Eudoxus in the "Parmenides"
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Mathematicians
MATHEMATICIANS [MATHEMATICIANS] Authors: Oliver Knill: 2000 Literature: Started from a list of names with birthdates grabbed from mactutor in 2000. Abbe [Abbe] Abbe Ernst (1840-1909) Abel [Abel] Abel Niels Henrik (1802-1829) Norwegian mathematician. Significant contributions to algebra and anal- ysis, in particular the study of groups and series. Famous for proving the insolubility of the quintic equation at the age of 19. AbrahamMax [AbrahamMax] Abraham Max (1875-1922) Ackermann [Ackermann] Ackermann Wilhelm (1896-1962) AdamsFrank [AdamsFrank] Adams J Frank (1930-1989) Adams [Adams] Adams John Couch (1819-1892) Adelard [Adelard] Adelard of Bath (1075-1160) Adler [Adler] Adler August (1863-1923) Adrain [Adrain] Adrain Robert (1775-1843) Aepinus [Aepinus] Aepinus Franz (1724-1802) Agnesi [Agnesi] Agnesi Maria (1718-1799) Ahlfors [Ahlfors] Ahlfors Lars (1907-1996) Finnish mathematician working in complex analysis, was also professor at Harvard from 1946, retiring in 1977. Ahlfors won both the Fields medal in 1936 and the Wolf prize in 1981. Ahmes [Ahmes] Ahmes (1680BC-1620BC) Aida [Aida] Aida Yasuaki (1747-1817) Aiken [Aiken] Aiken Howard (1900-1973) Airy [Airy] Airy George (1801-1892) Aitken [Aitken] Aitken Alec (1895-1967) Ajima [Ajima] Ajima Naonobu (1732-1798) Akhiezer [Akhiezer] Akhiezer Naum Ilich (1901-1980) Albanese [Albanese] Albanese Giacomo (1890-1948) Albert [Albert] Albert of Saxony (1316-1390) AlbertAbraham [AlbertAbraham] Albert A Adrian (1905-1972) Alberti [Alberti] Alberti Leone (1404-1472) Albertus [Albertus] Albertus Magnus -
Plato As "Architectof Science"
Plato as "Architectof Science" LEONID ZHMUD ABSTRACT The figureof the cordialhost of the Academy,who invitedthe mostgifted math- ematiciansand cultivatedpure research, whose keen intellectwas able if not to solve the particularproblem then at least to show the methodfor its solution: this figureis quite familiarto studentsof Greekscience. But was the Academy as such a centerof scientificresearch, and did Plato really set for mathemati- cians and astronomersthe problemsthey shouldstudy and methodsthey should use? Oursources tell aboutPlato's friendship or at leastacquaintance with many brilliantmathematicians of his day (Theodorus,Archytas, Theaetetus), but they were neverhis pupils,rather vice versa- he learnedmuch from them and actively used this knowledgein developinghis philosophy.There is no reliableevidence that Eudoxus,Menaechmus, Dinostratus, Theudius, and others, whom many scholarsunite into the groupof so-called"Academic mathematicians," ever were his pupilsor close associates.Our analysis of therelevant passages (Eratosthenes' Platonicus, Sosigenes ap. Simplicius, Proclus' Catalogue of geometers, and Philodemus'History of the Academy,etc.) shows thatthe very tendencyof por- trayingPlato as the architectof sciencegoes back to the earlyAcademy and is bornout of interpretationsof his dialogues. I Plato's relationship to the exact sciences used to be one of the traditional problems in the history of ancient Greek science and philosophy.' From the nineteenth century on it was examined in various aspects, the most significant of which were the historical, philosophical and methodological. In the last century and at the beginning of this century attention was paid peredominantly, although not exclusively, to the first of these aspects, especially to the questions how great Plato's contribution to specific math- ematical research really was, and how reliable our sources are in ascrib- ing to him particular scientific discoveries. -
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. -
Chapter Two Democritus and the Different Limits to Divisibility
CHAPTER TWO DEMOCRITUS AND THE DIFFERENT LIMITS TO DIVISIBILITY § 0. Introduction In the previous chapter I tried to give an extensive analysis of the reasoning in and behind the first arguments in the history of philosophy in which problems of continuity and infinite divisibility emerged. The impact of these arguments must have been enormous. Designed to show that rationally speaking one was better off with an Eleatic universe without plurality and without motion, Zeno’s paradoxes were a challenge to everyone who wanted to salvage at least those two basic features of the world of common sense. On the other hand, sceptics, for whatever reason weary of common sense, could employ Zeno-style arguments to keep up the pressure. The most notable representative of the latter group is Gorgias, who in his book On not-being or On nature referred to ‘Zeno’s argument’, presumably in a demonstration that what is without body and does not have parts, is not. It is possible that this followed an earlier argument of his that whatever is one, must be without body.1 We recognize here what Aristotle calls Zeno’s principle, that what does not have bulk or size, is not. Also in the following we meet familiar Zenonian themes: Further, if it moves and shifts [as] one, what is, is divided, not being continuous, and there [it is] not something. Hence, if it moves everywhere, it is divided everywhere. But if that is the case, then everywhere it is not. For it is there deprived of being, he says, where it is divided, instead of ‘void’ using ‘being divided’.2 Gorgias is talking here about the situation that there is motion within what is. -
