Theories of Knowledge in the Old Academy
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Theon of Alexandria and Hypatia
CREATIVE MATH. 12 (2003), 111 - 115 Theon of Alexandria and Hypatia Michael Lambrou Abstract. In this paper we present the story of the most famous ancient female math- ematician, Hypatia, and her father Theon of Alexandria. The mathematician and philosopher Hypatia flourished in Alexandria from the second part of the 4th century until her violent death incurred by a mob in 415. She was the daughter of Theon of Alexandria, a math- ematician and astronomer, who flourished in Alexandria during the second part of the fourth century. Information on Theon’s life is only brief, coming mainly from a note in the Suda (Suida’s Lexicon, written about 1000 AD) stating that he lived in Alexandria in the times of Theodosius I (who reigned AD 379-395) and taught at the Museum. He is, in fact, the Museum’s last attested member. Descriptions of two eclipses he observed in Alexandria included in his commentary to Ptolemy’s Mathematical Syntaxis (Almagest) and elsewhere have been dated as the eclipses that occurred in AD 364, which is consistent with Suda. Although originality in Theon’s works cannot be claimed, he was certainly immensely influential in the preservation, dissemination and editing of clas- sic texts of previous generations. Indeed, with the exception of Vaticanus Graecus 190 all surviving Greek manuscripts of Euclid’s Elements stem from Theon’s edition. A comparison to Vaticanus Graecus 190 reveals that Theon did not actually change the mathematical content of the Elements except in minor points, but rather re-wrote it in Koini and in a form more suitable for the students he taught (some manuscripts refer to Theon’s sinousiai). -
Golden Ratio: a Subtle Regulator in Our Body and Cardiovascular System?
See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/306051060 Golden Ratio: A subtle regulator in our body and cardiovascular system? Article in International journal of cardiology · August 2016 DOI: 10.1016/j.ijcard.2016.08.147 CITATIONS READS 8 266 3 authors, including: Selcuk Ozturk Ertan Yetkin Ankara University Istinye University, LIV Hospital 56 PUBLICATIONS 121 CITATIONS 227 PUBLICATIONS 3,259 CITATIONS SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: microbiology View project golden ratio View project All content following this page was uploaded by Ertan Yetkin on 23 August 2019. The user has requested enhancement of the downloaded file. International Journal of Cardiology 223 (2016) 143–145 Contents lists available at ScienceDirect International Journal of Cardiology journal homepage: www.elsevier.com/locate/ijcard Review Golden ratio: A subtle regulator in our body and cardiovascular system? Selcuk Ozturk a, Kenan Yalta b, Ertan Yetkin c,⁎ a Abant Izzet Baysal University, Faculty of Medicine, Department of Cardiology, Bolu, Turkey b Trakya University, Faculty of Medicine, Department of Cardiology, Edirne, Turkey c Yenisehir Hospital, Division of Cardiology, Mersin, Turkey article info abstract Article history: Golden ratio, which is an irrational number and also named as the Greek letter Phi (φ), is defined as the ratio be- Received 13 July 2016 tween two lines of unequal length, where the ratio of the lengths of the shorter to the longer is the same as the Accepted 7 August 2016 ratio between the lengths of the longer and the sum of the lengths. -
Alexandrea Ad Aegyptvm the Legacy of Multiculturalism in Antiquity
