Chapter 1: Introduction
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Greeks Doing Algebra
Greeks Doing Algebra There is a long-standing consensus in the history of mathematics that geometry came from ancient Greece, algebra came from medieval Persia, and the two sciences did not meet until seventeenth-century France (e.g. Bell 1945). Scholars agree that the Greek mathematicians had no methods comparable to algebra before Diophantus (3rd c. CE) or, many hold, even after him (e.g. Szabó 1969, Unguru and Rowe 1981, Grattan-Guinness 1996, Vitrac 2005. For a survey of arguments see Blåsjö 2016). The problems that we would solve with algebra, the Greeks, especially the authors of the canonical and most often studied works (such as Euclid and Apollonius of Perga), approached with spatial geometry or not at all. This paper argues, however, that the methods which uniquely characterize algebra, such as information compression, quantitative abstraction, and the use of unknowns, do in fact feature in Greek mathematical works prior to Diophantus. We simply have to look beyond the looming figures of Hellenistic geometry. In this paper, we shall examine three instructive cases of algebraic problem-solving methods in Greek mathematical works before Diophantus: The Sand-reckoner of Archimedes, the Metrica of Hero of Alexandria, and the Almagest of Ptolemy. In the Sand-reckoner, Archimedes develops a system for expressing extremely large numbers, in which the base unit is a myriad myriad. His process is indefinitely repeatable, and theoretically scalable to express a number of any size. Simple though it sounds to us, this bit of information compression, by which a cumbersome quantity is set to one in order to simplify notation and computation, is a common feature of modern mathematics but was almost alien to the Greeks. -
Great Inventors of the Ancient World Preliminary Syllabus & Course Outline
CLA 46 Dr. Patrick Hunt Spring Quarter 2014 Stanford Continuing Studies http://www.patrickhunt.net Great Inventors Of the Ancient World Preliminary Syllabus & Course Outline A Note from the Instructor: Homo faber is a Latin description of humans as makers. Human technology has been a long process of adapting to circumstances with ingenuity, and while there has been gradual progress, sometimes technology takes a downturn when literacy and numeracy are lost over time or when humans forget how to maintain or make things work due to cataclysmic change. Reconstructing ancient technology is at times a reminder that progress is not always guaranteed, as when Classical civilization crumbled in the West, but the history of technology is a fascinating one. Global revolutions in technology occur in cycles, often when necessity pushes great minds to innovate or adapt existing tools, as happened when humans first started using stone tools and gradually improved them, often incrementally, over tens of thousands of years. In this third course examining the greats of the ancient world, we take a close look at inventions and their inventors (some of whom might be more legendary than actually known), such as vizier Imhotep of early dynastic Egypt, who is said to have built the first pyramid, and King Gudea of Lagash, who is credited with developing the Mesopotamian irrigation canals. Other somewhat better-known figures are Glaucus of Chios, a metallurgist sculptor who possibly invented welding; pioneering astronomer Aristarchus of Samos; engineering genius Archimedes of Siracusa; Hipparchus of Rhodes, who made celestial globes depicting the stars; Ctesibius of Alexandria, who invented hydraulic water organs; and Hero of Alexandria, who made steam engines. -
A Centennial Celebration of Two Great Scholars: Heiberg's
A Centennial Celebration of Two Great Scholars: Heiberg’s Translation of the Lost Palimpsest of Archimedes—1907 Heath’s Publication on Euclid’s Elements—1908 Shirley B. Gray he 1998 auction of the “lost” palimp- tains four illuminated sest of Archimedes, followed by col- plates, presumably of laborative work centered at the Walters Matthew, Mark, Luke, Art Museum, the palimpsest’s newest and John. caretaker, remind Notices readers of Heiberg was emi- Tthe herculean contributions of two great classical nently qualified for scholars. Working one century ago, Johan Ludvig support from a foun- Heiberg and Sir Thomas Little Heath were busily dation. His stature as a engaged in virtually “running the table” of great scholar in the interna- mathematics bequeathed from antiquity. Only tional community was World War I and a depleted supply of manuscripts such that the University forced them to take a break. In 2008 we as math- of Oxford had awarded ematicians should honor their watershed efforts to him an honorary doc- make the cornerstones of our discipline available Johan Ludvig Heiberg. torate of literature in Photo courtesy of to even mathematically challenged readers. The Danish Royal Society. 1904. His background in languages and his pub- Heiberg lications were impressive. His first language was In 1906 the Carlsberg Foundation awarded 300 Danish but he frequently published in German. kroner to Johan Ludvig Heiberg (1854–1928), a He had publications in Latin as well as Arabic. But classical philologist at the University of Copenha- his true passion was classical Greek. In his first gen, to journey to Constantinople (present day Is- position as a schoolmaster and principal, Heiberg tanbul) to investigate a palimpsest that previously insisted that his students learn Greek and Greek had been in the library of the Metochion, i.e., the mathematics—in Greek. -
Lycophron: a Minor Sophist Or a Minor Socratic?
