Plutarch's "De E Apud Delphos": Translation and Commentary
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9N1.5 Determine the Square Root of Positive Rational Numbers That Are Perfect Squares
9N1.5 Determine the square root of positive rational numbers that are perfect squares. Square Roots and Perfect Squares The square root of a given number is a value that when multiplied by itself results in the given number. For example, the square root of 9 is 3 because 3 × 3 = 9 . Example Use a diagram to determine the square root of 121. Solution Step 1 Draw a square with an area of 121 units. Step 2 Count the number of units along one side of the square. √121 = 11 units √121 = 11 units The square root of 121 is 11. This can also be written as √121 = 11. A number that has a whole number as its square root is called a perfect square. Perfect squares have the unique characteristic of having an odd number of factors. Example Given the numbers 81, 24, 102, 144, identify the perfect squares by ordering their factors from smallest to largest. Solution The square root of each perfect square is bolded. Factors of 81: 1, 3, 9, 27, 81 Since there are an odd number of factors, 81 is a perfect square. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Since there are an even number of factors, 24 is not a perfect square. Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102 Since there are an even number of factors, 102 is not a perfect square. Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 Since there are an odd number of factors, 144 is a perfect square. -
TOWARD a POETICS of NEW MEDIA By
'A Kind of Thing That Might Be': Toward A Poetics of New Media Item Type text; Electronic Dissertation Authors Thompson, Jason Craig Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 28/09/2021 20:28:02 Link to Item http://hdl.handle.net/10150/194959 ‘A KIND OF THING THAT MIGHT BE’: TOWARD A POETICS OF NEW MEDIA by Jason Thompson _____________________ Copyright © Jason Thompson 2008 A Dissertation Submitted to the Faculty of the DEPARTMENT OF ENGLISH In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY WITH A MAJOR IN RHETORIC, COMPOSITION, AND THE TEACHING OF ENGLISH In the Graduate College THE UNIVERSITY OF ARIZONA 2008 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dissertation prepared by Jason Thompson entitled A Kind of Thing that Might Be: Toward a Rhetoric of New Media and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy. ______________________________________________________________________ Date: 07/07/2008 Ken McAllister _______________________________________________________________________ Date: 07/07/2008 Theresa Enos _______________________________________________________________________ Date: 07/07/2008 John Warnock Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. -
Marathon 2,500 Years Edited by Christopher Carey & Michael Edwards
MARATHON 2,500 YEARS EDITED BY CHRISTOPHER CAREY & MICHAEL EDWARDS INSTITUTE OF CLASSICAL STUDIES SCHOOL OF ADVANCED STUDY UNIVERSITY OF LONDON MARATHON – 2,500 YEARS BULLETIN OF THE INSTITUTE OF CLASSICAL STUDIES SUPPLEMENT 124 DIRECTOR & GENERAL EDITOR: JOHN NORTH DIRECTOR OF PUBLICATIONS: RICHARD SIMPSON MARATHON – 2,500 YEARS PROCEEDINGS OF THE MARATHON CONFERENCE 2010 EDITED BY CHRISTOPHER CAREY & MICHAEL EDWARDS INSTITUTE OF CLASSICAL STUDIES SCHOOL OF ADVANCED STUDY UNIVERSITY OF LONDON 2013 The cover image shows Persian warriors at Ishtar Gate, from before the fourth century BC. Pergamon Museum/Vorderasiatisches Museum, Berlin. Photo Mohammed Shamma (2003). Used under CC‐BY terms. All rights reserved. This PDF edition published in 2019 First published in print in 2013 This book is published under a Creative Commons Attribution-NonCommercial- NoDerivatives (CC-BY-NC-ND 4.0) license. More information regarding CC licenses is available at http://creativecommons.org/licenses/ Available to download free at http://www.humanities-digital-library.org ISBN: 978-1-905670-81-9 (2019 PDF edition) DOI: 10.14296/1019.9781905670819 ISBN: 978-1-905670-52-9 (2013 paperback edition) ©2013 Institute of Classical Studies, University of London The right of contributors to be identified as the authors of the work published here has been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Designed and typeset at the Institute of Classical Studies TABLE OF CONTENTS Introductory note 1 P. J. Rhodes The battle of Marathon and modern scholarship 3 Christopher Pelling Herodotus’ Marathon 23 Peter Krentz Marathon and the development of the exclusive hoplite phalanx 35 Andrej Petrovic The battle of Marathon in pre-Herodotean sources: on Marathon verse-inscriptions (IG I3 503/504; Seg Lvi 430) 45 V. -
Herakleitos (121.6Kb)