Alexandrea ad aegyptvm the legacy of multiculturalism in antiquity editors rogério sousa maria do céu fialho mona haggag nuno simões rodrigues Título: Alexandrea ad Aegyptum – The Legacy of Multiculturalism in Antiquity Coord.: Rogério Sousa, Maria do Céu Fialho, Mona Haggag e Nuno Simões Rodrigues Design gráfico: Helena Lobo Design | www.hldesign.pt Revisão: Paula Montes Leal Inês Nemésio Obra sujeita a revisão científica Comissão científica: Alberto Bernabé, Universidade Complutense de Madrid; André Chevitarese, Universidade Federal, Rio de Janeiro; Aurélio Pérez Jiménez, Universidade de Málaga; Carmen Leal Soares, Universidade de Coimbra; Fábio Souza Lessa, Universidade Federal, Rio de Janeiro; José Augusto Ramos, Universidade de Lisboa; José Luís Brandão, Universidade de Coimbra; Natália Bebiano Providência e Costa, Universidade de Coimbra; Richard McKirahan, Pomona College, Claremont Co-edição: CITCEM – Centro de Investigação Transdisciplinar «Cultura, Espaço e Memória» Via Panorâmica, s/n | 4150-564 Porto | www.citcem.org | [email protected] CECH – Centro de Estudos Clássicos e Humanísticos | Largo da Porta Férrea, Universidade de Coimbra Alexandria University | Cornice Avenue, Shabty, Alexandria Edições Afrontamento , Lda. | Rua Costa Cabral, 859 | 4200-225 Porto www.edicoesafrontamento.pt | [email protected] N.º edição: 1152 ISBN: 978-972-36-1336-0 (Edições Afrontamento) ISBN: 978-989-8351-25-8 (CITCEM) ISBN: 978-989-721-53-2 (CECH) Depósito legal: 366115/13 Impressão e acabamento: Rainho & Neves Lda. | Santa Maria da Feira [email protected] Distribuição: Companhia das Artes – Livros e Distribuição, Lda. [email protected] Este trabalho é financiado por Fundos Nacionais através da FCT – Fundação para a Ciência e Tecnologia no âmbito do projecto PEst-OE/HIS/UI4059/2011 HYPATIA AND THE IDIOSCYNCRASIES OF CHRISTIANITY IN EGYPT – A STUDY OF THE EVENTS OCCURRED AT EASTER 415 A.D. -
Being the Treatises of the First Ennead With
Tufts College Library FROM THE INCOME OF THE SHIPMAN MEMORIAL FUND Digitized by the Internet Archive in 2016 https://archive.org/details/ethicaltreatises01plot I f ; « li s’ I I V Oo dum 5l<5ipe 0(^ i on6fu\ tiA h-6ipe^nn, 1 nDoriin^id-Dpoc t)jiile-^i!;4-CU-iC tioni, Sciopin tTiAC-ennii. TIo'dUaij 1916. LOTINUS: THE ETHICAL TREATISES BEING THE TREATISES OF THE FIRST ENNEAD WITH PORPHYRY’S LIFE OF PLOTINUS, AND THE PRELLER-RITTER EXTRACTS FORMING A CONSPECTUS OF THE PLOTINIAN SYSTEM, TRANSLATED FROM THE GREEK BY STEPHEN MACKENNA CHARLES T. BRANFORD COMPANY BOSTON, MASSACHUSETTS /1>.L % k95 ,E5 ,M-b v.l CONTENTS I'AQP. Porphyry’s Life of Plotinus ....... i THE BOOKS OF THE FIRST ENNEAD I. The Animate and the Man . .29 . II. On Virtue . • 41 III. Dialectic (or The Upward Way) . -.50 IV. On Happiness (or The Authentic Good of Life) . V. On Happiness and Extension of Time . -72 VI. On Beauty . *77 VII. On the Primal Good and its Secondary Forms . .89 VIII. On Evil, Its Nature and Source . .92 IX. On “The Reasoned Dismissal” ...... 108 BIBLIOGRAPHY AND EXPLANATORY MATTER Text, Previous Tr.\nslations . -113 Method of this Translation . .114 Commentaries ......... 116 Terminology ......... 117 The Divine Names ........ 118 The One .......... n8 The Intellectual-Principle ....... 119 The All-Soul ......... 120 The Divine-Triad as a Unity ....... 120 The Gods and Daimones ....... 121 • Man ; His Nature, Powers and Destiny ..... 121 Evil and Matter ........ 123 Morality ......... 123 The Term and the Way ....... 124 Minor Points of Terminology ....... 124 THE PRELLER-RITTER CONSPECTUS OF THE PLOTINIAN SYSTEM I. -
Thales of Miletus Sources and Interpretations Miletli Thales Kaynaklar Ve Yorumlar
Thales of Miletus Sources and Interpretations Miletli Thales Kaynaklar ve Yorumlar David Pierce October , Matematics Department Mimar Sinan Fine Arts University Istanbul http://mat.msgsu.edu.tr/~dpierce/ Preface Here are notes of what I have been able to find or figure out about Thales of Miletus. They may be useful for anybody interested in Thales. They are not an essay, though they may lead to one. I focus mainly on the ancient sources that we have, and on the mathematics of Thales. I began this work in preparation to give one of several - minute talks at the Thales Meeting (Thales Buluşması) at the ruins of Miletus, now Milet, September , . The talks were in Turkish; the audience were from the general popu- lation. I chose for my title “Thales as the originator of the concept of proof” (Kanıt kavramının öncüsü olarak Thales). An English draft is in an appendix. The Thales Meeting was arranged by the Tourism Research Society (Turizm Araştırmaları Derneği, TURAD) and the office of the mayor of Didim. Part of Aydın province, the district of Didim encompasses the ancient cities of Priene and Miletus, along with the temple of Didyma. The temple was linked to Miletus, and Herodotus refers to it under the name of the family of priests, the Branchidae. I first visited Priene, Didyma, and Miletus in , when teaching at the Nesin Mathematics Village in Şirince, Selçuk, İzmir. The district of Selçuk contains also the ruins of Eph- esus, home town of Heraclitus. In , I drafted my Miletus talk in the Math Village. Since then, I have edited and added to these notes. -