Lycophron: a Minor Sophist or a Minor Socratic? Stefania Giombini University of Girona Keywords: Lycophron, Minor Sophists, Minor Socratics, Ancient Social Contract Foreword Gregory Vlastos (1907-1991)1 was one of the greatest innovators in the studies of ancient philosophy, a scholar capable of changing methods and attitudes, a model of reference around the world for scholars who have taken his style and approach. In 2014 I have been able to frequent the Harry Ransom Center of the University of Texas at Austin -HRC-2 to study Vlastos’ work and personal materials in The Vlastos Archive. The archive is a variegated and pluri-thematic fund: firstly, I focused on Vlastos’ correspondence (especially the one with Italian scholars). This way, I could suddenly ascertain how the size of Vlastos as a researcher and human being was thick: he interacted with energy and interest with every interlocutor, and those closer to him and those unknown, meticulously preserving even small fragments with names, letters and so on, to avoid losing data and keep memory of everything. Subsequently, extending our investigation to the rest of the archive, an immense amount of notes, books with references, glosses and underlines. While reading the notes I ran across some pages, typewritten, dedicated to the contract theory in Glaucon, Protagoras, Antiphon (obviously including the positions of Plato and Socrates.)3 The pages are not dated, and they get into the themes of social contract and justice. Reading these notes he made me rediscover a minor author of Ancient Philosophy: Lycophron. The following work is born on the interest generated by these readings, from an approach towards the private world of Gregory Vlastos. -
Citations in Classics and Ancient History
Citations in Classics and Ancient History The most common style in use in the field of Classical Studies is the author-date style, also known as Chicago 2, but MLA is also quite common and perfectly acceptable. Quick guides for each of MLA and Chicago 2 are readily available as PDF downloads. The Chicago Manual of Style Online offers a guide on their web-page: http://www.chicagomanualofstyle.org/tools_citationguide.html The Modern Language Association (MLA) does not, but many educational institutions post an MLA guide for free access. While a specific citation style should be followed carefully, none take into account the specific practices of Classical Studies. They are all (Chicago, MLA and others) perfectly suitable for citing most resources, but should not be followed for citing ancient Greek and Latin primary source material, including primary sources in translation. Citing Primary Sources: Every ancient text has its own unique system for locating content by numbers. For example, Homer's Iliad is divided into 24 Books (what we might now call chapters) and the lines of each Book are numbered from line 1. Herodotus' Histories is divided into nine Books and each of these Books is divided into Chapters and each chapter into line numbers. The purpose of such a system is that the Iliad, or any primary source, can be cited in any language and from any publication and always refer to the same passage. That is why we do not cite Herodotus page 66. Page 66 in what publication, in what edition? Very early in your textbook, Apodexis Historia, a passage from Herodotus is reproduced. -
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). -
2 the Assyrian Empire, the Conquest of Israel, and the Colonization of Judah 37 I
ISRAEL AND EMPIRE ii ISRAEL AND EMPIRE A Postcolonial History of Israel and Early Judaism Leo G. Perdue and Warren Carter Edited by Coleman A. Baker LONDON • NEW DELHI • NEW YORK • SYDNEY 1 Bloomsbury T&T Clark An imprint of Bloomsbury Publishing Plc Imprint previously known as T&T Clark 50 Bedford Square 1385 Broadway London New York WC1B 3DP NY 10018 UK USA www.bloomsbury.com Bloomsbury, T&T Clark and the Diana logo are trademarks of Bloomsbury Publishing Plc First published 2015 © Leo G. Perdue, Warren Carter and Coleman A. Baker, 2015 All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage or retrieval system, without prior permission in writing from the publishers. Leo G. Perdue, Warren Carter and Coleman A. Baker have asserted their rights under the Copyright, Designs and Patents Act, 1988, to be identified as Authors of this work. No responsibility for loss caused to any individual or organization acting on or refraining from action as a result of the material in this publication can be accepted by Bloomsbury or the authors. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ISBN: HB: 978-0-56705-409-8 PB: 978-0-56724-328-7 ePDF: 978-0-56728-051-0 Library of Congress Cataloging-in-Publication Data A catalogue record for this book is available from the British Library. Typeset by Forthcoming Publications (www.forthpub.com) 1 Contents Abbreviations vii Preface ix Introduction: Empires, Colonies, and Postcolonial Interpretation 1 I. -
1 ETHNICITY and JEWISH IDENTITY in JOSEPHUS by DAVID
ETHNICITY AND JEWISH IDENTITY IN JOSEPHUS By DAVID McCLISTER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008 1 © 2008 David McClister 2 To the memory of my father, Dorval L. McClister, who instilled in me a love of learning; to the memory of Dr. Phil Roberts, my esteemed colleague; and to my wife, Lisa, without whose support this dissertation, or much else that I do, would not have been possible. 3 ACKNOWLEDGMENTS I gladly recognize my supervisory committee chair (Dr. Konstantinos Kapparis, Associate Professor in the Classics Department at the University of Florida). I also wish to thank the other supervisory commiteee members (Dr. Jennifer Rea, Dr. Gareth Schmeling, and Dr. Gwynn Kessler as a reader from the Religious Studies Department). It is an honor to have their contributions and to work under their guidance. I also wish to thank the library staff at the University of Florida and at Florida College (especially Ashley Barlar) who did their work so well and retrieved the research materials necessary for this project. I also wish to thank my family for their patient indulgence as I have robbed them of time to give attention to the work necessary to pursue my academic interests. BWGRKL [Greek] Postscript® Type 1 and TrueTypeT font Copyright © 1994-2006 BibleWorks, LLC. All rights reserved. These Biblical Greek and Hebrew fonts are used with permission and are from BibleWorks, software for Biblical -
The Purchasing Power of Silver in the Seleucid Empire and Beyond
Academy Colloquium “The efficiency of Markets in Pre-industrial societies: the case of Babylonia (c. 400-60 BC) in comparative perspective” (19 – 21 May 2011) Introduction. The relevance of the Babylonian price data for the study of market integration and market efficiciency. (provisional paper; not to be quoted) Bert van der Spek 0. Prolegomena The purpose of this paper is to introduce the topic of the conference. Because the point of departure is a new corpus of data from Babylonia in the first millennium BC, I shall first present some information on this corpus and on Babylonian economy in general. The paper by Michael Jursa shall provide a deeper insight into the Babylonian economy. For much more detailed information I recommend his magnum opus (2010), which is the result of a great research project in Vienna on the character of the Babylonian economy in the first millennium BC. In an appendix I present some basic historical facts and information on weights and measures, which may be of help for people who are not acquainted with the history of the Near East in Antiquity. My second point of attention will be a short introduction to the points of discussion which I regard as basic for this conference. 1. Introduction The aim of this conference is to include the history of Antiquity into the discussions on market efficiency which has been a major topic of research for the last decades. This topic has gained more attention since the study of economic institutions and structures necessary for economic growth has been brought further and further back in time. -
The Interpretation of the Old Testament in Greco-Roman Paganism
