IN MEMORIAM Evangelos S. Stamatis (1898-L 990)
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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 That is why we do not cite Herodotus page 66.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. -
Ancient Rhetoric and Greek Mathematics: a Response to a Modern Historiographical Dilemma
Science in Context 16(3), 391–412 (2003). Copyright © Cambridge University Press DOI: 10.1017/S0269889703000863 Printed in the United Kingdom Ancient Rhetoric and Greek Mathematics: A Response to a Modern Historiographical Dilemma Alain Bernard Dibner Institute, Boston To the memory of three days in the Negev Argument In this article, I compare Sabetai Unguru’s and Wilbur Knorr’s views on the historiography of ancient Greek mathematics. Although they share the same concern for avoiding anach- ronisms, they take very different stands on the role mathematical readings should have in the interpretation of ancient mathematics. While Unguru refuses any intrusion of mathematical practice into history, Knorr believes this practice to be a key tool for understanding the ancient tradition of geometry. Thus modern historians have to find their way between these opposing views while avoiding an unsatisfactory compromise. One approach to this, I propose, is to take ancient rhetoric into account. I illustrate this proposal by showing how rhetorical categories can help us to analyze mathematical texts. I finally show that such an approach accommodates Knorr’s concern about ancient mathematical practice as well as the standards for modern historical research set by Unguru 25 years ago. Introduction The title of the present paper indicates that this work concerns the relationship between ancient rhetoric and ancient Greek mathematics. Such a title obviously raises a simple question: Is there such a relationship? The usual appreciation of ancient science and philosophy is at odds with such an idea. This appreciation is rooted in the pregnant categorization that ranks rhetoric and science at very different levels. -
Bibliography
Bibliography Afshar, Iraj: Bibliographie des Catalogues des Manuscrits Persans. Tehran: 1958. Almagest: see Ptolemy. Apollonius: Apollonii Pergaei quae Graece exstant cum commentariis Eutocii (ed. J. L. Heiberg), 2 vols. Leipzig: 1891, 1893. Arberry, A. J. : The Chester Beatty Library, A Handlist of the Arabic Manuscripts, Vol. VII. Dublin: 1964. Archimedes: Archimedis Opera Omnia cum commentariis Eutocii, (iterum ed. J. L. Heiberg), 3 vols. Leipzig: 1910-1915. Archimedes: see also Heath. Aristarchus of Samos: On the Sizes and Distances of the Sun and Moon (ed. T. Heath). Oxford: 1913. Aristotle, Nicomachean Ethics: Aristotelis Ethica Nicomachea (ed. I. Bywater). Oxford: 1894. Aristotle, Prior Analytics: Aristotelis Analytica Priora et Posteriora (ed. W. D. Ross and L. Minio-Paluello). Oxford: 1964. Autolycus: J. Mogenet, Autolycus de Pitane. Louvain, 1950 (Universite de Louvain, Recueil de Travaux d'Histoire et de Philologie, 3e. Serie Fasc. 37). Awad, Gurgis: "Arabic Manuscripts in American Libraries". Sumer 1, 237-277 (1951). (Arabic). Bachmann, Peter: Galens Abhandlung dariiber, dal3 der vorziigliche Arzt Philosoph sein mul3. Gottingen: 1965 (Ak. Wiss. Gottingen, Nachrichten Phil. -hist. Kl. 1965.1). Belger, C.: "Ein neues Fragmentum Mathematicum Bobiense". Hermes 16, 261-84 (1881). Boilot, D. J.: "L'oeuvre d'al-Beruni, essai bibliographique". Melanges de l'Institut Dominicain d'Etudes Orientales du Caire ~, 161-256 (1955). Bretschneider, C. A.: Die Geometrie und die Geometer vor Eukleides. Leipzig: 1870. 217 Bib Ziography Brockelmann, Carl: Geschichte der Arabischen Litteratur, zweite den Supplementbanden angepasste Aunage, 2 vols. Leiden: 1943, 1949 [GAL] [and] Supplementbande I-III. Leiden: 1937, 1938, 1942 [S]. Bulmer-Thomas, I.: "Conon of Samos". Dictionary of Scientific Biography III, (New York), 391 (1971). -
A Short History of Greek Mathematics
Cambridge Library Co ll e C t i o n Books of enduring scholarly value Classics From the Renaissance to the nineteenth century, Latin and Greek were compulsory subjects in almost all European universities, and most early modern scholars published their research and conducted international correspondence in Latin. Latin had continued in use in Western Europe long after the fall of the Roman empire as the lingua franca of the educated classes and of law, diplomacy, religion and university teaching. The flight of Greek scholars to the West after the fall of Constantinople in 1453 gave impetus to the study of ancient Greek literature and the Greek New Testament. Eventually, just as nineteenth-century reforms of university curricula were beginning to erode this ascendancy, developments in textual criticism and linguistic analysis, and new ways of studying ancient societies, especially archaeology, led to renewed enthusiasm for the Classics. This collection offers works of criticism, interpretation and synthesis by the outstanding scholars of the nineteenth century. A Short History of Greek Mathematics James Gow’s Short History of Greek Mathematics (1884) provided the first full account of the subject available in English, and it today remains a clear and thorough guide to early arithmetic and geometry. Beginning with the origins of the numerical system and proceeding through the theorems of Pythagoras, Euclid, Archimedes and many others, the Short History offers in-depth analysis and useful translations of individual texts as well as a broad historical overview of the development of mathematics. Parts I and II concern Greek arithmetic, including the origin of alphabetic numerals and the nomenclature for operations; Part III constitutes a complete history of Greek geometry, from its earliest precursors in Egypt and Babylon through to the innovations of the Ionic, Sophistic, and Academic schools and their followers. -
