An Encyclopedist of the Dark Ages
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Orosius' Histories: a Digital Intertextual Investigation Into The
comprehensive and detailed manual exploration of all of Orosius’ references. Orosius’ Histories: A Digital “It would be burdensome to list all of the Vergilian Intertextual Investigation echoes [...]” (Coffin, 1936: 237) What Coffin describes as “burdensome” can be into the First Christian accomplished with machine assistance. To the best of History of Rome our knowledge, no existing study, traditional or computational, has quantified and analysed the reuse Greta Franzini habits of Orosius. [email protected] The Tesserae project, which specialises in allusion Georg-August-Universität Göttingen, Germany detection, is the most similar to the research presented here (Coffee, 2013), with the difference that it does not yet contain the text of Orosius nor many of Marco Büchler its sources, and that the results are automatically [email protected] computed without user input. Georg-August-Universität Göttingen, Germany In contrast, our approach, TRACER (Büchler et al., 2017), offers complete control over the algorithmic process, giving the user the choice between being Introduction guided by the software and to intervene by adjusting The research described in these pages is made pos- search parameters. In this way, results are produced sible by openly available Classical texts and linguistic through a critical evaluation of the detection. resources. It aims at performing semi-automatic anal- Research Questions and Goal yses of Paulus Orosius’ (385-420 AD) most celebrated work, the Historia adversum Paganos Libri VII, against Our research began with the following questions: its sources. The Histories, as this work is known in Eng- how does Orosius adapt Classical authors? Can we lish, constitute the first history (752 BC to 417 AD) to categorise his text reuse styles and what is the optimal have been written from a Christian perspective. -
Helden Am Himmel – Helden Im Himmel
Tanja S. Scheer Helden am Himmel – Helden im Himmel Sphärenwechsel zu den Sternen im griechischen Mythos Abstract: The Catasterisms of Pseudo-Eratosthenes and the Astronomia, written by an author named Hyginus are the most important extant sources concerning ancient Greek star-myths. Analysing these texts this paper discusses questions about the reasons and circumstances that lead mythical heroes and heroines to changing the earthly sphere for the heavens in Greek myth. Which conse- quences did these changes inflict on the protagonists concerned? What did it mean to be put among the stars? The texts allowed their audience a wide range of possibilities “to think with”, including divine compassion, gratitude and eternal memory of great deeds as well as presenting warning examples for man- kind on earth. Since when these examples were told, is difficult to assess. The case of the Arkadian heroine Callisto shows how strata of mythical subjects (mythische Stoffe) changed over the centuries. The Homeric Odysseus was told of the ‘Bear’ as an important heavenly constellation, but it seems that it took some centuries before the heroine Callisto reached the sky and this bear finally got a personal name. Authors like Pseudo-Eratosthenes and Hyginus do not express the belief that such a changing of spheres included a happy afterlife or immortal feasting in the presence of the Olympic gods. Nevertheless their read- ers were at liberty to hope for it. 1 Einführung: Himmelsbilder Nachdem Galileo Galilei im Jahr 1610 die Jupitermonde entdeckt hatte, stellten sich die neuzeitlichen Gelehrten in eine lange Tradition – als Fortschreiber des griechischen Mythos. -
Unaccountable Numbers
Unaccountable Numbers Fabio Acerbi In memoriam Alessandro Lami, a tempi migliori HE AIM of this article is to discuss and amend one of the most intriguing loci corrupti of the Greek mathematical T corpus: the definition of the “unknown” in Diophantus’ Arithmetica. To do so, I first expound in detail the peculiar ter- minology that Diophantus employs in his treatise, as well as the notation associated with it (section 1). Sections 2 and 3 present the textual problem and discuss past attempts to deal with it; special attention will be paid to a paraphrase contained in a let- ter of Michael Psellus. The emendation I propose (section 4) is shown to be supported by a crucial, and hitherto unnoticed, piece of manuscript evidence and by the meaning and usage in non-mathematical writings of an adjective that in Greek math- ematical treatises other than the Arithmetica is a sharply-defined technical term: ἄλογος. Section 5 offers some complements on the Diophantine sign for the “unknown.” 1. Denominations, signs, and abbreviations of mathematical objects in the Arithmetica Diophantus’ Arithmetica is a collection of arithmetical prob- lems:1 to find numbers which satisfy the specific constraints that 1 “Arithmetic” is the ancient denomination of our “number theory.” The discipline explaining how to calculate with particular, possibly non-integer, numbers was called in Late Antiquity “logistic”; the first explicit statement of this separation is found in the sixth-century Neoplatonic philosopher and mathematical commentator Eutocius (In sph. cyl. 2.4, in Archimedis opera III 120.28–30 Heiberg): according to him, dividing the unit does not pertain to arithmetic but to logistic. -