The Reign of the Whirlwind 122 Chapter 7 Herakleitos ----------- 1. Life and book We have very little reliable information about the life of Herakleitos son of Bloson, of Ephesos. It is clear from the biographical accounts that survive, that the Alexandrian scholars could find little, even though they were not fussy about reliability. They made up anecdotes to fit some of the more striking sayings of this paradox-loving writer; and as a result, “Herakleitos the Dark” became even more obscure. We have to guess, first, at his dates. He knows something about Pythagoras and Xenophanes; and Parmenides seems to know something about him. We can hazard the conjecture that his book was written by 500 BCE (when Xenophanes had still the last quarter of his long life to live, and Pythagoras was in his last years). This would make 545 BCE a reasonable guess for his birth date. He probably died before 480.i Herakleitos belonged to the ancient royal clan of Ephesos. He is said to have deposited his book in the great temple of Artemis for which his native city was famous (22 A 1).ii We can fairly suppose that it was in his eyes the worthy trophy of a greater victory than any triumph in arms. Whether he was actually melancholic (“the weeping philosopher” as he came to be called)iii we cannot say. He was certainly both an angry man, and an intellectual aristocrat. There are some The Reign of the Whirlwind 123 “sayings” of his that were not in the book. In one plausible story, he “upbraids the Ephesians . -
Grade 7/8 Math Circles the Scale of Numbers Introduction
Faculty of Mathematics Centre for Education in Waterloo, Ontario N2L 3G1 Mathematics and Computing Grade 7/8 Math Circles November 21/22/23, 2017 The Scale of Numbers Introduction Last week we quickly took a look at scientific notation, which is one way we can write down really big numbers. We can also use scientific notation to write very small numbers. 1 × 103 = 1; 000 1 × 102 = 100 1 × 101 = 10 1 × 100 = 1 1 × 10−1 = 0:1 1 × 10−2 = 0:01 1 × 10−3 = 0:001 As you can see above, every time the value of the exponent decreases, the number gets smaller by a factor of 10. This pattern continues even into negative exponent values! Another way of picturing negative exponents is as a division by a positive exponent. 1 10−6 = = 0:000001 106 In this lesson we will be looking at some famous, interesting, or important small numbers, and begin slowly working our way up to the biggest numbers ever used in mathematics! Obviously we can come up with any arbitrary number that is either extremely small or extremely large, but the purpose of this lesson is to only look at numbers with some kind of mathematical or scientific significance. 1 Extremely Small Numbers 1. Zero • Zero or `0' is the number that represents nothingness. It is the number with the smallest magnitude. • Zero only began being used as a number around the year 500. Before this, ancient mathematicians struggled with the concept of `nothing' being `something'. 2. Planck's Constant This is the smallest number that we will be looking at today other than zero. -
MONEY and the EARLY GREEK MIND: Homer, Philosophy, Tragedy
This page intentionally left blank MONEY AND THE EARLY GREEK MIND How were the Greeks of the sixth century bc able to invent philosophy and tragedy? In this book Richard Seaford argues that a large part of the answer can be found in another momentous development, the invention and rapid spread of coinage, which produced the first ever thoroughly monetised society. By transforming social relations, monetisation contributed to the ideas of the universe as an impersonal system (presocratic philosophy) and of the individual alienated from his own kin and from the gods (in tragedy). Seaford argues that an important precondition for this monetisation was the Greek practice of animal sacrifice, as represented in Homeric epic, which describes a premonetary world on the point of producing money. This book combines social history, economic anthropology, numismatics and the close reading of literary, inscriptional, and philosophical texts. Questioning the origins and shaping force of Greek philosophy, this is a major book with wide appeal. richard seaford is Professor of Greek Literature at the University of Exeter. He is the author of commentaries on Euripides’ Cyclops (1984) and Bacchae (1996) and of Reciprocity and Ritual: Homer and Tragedy in the Developing City-State (1994). MONEY AND THE EARLY GREEK MIND Homer, Philosophy, Tragedy RICHARD SEAFORD cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge cb2 2ru, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521832281 © Richard Seaford 2004 This publication is in copyright. -
(Eponymous) Heroes