The Ideas As Thoughts of God
Études platoniciennes 8 | 2011 Les Formes platoniciennes dans l'Antiquité tardive The Ideas as thoughts of God John Dillon Publisher Société d’Études Platoniciennes Electronic version Printed version URL: http:// Date of publication: 1 November 2011 etudesplatoniciennes.revues.org/448 Number of pages: 31-42 DOI: 10.4000/etudesplatoniciennes.448 ISSN: 2275-1785 Brought to you by Fondation Maison des sciences de l'homme Electronic reference John Dillon, « The Ideas as thoughts of God », Études platoniciennes [Online], 8 | 2011, Online since 16 December 2014, connection on 24 May 2017. URL : http://etudesplatoniciennes.revues.org/448 ; DOI : 10.4000/etudesplatoniciennes.448 © Société d’Études platoniciennes The Ideas as Thoughts of God John Dillon Xenocrates’ Nous-Monad The precise origin of the concept of the Platonic Forms, or Ideas, as thoughts of God is a long-standing puzzle in the history of Platonism, which I am on record as dismissing somewhat brusquely in various works.1 I am glad to have an opportunity to return to it now, in this distinguished company.2 I propose to begin my consideration of it on this occasion by returning to the seminal article of Audrey Rich, published in Mnemosyne back in 1954.3 As you may recall, Rich’s thesis in that article was that the concept arose, whenever it arose – sometime in the early Hellenistic age, was her guess – as a reaction to Aristotle’s concept of the Unmoved Mover of Met. Lambda as an intellect thinking itself, and “a desire to reconcile the Theory of Ideas with the Aristotelian doctrine of immanent form” (p. -
The Golden Relationships: an Exploration of Fibonacci Numbers and Phi
The Golden Relationships: An Exploration of Fibonacci Numbers and Phi Anthony Rayvon Watson Faculty Advisor: Paul Manos Duke University Biology Department April, 2017 This project was submitted in partial fulfillment of the requirements for the degree of Master of Arts in the Graduate Liberal Studies Program in the Graduate School of Duke University. Copyright by Anthony Rayvon Watson 2017 Abstract The Greek letter Ø (Phi), represents one of the most mysterious numbers (1.618…) known to humankind. Historical reverence for Ø led to the monikers “The Golden Number” or “The Devine Proportion”. This simple, yet enigmatic number, is inseparably linked to the recursive mathematical sequence that produces Fibonacci numbers. Fibonacci numbers have fascinated and perplexed scholars, scientists, and the general public since they were first identified by Leonardo Fibonacci in his seminal work Liber Abacci in 1202. These transcendent numbers which are inextricably bound to the Golden Number, seemingly touch every aspect of plant, animal, and human existence. The most puzzling aspect of these numbers resides in their universal nature and our inability to explain their pervasiveness. An understanding of these numbers is often clouded by those who seemingly find Fibonacci or Golden Number associations in everything that exists. Indeed, undeniable relationships do exist; however, some represent aspirant thinking from the observer’s perspective. My work explores a number of cases where these relationships appear to exist and offers scholarly sources that either support or refute the claims. By analyzing research relating to biology, art, architecture, and other contrasting subject areas, I paint a broad picture illustrating the extensive nature of these numbers. -
May Plato's Academy Be Considered As the First Academic Institution?
