchus, an astronomer from the “ancient” Greece manufactured earlier. -
The Project Gutenberg Ebook #31061: a History of Mathematics
The Project Gutenberg EBook of A History of Mathematics, by Florian Cajori This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: A History of Mathematics Author: Florian Cajori Release Date: January 24, 2010 [EBook #31061] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK A HISTORY OF MATHEMATICS *** Produced by Andrew D. Hwang, Peter Vachuska, Carl Hudkins and the Online Distributed Proofreading Team at http://www.pgdp.net transcriber's note Figures may have been moved with respect to the surrounding text. Minor typographical corrections and presentational changes have been made without comment. This PDF file is formatted for screen viewing, but may be easily formatted for printing. Please consult the preamble of the LATEX source file for instructions. A HISTORY OF MATHEMATICS A HISTORY OF MATHEMATICS BY FLORIAN CAJORI, Ph.D. Formerly Professor of Applied Mathematics in the Tulane University of Louisiana; now Professor of Physics in Colorado College \I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history."|J. W. L. Glaisher New York THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., Ltd. 1909 All rights reserved Copyright, 1893, By MACMILLAN AND CO. Set up and electrotyped January, 1894. Reprinted March, 1895; October, 1897; November, 1901; January, 1906; July, 1909. Norwood Pre&: J. S. Cushing & Co.|Berwick & Smith. -
The Ears of Hermes
The Ears of Hermes The Ears of Hermes Communication, Images, and Identity in the Classical World Maurizio Bettini Translated by William Michael Short THE OHIO STATE UNIVERSITY PRess • COLUMBUS Copyright © 2000 Giulio Einaudi editore S.p.A. All rights reserved. English translation published 2011 by The Ohio State University Press. Library of Congress Cataloging-in-Publication Data Bettini, Maurizio. [Le orecchie di Hermes. English.] The ears of Hermes : communication, images, and identity in the classical world / Maurizio Bettini ; translated by William Michael Short. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-8142-1170-0 (cloth : alk. paper) ISBN-10: 0-8142-1170-4 (cloth : alk. paper) ISBN-13: 978-0-8142-9271-6 (cd-rom) 1. Classical literature—History and criticism. 2. Literature and anthropology—Greece. 3. Literature and anthropology—Rome. 4. Hermes (Greek deity) in literature. I. Short, William Michael, 1977– II. Title. PA3009.B4813 2011 937—dc23 2011015908 This book is available in the following editions: Cloth (ISBN 978-0-8142-1170-0) CD-ROM (ISBN 978-0-8142-9271-6) Cover design by AuthorSupport.com Text design by Juliet Williams Type set in Adobe Garamond Pro Printed by Thomson-Shore, Inc. The paper used in this publication meets the minimum requirements of the American Na- tional Standard for Information Sciences—Permanence of Paper for Printed Library Materials. ANSI Z39.48–1992. 9 8 7 6 5 4 3 2 1 CONTENTS Translator’s Preface vii Author’s Preface and Acknowledgments xi Part 1. Mythology Chapter 1 Hermes’ Ears: Places and Symbols of Communication in Ancient Culture 3 Chapter 2 Brutus the Fool 40 Part 2. -
Cellini's Perseus and Medusa: Configurations of the Body
CELLINI’S PERSEUS AND MEDUSA: CONFIGURATIONS OF THE BODY OF STATE by CHRISTINE CORRETTI Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Dissertation Advisor: Professor Edward J. Olszewski Department of Art History CASE WESTERN RESERVE UNIVERSITY January, 2011 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the dissertation of Christine Corretti candidate for the Doctor of Philosophy degree.* (signed) Professor Edward J. Olszewski (chair of the committee) Professor Anne Helmreich Professor Holly Witchey Dr. Jon S. Seydl (date) November, 2010 *We also certify that written approval has been obtained for any proprietary material contained therein. 1 Copyright © 2011 by Christine Corretti All rights reserved 2 Table of Contents List of Illustrations 4 Abstract 9 Introduction 11 Chapter 1 The Story of Perseus and Medusa, an Interpretation 28 of its Meaning, and the Topos of Decapitation Chapter 2 Cellini’s Perseus and Medusa: the Paradigm of Control 56 Chapter 3 Renaissance Political Theory and Paradoxes of 100 Power Chapter 4 The Goddess as Other and Same 149 Chapter 5 The Sexual Symbolism of the Perseus and Medusa 164 Chapter 6 The Public Face of Justice 173 Chapter 7 Classical and Grotesque Polities 201 Chapter 8 Eleonora di Toledo and the Image of the Mother 217 Goddess Conclusion 239 Illustrations 243 Bibliography 304 3 List of Illustrations Fig. 1 Benvenuto Cellini, Perseus and Medusa, 1545-1555, 243 Loggia dei Lanzi, Florence, Italy. Fig. 2 Donatello, Judith and Holofernes, c. 1446-1460s, Palazzo 244 Vecchio, Florence, Italy. Fig. 3 Heracles killing an Amazon, red figure vase. -
Mathematics and Its History, Third Edition
Undergraduate Texts in Mathematics Editorial Board S. Axler K.A. Ribet For other titles published in this series, go to http://www.springer.com/series/666 John Stillwell Mathematics and Its History Third Edition 123 John Stillwell Department of Mathematics University of San Francisco San Francisco, CA 94117-1080 USA [email protected] Editorial Board S. Axler K.A. Ribet Mathematics Department Mathematics Department San Francisco State University University of California at Berkeley San Francisco, CA 94132 Berkeley, CA 94720-3840 USA USA [email protected] [email protected] ISSN 0172-6056 ISBN 978-1-4419-6052-8 e-ISBN 978-1-4419-6053-5 DOI 10.1007/978-1-4419-6053-5 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010931243 Mathematics Subject Classification (2010): 01-xx, 01Axx c Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer soft- ware, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) To Elaine, Michael, and Robert Preface to the Third Edition The aim of this book, announced in the first edition, is to give a bird’s- eye view of undergraduate mathematics and a glimpse of wider horizons. -
Hipparchus's Table of Chords
ApPENDIX 1 Hipparchus's Table of Chords The construction of this table is based on the facts that the chords of 60° and 90° are known, that starting from chd 8 we can calculate chd(180° - 8) as shown by Figure Al.1, and that from chd S we can calculate chd ~8. The calculation of chd is goes as follows; see Figure Al.2. Let the angle AOB be 8. Place F so that CF = CB, place D so that DOA = i8, and place E so that DE is perpendicular to AC. Then ACD = iAOD = iBOD = DCB making the triangles BCD and DCF congruent. Therefore DF = BD = DA, and so EA = iAF. But CF = CB = chd(180° - 8), so we can calculate CF, which gives us AF and EA. Triangles AED and ADC are similar; therefore ADIAE = ACIDA, which implies that AD2 = AE·AC and enables us to calculate AD. AD is chd i8. We can now find the chords of 30°, 15°, 7~0, 45°, and 22~0. This gives us the chords of 150°, 165°, etc., and eventually we have the chords of all R P chord 8 = PQ, C chord (180 - 8) = QR, QR2 = PR2 _ PQ2. FIGURE A1.l. 235 236 Appendix 1. Hipparchus's Table of Chords Ci"=:...-----""----...........~A FIGURE A1.2. multiples of 71°. The table starts: 2210 10 8 2 30° 45° 522 chd 8 1,341 1,779 2,631 3,041 We find the chords of angles not listed and angles whose chords are not listed by linear interpolation. For example, the angle whose chord is 2,852 is ( 2,852 - 2,631 1)0 .