Studien und Texte zu Antike und Christentum Studies and Texts in Antiquity and Christianity Herausgeber/Editor: CHRISTOPH MARKSCHIES (Berlin) Beirat/Advisory Board HUBERT CANCIK (Berlin) • GIOVANNI CASADIO (Salerno) SUSANNA ELM (Berkeley) • JOHANNES HAHN (Münster) JÖRG RÜPKE (Erfurt) 23 John Granger Cook The Interprétation of the Old Testament in Greco-Roman Paganism Mohr Siebeck JOHN GRANGER COOK, born 1955; 1976 B.A. in Philosophy, Davidson College; 1979 M. Div., Union Theological Seminary (VA); 1982-83 Doctoral research at the University of Gottin- gen; 1985 Ph.D. at Emory University; 1985-91 Pastor at Reems Creek Presbyterian Parish in Weaverville, NC/USA; 1991-94 post doctoral studies at Emory University; since 1994 Associate Professor of Religion and Philosophy at LaGrange College, GA/USA. ISBN 3-16-148474-6 ISSN 1436-3003 (Studien und Texte zu Antike und Christentum) Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliographie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de. © 2004 by Mohr Siebeck,Tübingen, Germany. This book may not be reproduced, in whole or in part, in any form (beyond that permitted by copyright law) without the publisher's written permission. This applies particularly to reproductions, translations, microfilms and storage and processing in electronic systems. The book was printed by Guide-Druck in Tübingen on non-aging paper and bound by Buchbinderei Held in Rottenburg. Printed in Germany. For my doctoral fathers, Prof. David Hellholm and the late Prof. William Beardslee, with heartfelt gratitude Table of Contents Introduction 1 0.1 Hecataeus of Abdera (ca 300 B.C.E.) 4 0.2 Manetho (III B.C.E.) 6 0.3 Ocellus Lucanus (II B.C.E.) 8 0.4 Lysimachus 9 0.5 Apollonius Molon (I B.C.E.) 11 0.6 Alexander Polyhistor (ca 105-35 B.C.E.) 13 0.7 Diodorus Siculus (I B.C.E.) 16 0.8 Nicolaus of Damascus 19 0.9 Strabo (ca 64 B.C.E. -
Handbücher Zur Sprach- Und Kommunikations- Wissenschaft
Handbücher zur Sprach- und Kommunikations- wissenschaft Handbooks of Linguistics and Communication Science Manuels de linguistique et des sciences de communication Mitbegründet von Gerold Ungeheuer (†) Mitherausgegeben 1985−2001 von Hugo Steger Herausgegeben von / Edited by / Edite´s par Herbert Ernst Wiegand Band 36 De Gruyter Mouton Brought to you by | Pontificio Istituto Biblico (Pontificio Istituto Biblico ) Authenticated | 172.16.1.226 Download Date | 3/2/12 1:49 PM The Semitic Languages An International Handbook Edited by Stefan Weninger In collaboration with Geoffrey Khan Michael P. Streck Janet C. E. Watson De Gruyter Mouton Brought to you by | Pontificio Istituto Biblico (Pontificio Istituto Biblico ) Authenticated | 172.16.1.226 Download Date | 3/2/12 1:49 PM ISBN 978-3-11-018613-0 e-ISBN 978-3-11-025158-6 ISSN 1861-5090 Library of Congress Cataloging-in-Publication Data Semitic languages : an international handbook / edited by Stefan Weninger ; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C. E.Watson. p. cm. Ϫ (Handbooks of linguistics and communication science; 36) Includes bibliographical references and index. ISBN 978-3-11-018613-0 (hardcover : alk. paper) 1. Semitic languages Ϫ History Ϫ Handbooks, manuals, etc. 2. Semitic languages Ϫ Grammar Ϫ Handbooks, manuals, etc. I. Weninger, Stefan. II. Khan, Geoffrey. III. Streck, Michael P. IV. Watson, Janet C. E. PJ3014.S46 2012 492Ϫdc23 2011042304 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de. © 2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston Typesetting: META Systems GmbH, Wustermark Printing: Hubert & Co. -
Aristotle's Contribution to Scholarly Communication
University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 12-2008 Aristotle’s Contribution to Scholarly Communication Stephen Edward Bales University of Tennessee - Knoxville Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Communication Commons Recommended Citation Bales, Stephen Edward, "Aristotle’s Contribution to Scholarly Communication. " PhD diss., University of Tennessee, 2008. https://trace.tennessee.edu/utk_graddiss/475 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Stephen Edward Bales entitled "Aristotle’s Contribution to Scholarly Communication." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, with a major in Communication and Information. J. Michael Pemberton, Major Professor We have read this dissertation and recommend its acceptance: Suzie Allard, Barbara J. Thayer-Bacon, Dwight Teeter Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) To the Graduate Council: I am submitting herewith a dissertation written by Stephen Edward Bales entitled “Aristotle’s Contribution to Scholarly Communication.” I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, with a major in Communication & Information.