15 Famous Greek Mathematicians and Their Contributions 1. Euclid
15 Famous Greek Mathematicians and Their Contributions 1. Euclid He was also known as Euclid of Alexandria and referred as the father of geometry deduced the Euclidean geometry. The name has it all, which in Greek means “renowned, glorious”. He worked his entire life in the field of mathematics and made revolutionary contributions to geometry. 2. Pythagoras The famous ‘Pythagoras theorem’, yes the same one we have struggled through in our childhood during our challenging math classes. This genius achieved in his contributions in mathematics and become the father of the theorem of Pythagoras. Born is Samos, Greece and fled off to Egypt and maybe India. This great mathematician is most prominently known for, what else but, for his Pythagoras theorem. 3. Archimedes Archimedes is yet another great talent from the land of the Greek. He thrived for gaining knowledge in mathematical education and made various contributions. He is best known for antiquity and the invention of compound pulleys and screw pump. 4. Thales of Miletus He was the first individual to whom a mathematical discovery was attributed. He’s best known for his work in calculating the heights of pyramids and the distance of the ships from the shore using geometry. 5. Aristotle Aristotle had a diverse knowledge over various areas including mathematics, geology, physics, metaphysics, biology, medicine and psychology. He was a pupil of Plato therefore it’s not a surprise that he had a vast knowledge and made contributions towards Platonism. Tutored Alexander the Great and established a library which aided in the production of hundreds of books. -
Fiboquadratic Sequences and Extensions of the Cassini Identity Raised from the Study of Rithmomachia
Fiboquadratic sequences and extensions of the Cassini identity raised from the study of rithmomachia Tom´asGuardia∗ Douglas Jim´enezy October 17, 2018 To David Eugene Smith, in memoriam. Mathematics Subject Classification: 01A20, 01A35, 11B39 and 97A20. Keywords: pythagoreanism, golden ratio, Boethius, Nicomachus, De Arithmetica, fiboquadratic sequences, Cassini's identity and rithmomachia. Abstract In this paper, we introduce fiboquadratic sequences as a consequence of an extension to infinity of the board of rithmomachia. Fiboquadratic sequences approach the golden ratio and provide extensions of Cassini's Identity. 1 Introduction Pythagoreanism was a philosophical tradition, that left a deep influence over the Greek mathematical thought. Its path can be traced until the Middle Ages, and even to present. Among medieval scholars, which expanded the practice of the pythagoreanism, we find Anicius Manlius Severinus Boethius (480-524 A.D.) whom by a free translation of De Institutione Arithmetica by Nicomachus of Gerasa, preserved the pythagorean teaching inside the first universities. In fact, Boethius' book became the guide of study for excellence during quadriv- ium teaching, almost for 1000 years. The learning of arithmetic during the arXiv:1509.03177v3 [math.HO] 22 Nov 2016 quadrivium, made necessary the practice of calculation and handling of basic mathematical operations. Surely, with the mixing of leisure with this exercise, Boethius' followers thought up a strategy game in which, besides the training of mind calculation, it was used to preserve pythagorean traditions coming from the Greeks and medieval philosophers. Maybe this was the origin of the philoso- phers' game or rithmomachia. Rithmomachia (RM, henceforward) became the ∗Department of Mathematics. -
Hypatia of Alexandria A. W. Richeson National Mathematics Magazine
Hypatia of Alexandria A. W. Richeson National Mathematics Magazine, Vol. 15, No. 2. (Nov., 1940), pp. 74-82. Stable URL: http://links.jstor.org/sici?sici=1539-5588%28194011%2915%3A2%3C74%3AHOA%3E2.0.CO%3B2-I National Mathematics Magazine is currently published by Mathematical Association of America. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/maa.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact [email protected]. http://www.jstor.org Sun Nov 18 09:31:52 2007 Hgmdnism &,d History of Mdtbenzdtics Edited by G. -
Saturn As the “Sun of Night” in Ancient Near Eastern Tradition ∗