Platonist Philosopher Hypatia of Alexandria in Amenabar’S Film Agorá
A STUDY OF THE RECEPTION OF THE LIFE AND DEATH OF THE NEO- PLATONIST PHILOSOPHER HYPATIA OF ALEXANDRIA IN AMENABAR’S FILM AGORÁ GILLIAN van der HEIJDEN Submitted in partial fulfilment of the requirement for the degree of MASTER OF ARTS In the Faculty of Humanities School of Religion, Philosophy and Classics at the UNIVERSITY OF KWAZULU-NATAL, DURBAN SUPERVISOR: PROFESSOR J.L. HILTON MARCH 2016 DECLARATION I, Gillian van der Heijden, declare that: The research reported in this dissertation, except where otherwise indicated, is my original research; This dissertation has not been submitted for any degree or examination at any other university; This dissertation does not contain other persons’ data, pictures, graphs or other information, unless specifically acknowledged as being sourced from other persons; The dissertation does not contain other persons’ writing, unless specifically acknowledged as being sourced from other researchers. Where other written sources have been quoted, then: a) their words have been re-written but the general information attributed to them has been referenced; b) where their exact words have been used, their writing has been paragraphed and referenced; c) This dissertation/thesis does not contain text, graphics or tables copied and pasted from the Internet, unless specifically acknowledged, and the source being detailed in the dissertation/thesis and in the References sections. Signed: Gillian van der Heijden (Student Number 209541374) Professor J. L. Hilton ii ABSTRACT The film Agorá is better appreciated through a little knowledge of the rise of Christianity and its opposition to Paganism which professed ethical principles inherited from Greek mythology and acknowledged, seasonal rituals and wealth in land and livestock. -
Meet the Philosophers of Ancient Greece
Meet the Philosophers of Ancient Greece Everything You Always Wanted to Know About Ancient Greek Philosophy but didn’t Know Who to Ask Edited by Patricia F. O’Grady MEET THE PHILOSOPHERS OF ANCIENT GREECE Dedicated to the memory of Panagiotis, a humble man, who found pleasure when reading about the philosophers of Ancient Greece Meet the Philosophers of Ancient Greece Everything you always wanted to know about Ancient Greek philosophy but didn’t know who to ask Edited by PATRICIA F. O’GRADY Flinders University of South Australia © Patricia F. O’Grady 2005 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the publisher. Patricia F. O’Grady has asserted her right under the Copyright, Designs and Patents Act, 1988, to be identi.ed as the editor of this work. Published by Ashgate Publishing Limited Ashgate Publishing Company Wey Court East Suite 420 Union Road 101 Cherry Street Farnham Burlington Surrey, GU9 7PT VT 05401-4405 England USA Ashgate website: http://www.ashgate.com British Library Cataloguing in Publication Data Meet the philosophers of ancient Greece: everything you always wanted to know about ancient Greek philosophy but didn’t know who to ask 1. Philosophy, Ancient 2. Philosophers – Greece 3. Greece – Intellectual life – To 146 B.C. I. O’Grady, Patricia F. 180 Library of Congress Cataloging-in-Publication Data Meet the philosophers of ancient Greece: everything you always wanted to know about ancient Greek philosophy but didn’t know who to ask / Patricia F. -
Eudoxus Erin Sondgeroth 9/1/14
Eudoxus Erin Sondgeroth 9/1/14 There were many brilliant mathematicians from the time period of 500 BC until 300 BC, including Pythagoras and Euclid. Another fundamental figure from that era was Greek mathematician Eudoxus of Cnidus. Eudoxus was born in Cnidus (present-day Turkey) in approximately 408 BC and died in 355 BC at the age of 53. Eudoxus studied math under Archytus in Tarentum, medicine under Philistium in Sicily, astronomy in Egytpt, and philosophy and rhetoric under Plato in Athens. After his many years of studying, Eudoxus established his own school at Cyzicus, where had many pupils. In 365 BC Eudoxus moved his school to Athens in order to work as a colleague of Plato. It was during this time that Eudoxus completed some of his best work and the reasoning for why he is considered the leading mathematician and astronomer of his day. In the field of astronomy, Eudoxus`s best-known work was his planetary model. This model had a spherical Earth that was at rest in the center of the universe and twenty-seven concentric spheres that held the fixed stars, sun, moon, and other planets that moved in orbit around the Earth. While this model has clearly been disproved, it was a prominent model for at least fifty years because it explained many astronomical phenomenon of that time, including the sunrise and sunset, the fixed constellations, and movement of other planets in orbits. Luckily, Eudoxus`s theories had much more success in the field of mathemat- ics. Many of his proposition, theories, and proofs are common knowledge in the math world today. -