is is a version of an electronic document, part of the series, Dēmos: Clas- sical Athenian Democracy, a publicationpublication ofof e Stoa: a consortium for electronic publication in the humanities [www.stoa.org]. e electronic version of this article off ers contextual information intended to make the study of Athenian democracy more accessible to a wide audience. Please visit the site at http:// www.stoa.org/projects/demos/home. Athenian Political Art from the fi h and fourth centuries: Images of Tribal (Eponymous) Heroes S e Cleisthenic reforms of /, which fi rmly established democracy at Ath- ens, imposed a new division of Attica into ten tribes, each of which consti- tuted a new political and military unit, but included citizens from each of the three geographical regions of Attica – the city, the coast, and the inland. En- rollment in a tribe (according to heredity) was a manda- tory prerequisite for citizenship. As usual in ancient Athenian aff airs, politics and reli- gion came hand in hand and, a er due consultation with Apollo’s oracle at Delphi, each new tribe was assigned to a particular hero a er whom the tribe was named; the ten Amy C. Smith, “Athenian Political Art from the Fi h and Fourth Centuries : Images of Tribal (Eponymous) Heroes,” in C. Blackwell, ed., Dēmos: Classical Athenian Democracy (A.(A. MahoneyMahoney andand R.R. Scaife,Scaife, edd.,edd., e Stoa: a consortium for electronic publication in the humanities [www.stoa.org], . © , A.C. Smith. tribal heroes are thus known as the eponymous (or name giving) heroes. T : Aristotle indicates that each hero already received worship by the time of the Cleisthenic reforms, although little evi- dence as to the nature of the worship of each hero is now known (Aristot. -
Plato: Influences and Context1
Θεαίτητος | Theaetetus 1 1. Plato: Influences and Context1 1. Socrates. Plato is a member of his inner circle (Apology 34a, Phaedo 59b). Like others, he began to write ‘Socratic discourses’ (Aristotle) after Socrates’s death, continuing for forty years. Philosophy is a dialectical inquiry. Lifelong engagement with sophists. 2. Politics in Athens. The trial and execution of Socrates in 399 BCE shatters Plato’s political confidence. His aristocratic origin contributes to scepticism about democracy and the philosopher’s role in the city (cf. Tht. 172c). Yet: philosophy flourished in late 5th-century Athens. 3. Italy, Sicily. Plato visits Syracuse three times (see next page). He aimed to meet Pythagoreans, in particular Archytas (Tarentum), whose ideas are discernible in his work: immortality of the soul, mathematics, philosophical community. Consequence: founding of Academy in c. 387 BCE (dissolved in 527 CE). 4. Isokrates. The highly influential rhetor (orator) was a life-long foe. Tyranny at home: political rhetoric does (even) more harm than the Sophists (cf. the confusing logic-chopping in Euthydemus; cf. Tht. 164 c, 197a). Rivalry shapes Plato’s mature philosophy. 5. Parmenides, Heraclitus. Before joining Socrates, Plato studied with Cratylus and thus knew Heraclitean views (flux theory). Parmenides of Elea (Italy, early 5th century): only what is could be an intelligible object of thought—the forms. 6. Academy. Plato’s late work depends increasingly less on Socrates. His own views develop in the academy, in conversation with fellow ‘academics’, such as Aristotle. In 347, there are about 20 ‘disciples’, including two women.2 Leaves no dogmatic canon. Successors: Speusippus, Xenocrates, and Polemo (i.e. -
Representing Square Numbers Copyright © 2009 Nelson Education Ltd
Representing Square 1.1 Numbers Student book page 4 You will need Use materials to represent square numbers. • counters A. Calculate the number of counters in this square array. ϭ • a calculator number of number of number of counters counters in counters in in a row a column the array 25 is called a square number because you can arrange 25 counters into a 5-by-5 square. B. Use counters and the grid below to make square arrays. Complete the table. Number of counters in: Each row or column Square array 525 4 9 4 1 Is the number of counters in each square array a square number? How do you know? 8 Lesson 1.1: Representing Square Numbers Copyright © 2009 Nelson Education Ltd. NNEL-MATANSWER-08-0702-001-L01.inddEL-MATANSWER-08-0702-001-L01.indd 8 99/15/08/15/08 55:06:27:06:27 PPMM C. What is the area of the shaded square on the grid? Area ϭ s ϫ s s units ϫ units square units s When you multiply a whole number by itself, the result is a square number. Is 6 a whole number? So, is 36 a square number? D. Determine whether 49 is a square number. Sketch a square with a side length of 7 units. Area ϭ units ϫ units square units Is 49 the product of a whole number multiplied by itself? So, is 49 a square number? The “square” of a number is that number times itself. For example, the square of 8 is 8 ϫ 8 ϭ . -
Parmenides' Theistic Metaphysics