Saturn as the “Sun of Night” in Ancient Near Eastern Tradition ∗ Marinus Anthony van der Sluijs – Seongnam (Korea) Peter James – London [This article tackles two issues in the “proto-astronomical” conception of the planet Saturn, first attested in Mesopotamia and followed by the Greeks and Hindus: the long-standing problem of Saturn’s baffling association with the Sun; and why Saturn was deemed to be “black”. After an extensive consideration of explanations offered from the 5th century to the 21st, as well as some new “thought experiments”, we suggest that Saturn’s connection with the Sun had its roots in the observations that Saturn’s course appears to be the steadiest one among the planets and that its synodic period – of all the planets – most closely resembles the length of the solar year. For the black colour attributed to Saturn we propose a solution which is partly lexical and partly observational (due to atmospheric effects). Finally, some thoughts are offered on the question why in Hellenistic times some considered the “mock sun” Phaethon of Greek myth to have been Saturn]. Keywords: Saturn, planets, Sun, planet colour. 1. INTRODUCTION Since the late 19th century scholars have been puzzled by a conspicuous peculiarity in the Babylonian nomenclature for the planet Saturn: a number of texts refer to Saturn as the “Sun” ( dutu/20 or Šamaš ), instead of its usual astronomical names Kayam ānu and mul UDU.IDIM. 1 This curious practice was in vogue during the period c. 750-612 BC 2 and is not known from earlier periods, with a single possible exception, discussed below. -
Martyred for the Church
Wissenschaftliche Untersuchungen zum Neuen Testament · 2. Reihe Herausgeber / Editor Jörg Frey (Zürich) Mitherausgeber/Associate Editors Markus Bockmuehl (Oxford) · James A. Kelhoffer (Uppsala) Tobias Nicklas (Regensburg) · J. Ross Wagner (Durham, NC) 471 Justin Buol Martyred for the Church Memorializations of the Effective Deaths of Bishop Martyrs in the Second Century CE Mohr Siebeck Justin Buol, born 1983; 2005 BA in Biblical and Theological Studies, Bethel University; 2007 MA in New Testament, Trinity Evangelical Divinity School; 2009 MA in Classical and Near Eastern Studies, University of Minnesota; 2017 PhD in Christianity and Judaism in Antiquity, University of Notre Dame; currently an adjunct professor at Bethel University. ISBN 978-3-16-156389-8 / eISBN 978-3-16-156390-4 DOI 10.1628/978-3-16-156390-4 ISSN 0340-9570 / eISSN 2568-7484 (Wissenschaftliche Untersuchungen zum Neuen Testament, 2. Reihe) The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliographie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2018 Mohr Siebeck Tübingen, Germany. www.mohrsiebeck.com 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 repro- ductions, translations and storage and processing in electronic systems. The book was printed by Laupp & Göbel in Gomaringen on non-aging paper and bound by Buchbinderei Nädele in Nehren. Printed in Germany. Preface This monograph represents a revised version of my doctoral dissertation. It has been updated to take into account additional scholarly literature, bring in new argumentation, and shorten some sections for relevance. -
Adversus Paganos: Disaster, Dragons, and Episcopal Authority in Gregory of Tours
Adversus paganos: Disaster, Dragons, and Episcopal Authority in Gregory of Tours David J. Patterson Comitatus: A Journal of Medieval and Renaissance Studies, Volume 44, 2013, pp. 1-28 (Article) Published by Center for Medieval and Renaissance Studies, UCLA DOI: 10.1353/cjm.2013.0000 For additional information about this article http://muse.jhu.edu/journals/cjm/summary/v044/44.patterson.html Access provided by University of British Columbia Library (29 Aug 2013 02:49 GMT) ADVERSUS PAGANOS: DISASTER, DRAGONS, AND EPISCOPAL AUTHORITY IN GREGORY OF TOURS David J. Patterson* Abstract: In 589 a great flood of the Tiber sent a torrent of water rushing through Rome. According to Gregory of Tours, the floodwaters carried some remarkable detritus: several dying serpents and, perhaps most strikingly, the corpse of a dragon. The flooding was soon followed by plague and the death of a pope. This remarkable chain of events leaves us with puzzling questions: What significance would Gregory have located in such a narrative? For a modern reader, the account (apart from its dragon) reads like a descrip- tion of a natural disaster. Yet how did people in the early Middle Ages themselves per- ceive such events? This article argues that, in making sense of the disasters at Rome in 589, Gregory revealed something of his historical consciousness: drawing on both bibli- cal imagery and pagan historiography, Gregory struggled to identify appropriate objects of both blame and succor in the wake of calamity. Keywords: plague, natural disaster, Gregory of Tours, Gregory the Great, Asclepius, pagan survivals, dragon, serpent, sixth century, Rome. In 589, a great flood of the Tiber River sent a torrent of water rushing through the city of Rome. -
The Poetics of Science: Intertextual and Metatextual Themes in Ovid's Depiction of Cosmic and Human Origins