``Mathematics'' and ``Physics'' in the Science of Harmonics
NISSUNA UMANA INVESTIGAZIONE SI PUO DIMANDARE VERA SCIENZIA S’ESSA NON PASSA PER LE MATEMATICHE DIMOSTRAZIONI LEONARDO DA VINCI vol. 4 no. 3-4 2016 Mathematics and Mechanics of Complex Systems STEFANO ISOLA “MATHEMATICS” AND “PHYSICS” IN THE SCIENCE OF HARMONICS msp MATHEMATICS AND MECHANICS OF COMPLEX SYSTEMS Vol. 4, No. 3-4, 2016 dx.doi.org/10.2140/memocs.2016.4.213 ∩ MM “MATHEMATICS” AND “PHYSICS” IN THE SCIENCE OF HARMONICS STEFANO ISOLA Some aspects of the role that the science of harmonics has played in the history of science are discussed in light of Russo’s investigation of the history of the concepts of “mathematics” and “physics”. 1. The rambling route of the ancient scientific method In several places in Russo’s writings on the history of science, one can find en- lightening discussions about the meanings of the concepts of “physics” and “math- ematics”, along with the particular notions of truth involved in them; see, e.g., [58, Chapter 6.6; 60, Chapter 15; 56; 57]. Both terms derive from the Greek: the original meaning of the former was the investigation of everything that lives, grows or, more generally, comes into existence, whereas the latter referred to all that is studied, thus deriving its meaning not from its content but from its method. In the Hellenistic period, the term “physics” continued to be used to indicate that sector of philosophy that addressed nature (the other sectors being ethics and logic), thus corresponding to what came to be called “natural philosophy” in modern times. On the other hand, the term “mathematics” was used to indicate all the disciplines (including geometry, arithmetic, harmonics, astronomy, optics, mechanics, hydro- statics, pneumatics, geodesy and mathematical geography) that shared the same method of investigation, based on the construction of theories by which “theorems” are proved, leaning on explicitly stated initial assumptions. -
Proclus and Artemis: on the Relevance of Neoplatonism to the Modern Study of Ancient Religion
Kernos Revue internationale et pluridisciplinaire de religion grecque antique 13 | 2000 Varia Proclus and Artemis: On the Relevance of Neoplatonism to the Modern Study of Ancient Religion Spyridon Rangos Electronic version URL: http://journals.openedition.org/kernos/1293 DOI: 10.4000/kernos.1293 ISSN: 2034-7871 Publisher Centre international d'étude de la religion grecque antique Printed version Date of publication: 1 January 2000 ISSN: 0776-3824 Electronic reference Spyridon Rangos, « Proclus and Artemis: On the Relevance of Neoplatonism to the Modern Study of Ancient Religion », Kernos [Online], 13 | 2000, Online since 21 April 2011, connection on 01 May 2019. URL : http://journals.openedition.org/kernos/1293 ; DOI : 10.4000/kernos.1293 Kernos Kernos, 13 (2000), p. 47-84. Proclus and Artemis: On the Relevance of Neoplatonism to the Modern Study of Andent Religion* Imagine the situation in which contemporary philosophers would find themselves if Wittgenstein introduced, in his Philosophical Investigations, the religious figure of Jesus as Logos and Son of God in order to illuminate the puzzlement ofthe private-language paradox, or if in the second division of Being and Time Heidegger mentioned the archangel Michael to support the argument of 'being toward death'. Similar is the perplexity that a modern reader is bound to encounter when, after a highly sophisticated analysis of demanding metaphysical questions about the relationship of the one and the many, finitude and infinity, mind and body, Proclus, l in ail seriousness and without the slightest touch of irony, assigns to some traditional gods of Greek polytheism a definitive place in the structure of being. -
PROCLUS on HESIOD's WORKS and DAYS Patrizia Marzillo
PERFORMING AN ACADEMIC TALK: PROCLUS ON HESIOD’S WORKS AND DAYS Patrizia Marzillo Abstract From Socrates onwards orality was the favoured means of expression for those wholaterlovedtocallthemselves‘Platonic’.Theyusedtodiscussphilosophical issues in debates that turned into academic lectures and seminars. According to Plato’s original teaching, these talks should have not been “fixed” in written compositions, yet Plato himself put most of his doctrine into fictive “written dia- logues”.His followers intensified their connection with writing, above all for the purposes of teaching. On the one hand, they made notes on the lessons of their teachers; on the other, they enlarged their own talks in written compositions. Neoplatonists’ commentaries are often an amplification of their academic talks. The lessons held in the school of Athens or in Platonic