Center for Open Access in Science ▪ https://www.centerprode.com/ojsh.html Open Journal for Studies in History, 2019, 2(2), 35-42. ISSN (Online) 2620-066X ▪ https://doi.org/10.32591/coas.ojsh.0202.02035s _________________________________________________________________________ May Plato’s Academy be Considered as the First Academic Institution? Zhulduz Amangelidyevna Seitkasimova M. Auezov South Kazakhstan State University, KAZAKHSTAN Faculty of Pedagogy and Culture, Shymkent Received 8 November 2019 ▪ Revised 17 December 2019 ▪ Accepted 23 December 2019 Abstract Plato’s Academy is undoubtedly the first higher education institution in history, and in ancient Athens itself represents the most important educational institution. It constituted in the context of the universal development that took place in ancient Athens, in the 5th and 4th century BC, and it continued to work until the Byzantine Emperor Justinian forbade the work of all schools of philosophy (529 AD). This development, which is part of the so-called Golden Age of ancient Athens, represents the period of Greek history in which the foundations of Western civilization originated, as we know it today. Plato appears as one of the greatest philosophers of ancient Greece, along with Socrates and Aristotle, to the first of whom appears as a student and to the second as a teacher. Philosophy in the true sense of the word was created in Plato’s era in ancient Athens (Russell, 1975), and Plato’s Academy, in which he, along with his students, talked about various philosophical topics through the Garden of Akademos, was the impetus for this development. There are also opinions that the development of philosophy after Socrates, Plato, and Aristotle is only of reproductive character when it comes to the basics of philosophy. -
A Reading of Porphyry's on Abstinence From
UNIVERSITY OF CALIFORNIA Los Angeles Justice Purity Piety: A Reading of Porphyry’s On Abstinence from Ensouled Beings A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Classics by Alexander Press 2020 © Copyright by Alexander Press 2020 ABSTRACT OF THE DISSERTATION Justice Purity Piety: A Reading of Porphyry’s On Abstinence from Ensouled Beings by Alexander Press Doctor of Philosophy in Classics University of California, Los Angeles, 2020 Professor David Blank, Chair Abstract: Presenting a range of arguments against meat-eating, many strikingly familiar, Porphyry’s On Abstinence from Ensouled Beings (Greek Περὶ ἀποχῆς ἐµψύχων, Latin De abstinentia ab esu animalium) offers a sweeping view of the ancient debate concerning animals and their treatment. At the same time, because of its advocacy of an asceticism informed by its author’s Neoplatonism, Abstinence is often taken to be concerned primarily with the health of the human soul. By approaching Abstinence as a work of moral suasion and a work of literature, whose intra- and intertextual resonances yield something more than a collection of propositions or an invitation to Quellenforschung, I aim to push beyond interpretations that bracket the arguments regarding animals as merely dialectical; cast the text’s other-directed principle of justice as wholly ii subordinated to a self-directed principle of purity; or accept as decisive Porphyry’s exclusion of craftsmen, athletes, soldiers, sailors, and orators from his call to vegetarianism. -
Notes on Greek Mathematics
MATHEMATICS IN ANCIENT GREECE Periods in Greek history [AG]. Archaic Period: 750 BC to 490 BC (Emergence of city- states to Battle of Marathon) The Iliad and the Odyssey were composed c. 750-720 (based on the `Trojan war’ of 1250-1225 BC.) Between 670-500 BC, many city-states were ruled by tyrants (a word borrowed into the Greek language from Asia Minor, to signify a man who seizes control of the state by a coup and governs illegally.) Classical Period: 490 to 323 BC (Battle of Marathon to death of Alexander). The years from 480 (Persians driven from Greece) to 430 saw the rise of Athenian democracy (under Pericles). The Parthenon was built, 447-432. Playwrights Sophocles, Aristophanes, Euripides were active in Athens (c. 430-400). Following undeclared war between Athens and Sparta from 460-445, the Peloponnesian war (431-404; account by Thucydides) kept these