Provided by the author(s) and NUI Galway in accordance with publisher policies. Please cite the published version when available. Title The poetics of science: intertextual and metatextual themes in Ovid's depiction of cosmic and human origins Author(s) Kelly, Peter Publication Date 2016-09-09 Item record http://hdl.handle.net/10379/6075 Downloaded 2021-09-28T20:42:11Z Some rights reserved. For more information, please see the item record link above. The Poetics of Science Intertextual and Metatextual Themes in Ovid’s Depiction of Cosmic and Human Origins By Peter M. J. Kelly A Thesis Submitted to the National University of Ireland, Galway in the College of Arts, Social Sciences and Celtic Studies for the degree of Doctor of Philosophy in Classics September 2016 Supervisor: Prof. Michael Clarke ii Preface This work explores ancient views of cosmogony and the material structure of the universe in Ovid’s Metamorphoses. In particular it focuses on the way in which Ovid problematizes how we define myth and poetry versus science and philosophy. It examines how Ovid generates a parallel between the form and content of the text in order to depict a world where abstract scientific principles can become personified deities. This work will seek to reevaluate the impact of Greek Philosophy on Roman poetry through extending the series of intertexts which we may observe Ovid alluding to. Through following and analysing these sets of allusions this work will seek to gain an insight into Ovid’s depiction of the metatextual universe. iii iv For my Parents The scientist’s demand that nature shall be lawful is a demand for unity. -
The Fathers of the Church ; V
THE FATHERS OF THE CHURCH A NEW TRANSLATION VOLUME 99 THE FATHERS OF THE CHURCH A NEW TRANSLATION EDITORIAL BOARD Thomas P. Halton The Catholic University of America Editorial Director Elizabeth Clark Robert D. Sider Duke University Dickinson College Joseph T. Lienhard, S.J. Michael Slusser Fordham University Duquesne University Frank A.C. Mantello Cynthia White The Catholic University of America The University of Arizona Kathleen McVey Robin Darling Young Princeton Theological Seminary The Catholic University of America David J. McGonagle Director The Catholic University of America Press FORMER EDITORIAL DIRECTORS Ludwig Schopp, Roy J. Deferrari, Bernard M. Peebles, Hermigild Dressler, O.F.M. Cornelia Horn Staff Editor IBERIAN FATHERS volume 3 PACIAN OF BARCELONA OROSIUS OF BRAGA Translated by CRAIG L. HANSON Muskingum College New Concord, Ohio THE CATHOLIC UNIVERSITY OF AMERICA PRESS Washington, D.C. Copyright © 1999 THE CATHOLIC UNIVERSITY OF AMERICA PRESS All rights reserved Printed in the United States of America The paper used in this publication meets the minimum requirements of the American National Standards for Information Science— Permanence of Paper for Printed Library Materials, ansi z39.48–1984. ∞ library of congress cataloging-in-publication data Iberian fathers : Pacian of Barcelona and Orosius of Braga : [writings] / translated by Craig L. Hanson. p. cm. — (The fathers of the church ; v. 99) Includes bibliographical references and Indexes. ISBN 0-8132- 0099-7 (alk. paper) 1. Theology—Early works to 1800. 2. Apologetics—Early -
Did Hypatia Know About Negative Numbers?
Did Hypatia Know about Negative Numbers? Hypatia lived in Alexandria in the 4th-5th century AD. She was one of the most remarkable women in history. Her father Theon, presumably the last member of the Museum, instructed her in mathematics, philosophy and clas- sical Greek literature. With time she herself became a brilliant teacher of Neoplatonic philosophy and mathematics. Numerous young aspirants from wealthy Christian and pagan families came to Alexandria with the sole pur- pose of joining the sophisticated inner circle of her students. Theon and Hyptia edited several of the major mathematical treatises avail- able in their time: Arithmetica by Diophantus, Almagest by Ptolemy, Conics by Appolonius of Perga, and Elements by Euclid. A significant part of this work, in particular on the most difficult and demanding Arithmetica, she did alone. To some of these treatises she added commentaries and exemplary exercises. A charismatic figure in the city’s intellectual life and a close friend to many important officials, Hypatia had a significant influence on the Alexandrian elite and politics. She was admired for her knowledge, wisdom, righteousness and personal charm. Her public lectures for the Alexandrian intelligentsia attracted a great deal of interest. However, her elevated social position and popularity did not prevent her from becoming the victim of a brutal murder in 415 AD by the fanatic mob who accused her of conducting forbidden magical practices. Groundless rumors about Hypatia’s dealings with witchcraft were most likely inspired by her political enemies. Bishop Cyril was certainly one of them, but the allegations concerning his direct involvement have never been proven.