circles coalesced into texts that mostly constitute Neoplatonic propaganda intended for the outside world. When Proclus directed the school in Athens, Plato and Aristotle were taught, but also theologian poets such as Homer, Orpheus, Hesiod. As the Suda reports, Proclus wrote commentaries on all of these poets, but the only onepreservedisthecommentaryonHesiod’sWorks and Days.Througha comparison of some passages from this commentary, I show how Proclus’ commentary on Hesiod is not only a good example of an oral lesson that has become a written commentary, but also, importantly, of a text that aimed at the diffusion of Neoplatonic ideas among an audience of non-adherents. As his biographer and disciple Marinus of Neapolis relates, the neo- Platonist Proclus was accustomed to write about lines a day.1 Besides being a very prolific author, he was also an indefatigable teacher since in addition to his writing he held several classes during the day and also gave evening talks.2 What I propose to show in this paper is the profound interaction between the oral communication in his school and the written performance of his commentaries. -
Neoplatonic Asclepius: Science and Religion at the Crossroads of Aristotelian Biology, Hippocratic Medicine and Platonic Theurgy
Studia Antiqua et Archaeologica 23(2): 333–349 Neoplatonic Asclepius: Science and religion at the crossroads of Aristotelian biology, Hippocratic medicine and Platonic theurgy Eugene AFONASIN1 Abstract. In the first part of the paper, I will briefly discuss certain peculiarities of the medical profession in antiquity. In his Philosophical History (fr. 80–84 Athanassiadi) Damascius narrates about a philosopher, named Asclepiodotus, whose interests ranged from Platonic philosophy to Aristotelian natural sciences. Asclepiodotus’ instructor in medical matters, a son of a doctor from the island of Rhodos, Iacobus, is pictured by Damascius as an exemplary figure (fr. 84), who, unlike many of his contemporaries, always tested the opinions of others and gained a reputation of an extremely successful physician, although the methods of treatment, ascribed to him by Damascius, are highly reminiscent of those presented as the Pythagorean by Iamblichus (On the Pythagorean way of life 244). In this respect both Iacobus and Asclepiodotus are conformed to the best standards of medical ethics, and pass the test set by Galen in his “On examination by which the best physicians are recognized”, except perhaps by the fact that they preferred to base their activities on such authorities as Aristotle and the Methodist Soranus rather than on a list of the “dogmatists” proposed by Galen. In the second part of the paper, dedicated to the cult of Asclepius in Late Antiquity, I will look at various kinds of evidence taken from the Neoplatonic philosophers. Having discussed first the principal philosophical interpretations of Asclepius found in Apuleius, Aelianus, Macrobius, Julian, Porphyry, Iamblichus, Proclus, Damascius, etc., we turn to Proclus’ attitude to Athena and Asclepius as reflected in Marinus’ Vita Procli and finally discuss the cult of Eshmun as found in Damascius. -
Democritus (460-370 BC) on Embryology, Anatomy and Pediatrics: the Unknown Aspects of the Greek Atomic Scientist
IJAE Vol. 117, n. 3: 199-204, 2012 ITALIAN JOURNAL OF ANATOMY AND EMBRYOLOGY Research Article: History Of Anatomy and Embryology Democritus (460-370 BC) on Embryology, Anatomy and Pediatrics: the unknown aspects of the Greek atomic scientist Gregory Tsoucalas, Marianna Karamanou*, Antonis A. Kousoulis, George Androutsos History of Medicine Department, Medical School, University of Athens, Greece Submitted January 29, 2012; accepted June 17, 2012 Abstract Democritus was born in Abdera, Thrace, in the 5th century BC. He travelled to the East while being the student of famous philosophers. His philosophical ideas and the establishment of particles, “the atoms”, gave him a leading position in world history. However, his medical knowledge was vast especially in the field of pediatric pharmacology. Numerous are also the reports of his passion for anatomy. Democritus’ views regarding the issue of Human Nature and Anatomy are depicted in a letter he sent to Hippocrates of Kos. He died in old age, possi- bly of infection after having totally neglected his personal hygiene. Keywords Democritus; philosophy; atom; embryology; pediatrics; anatomy. Note: for ancient authors, citations in the text do not include the year of publication of the original writings; the reference list reports the year of publication of the critical edition which was used for this study. Introductory note and brief biography Democritus of Igisistratos or Athinocratos or Damasippos (Precope, 1961; Marcov- ich, 1999) was born in Abdera, Thrace, Greece, around the 80th Olympic Games, 460- 457 BC (Herodotus; Strabo) or earlier (Anaksagoras Klazomenios). He visited Egypt where, in the sanctuary of Memphis, he was initiated to Jewish spirituality by a sage woman named Maria.