two states (and their allies throughout the region) busy. This led to the ascendance of Sparta and the `rule of thirty tyrants’ in Athens (404-403). Socrates was tried and executed in 399. His follower Plato wrote his dialogues (399-347) and founded the Academy. The accession of Philip II of Macedon (359) signals the beginning of a period of Macedonian rule. Philip invaded Asia in 336, and was assassinated the same year. His successor Alexander III (`the Great’, 356-323 BC) continued the program of world conquest over the next 13 years, invading India in 325 BC. Hellenistic Period (323-30 BC). Science, mathematics (Euclid) and culture flourished in Egypt (Alexandria) under the Ptolemaic dynasty. -
The First Six Books of the Elements of Euclid, in Which
&, OTll llOkSr mm ma /zm $fj- <a 2KX '•' JTMs. ^n r.yjOQS ¥\*f El/1 ffi* 3^» ^^ 'ff.tfv ,^/^e*- Library of the University of Toronto Aaa BYRNE'S EUCLID THE FIRST SIX BOOKS OF THE ELEMENTS OF EUCLID WITH COLOURED DIAGRAMS AND SYMBOLS ? THE FIRST SIX BOOKS OF THE ELEMENTS OF EUCLID IN WHICH COLOURED DIAGRAMS AND SYMBOLS ARE USED INSTEAD OF LETTERS FOR THE GREATER EASE OF LEARNERS BY OLIVER BYRNE SURVEYOR OF HER MAJESTY'S SETTLEMENTS IN THE FALKLAND ISLANDS AND AUTHOR OF NUMEROUS MATHEMATICAL WORKS LONDON WILLIAM PICKERING 1847 TO THE RIGHT HONOURABLE THE EARL FITZWILLIAM, ETC. ETC. ETC. THIS WORK IS DEDICATED BY HIS LORDSHIP S OBEDIENT AND MUCH OBLIGED SERVANT, OLIVER BYRNE. Digitized by the Internet Archive in 2011 with funding from University of Toronto http://www.archive.org/details/firstsixbooksofeOOeucl SS3 INTRODUCTION. HE arts and fciences have become fo extenfive, that to facilitate their acquirement is of as much importance as to extend their boundaries. Illuftration, if it does not fhorten the time of ftudy, will at leaft make it more agreeable. This Work has a greater aim than mere illuftration ; we do not intro- duce colours for the purpofe of entertainment, or to amuie by certain cottibinations of tint andform, but to affift the mind in its refearches after truth, to increafe the facilities of instruction, and to diffufe permanent knowledge. If we wanted authorities to prove the importance and ufefulnefs of geometry, we might quote every philofopher fince the days of Plato. Among the Greeks, in ancient, as in the fchool of Peftalozzi and others in recent times, geometry was adopted as the beft gymnaftic of the mind. -
Contribution to Academy Colloquium Athens, Dec. 2012 Polemon, Der Grosse Schatten of the Old Academy John Dillon, Trinity Colle
Contribution to Academy Colloquium Athens, Dec. 2012 Polemon, der grosse Schatten of the Old Academy John Dillon, Trinity College Dublin Illustrative Passages 1. “Polemon used to say that we should exercise ourselves with facts ( pragmata), and not with logical speculations ( dialektika theôrêmata ), which leave us, like a man who has got up some paltry handbook on harmony but never practised, able, indeed, to win admiration for skill in asking questions ( erôtêsis ), but utterly at variance with ourselves in the ordering of our lives ( diathesis ).” (trans. Hicks). 2. As to the former group, as I was reading over the account of Polemon’s conversion to philosophy, something possibly significant struck me, which had not done so previously. 1 This is a very popular anecdote, of which Gigante is able to list fully 19 versions in his collection of the ‘fragments,’’ 2 which involves Polemon, who at this stage is a notorious rake, on the head of an agreement with his young friends ( synthemenos tois neois ) – presumably some sort of wager was involved – lurching into Xenocrates’ seminar, drunk and garlanded (methyôn kai estephanômenos ), with the purpose, we must imagine, of causing some sort of mayhem, and discomfiting the notoriously unflappable Xenocrates. Instead, however, Polemon slumps down at the back of the lecture-room, and finds himself listening to Xenocrates calmly continuing to deliver a lecture on sôphrosynê, which results in his becoming hooked on philosophy as a way of life, the bios philosophikos . 3. His colleague Crantor, when asked what especially attracted him to Polemon, is said to have replied, “The fact that I never heard him raise or lower his voice in speaking” (ibid.