Parmenides’ Theistic Metaphysics BY ©2016 Jeremy C. DeLong Submitted to the graduate degree program in Philosophy and the Graduate Faculty of the University of Kansas in partial fulfillment of the requirements for the degree of Doctor of Philosophy. ________________________________ Chairperson: Tom Tuozzo ________________________________ Eileen Nutting ________________________________ Scott Jenkins ________________________________ John Symons ________________________________ John Younger Date Defended: May 6th, 2016 ii The Dissertation Committee for Jeremy C. DeLong certifies that this is the approved version of the following thesis: Parmenides’ Theistic Metaphysics ________________________________ Chairperson: Thomas Tuozzo Date Defended: May 6th, 2016 iii Abstract: The primary interpretative challenge for understanding Parmenides’ poem revolves around explaining both the meaning of, and the relationship between, its two primary sections: a) the positively endorsed metaphysical arguments which describe some unified, unchanging, motionless, and eternal “reality” (Aletheia), and b) the ensuing cosmology (Doxa), which incorporates the very principles explicitly denied in Aletheia. I will refer to this problem as the “A-D Paradox.” I advocate resolving this paradoxical relationship by reading Parmenides’ poem as a ring-composition, and incorporating a modified version of Palmer’s modal interpretation of Aletheia. On my interpretation, Parmenides’ thesis in Aletheia is not a counter-intuitive description of how all the world (or its fundamental, genuine entities) must truly be, but rather a radical rethinking of divine nature. Understanding Aletheia in this way, the ensuing “cosmology” (Doxa) can be straightforwardly rejected as an exposition of how traditional, mythopoetic accounts have misled mortals in their understanding of divinity. Not only does this interpretative view provide a resolution to the A-D Paradox, it offers a more holistic account of the poem by making the opening lines of introduction (Proem) integral to understanding Parmenides’ message. -
Waiting for Solon: Audience Expectations in Herodotus ∗
Histos () – WAITING FOR SOLON: AUDIENCE EXPECTATIONS IN HERODOTUS ∗ Abstract: In this article, I focus not so much on what Solon actually says and does in his conversation with Croesus, but on what Herodotus’ readers, as well as Croesus himself, think Solon might say or do. I argue that Herodotus uses analogous episodes, those of Gyges, Candaules, and Candaules’ wife, of Arion and Periander, and of Bias/Pittacus and Croesus, to shape readers’ expectations of Solon’s conversation with Croesus, but he then subverts many of those expectations within the conversation itself. In so doing, Herodotus emphasises the programmatic function for the Histories of much of what Solon tells Croesus. Keywords: Herodotus, Arion, artistic patronage, audience expectations, Candaules, Croesus, Seven Sages, Solon cholars have long recognised the programmatic quality that the encounter between Solon and Croesus (.– ) has for Herodotus’ S Histories .1 Croesus’ importance alone for Herodotus’ work cannot be underestimated. In a sense, Herodotus begins the Histories with Croesus; he follows the story of Croesus and the Lydian Mermnad dynasty from its beginning with Gyges’ murder of Candaules all the way to its conclusion with Croesus’ defeat by the Persian king Cyrus. Croesus also occupies a primary position in the Histories as the first in the line of great eastern imperialists that culminates with the Persian Xerxes. On the one hand, the Solon–Croesus episode foreshadows Croesus’ impending downfall. On the other hand, the episode reflects many of Herodotus’ chief thematic concerns: the conflict between East and West and the clash between different cultures in general; the mutability of human fortune and the gods’ jealousy of human excess; the wise advisor motif and the challenge of acquiring knowledge. -
An Art of Translation: Churchill's Uses of Eighteenth-Century British History
An Art of Translation: Churchill’s Uses of Eighteenth-Century British History Charles-Edouard Levillain To cite this version: Charles-Edouard Levillain. An Art of Translation: Churchill’s Uses of Eighteenth-Century British His- tory. XVII-XVIII Revue de la Société d’études anglo-américaines des XVIIe et XVIIIe siècles , Société d’études anglo-américaines des dix-septième et dix-huitième siècles, Lille, 2020, 10.4000/1718.3779. hal-03251134 HAL Id: hal-03251134 https://hal.archives-ouvertes.fr/hal-03251134 Submitted on 6 Jun 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. XVII-XVIII Revue de la Société d’études anglo-américaines des XVIIe et XVIIIe siècles 76 | 2019 Crimes et criminels An Art of Translation: Churchill’s Uses of Eighteenth-Century British History Charles-Édouard Levillain Electronic version URL: http://journals.openedition.org/1718/3779 DOI: 10.4000/1718.3779 ISSN: 2117-590X Publisher Société d'études anglo-américaines des XVIIe et XVIIIe siècles Electronic reference Charles-Édouard Levillain, « An Art of Translation: Churchill’s Uses of Eighteenth-Century British History », XVII-XVIII [Online], 76 | 2019, Online since 31 December 2019, connection on 07 January 2020.