Welcome to the Complete Pythagoras
Welcome to The Complete Pythagoras A full-text, public domain edition for the generalist & specialist Edited by Patrick Rousell for the World Wide Web. I first came across Kenneth Sylvan Guthrie’s edition of the Complete Pythagoras while researching a book on Leonardo. I had been surfing these deep waters for a while and so the value of Guthrie’s publication was immediately apparent. As Guthrie explains in his own introduction, which is at the beginning of the second book (p 168), he was initially prompted to publish these writings in the 1920’s for fear that this information would become lost. As it is, much of this information has since been published in fairly good modern editions. However, these are still hard to access and there is no current complete collection as presented by Guthrie. The advantage here is that we have a fairly comprehensive collection of works on Pythagoras and the Pythagoreans, translated from the origin- al Greek into English, and presented as a unified, albeit electronic edition. The Complete Pythagoras is a compilation of two books. The first is entitled The Life Of Py- thagoras and contains the four biographies of Pythagoras that have survived from antiquity: that of Iamblichus (280-333 A.D.), Porphry (233-306 A.D.), Photius (ca 820- ca 891 A.D.) and Diogenes Laertius (180 A.D.). The second is entitled Pythagorean Library and is a complete collection of the surviving fragments from the Pythagoreans. The first book was published in 1920, the second a year later, and released together as a bound edition. -
Pythagoras and the Pythagoreans1
Pythagoras and the Pythagoreans1 Historically, the name Pythagoras meansmuchmorethanthe familiar namesake of the famous theorem about right triangles. The philosophy of Pythagoras and his school has become a part of the very fiber of mathematics, physics, and even the western tradition of liberal education, no matter what the discipline. The stamp above depicts a coin issued by Greece on August 20, 1955, to commemorate the 2500th anniversary of the founding of the first school of philosophy by Pythagoras. Pythagorean philosophy was the prime source of inspiration for Plato and Aristotle whose influence on western thought is without question and is immeasurable. 1 c G. Donald Allen, 1999 ° Pythagoras and the Pythagoreans 2 1 Pythagoras and the Pythagoreans Of his life, little is known. Pythagoras (fl 580-500, BC) was born in Samos on the western coast of what is now Turkey. He was reportedly the son of a substantial citizen, Mnesarchos. He met Thales, likely as a young man, who recommended he travel to Egypt. It seems certain that he gained much of his knowledge from the Egyptians, as had Thales before him. He had a reputation of having a wide range of knowledge over many subjects, though to one author as having little wisdom (Her- aclitus) and to another as profoundly wise (Empedocles). Like Thales, there are no extant written works by Pythagoras or the Pythagoreans. Our knowledge about the Pythagoreans comes from others, including Aristotle, Theon of Smyrna, Plato, Herodotus, Philolaus of Tarentum, and others. Samos Miletus Cnidus Pythagoras lived on Samos for many years under the rule of the tyrant Polycrates, who had a tendency to switch alliances in times of conflict — which were frequent. -
Too Many Metrodoruses? the Compiler of the Ἀριθμητικά from AP XIV
Grillo, F. (2019) Too many Metrodoruses? The compiler of the ἀριθμητικά from AP XIV. Eikasmós, 30, pp. 249-264. There may be differences between this version and the published version. You are advised to consult the publisher’s version if you wish to cite from it. http://eprints.gla.ac.uk/204331/ Deposited on: 29 November 2019 Enlighten – Research publications by members of the University of Glasgow http://eprints.gla.ac.uk This is the author’s accepted manuscript. Please refer to the published journal article as follows: Grillo, F. (2019) ‘Too many Metrodoruses? The compiler of the ἀριθμητικά from AP XIV’, Eikasmós 30: 249-264. For the published version, see http://www2.classics.unibo.it/eikasmos/index.php?page=schedasingola&schedavis=1572 1 Too many Metrodoruses? The compiler of the ἀριθμητικά from AP XIV* In book fourteen of the Palatine Anthology we find a number of arithmetic problems (1-4, 6f., 11-13, 48-51, 116-147), the vast majority provided with mathematical scholia1. Most of the poems are attributed to a certain Metrodorus (116-146; cf. lemma to 116 Μητροδώρου ἐπιγράμματα ἀριθμητικά)2, a shadowy figure whose original collection comprised also problems 2f., 6f. and possibly 11-133. The identity of Metrodorus has received some attention, especially in late eighteenth- and nineteenth-century scholarship, but some crucial evidence has been repeatedly overlooked or misconstrued. Moreover, despite recent discussions, the question still remains unsettled, and it is unclear whether Metrodorus limited himself to compiling his collection or whether he also authored some poems4. Either way, a broad terminus post quem (or, less probably, ad quem) for his activity is provided by the epigram about the life-span of Diophantus (AP XIV 126), whose date is uncertain, but who is traditionally supposed to have lived in the mid- to late third century AD5. -
A History of Elementary Mathematics, with Hints on Methods of Teaching
;-NRLF I 1 UNIVERSITY OF CALIFORNIA PEFARTMENT OF CIVIL ENGINEERING BERKELEY, CALIFORNIA Engineering Library A HISTORY OF ELEMENTARY MATHEMATICS THE MACMILLAN COMPANY NEW YORK BOSTON CHICAGO DALLAS ATLANTA SAN FRANCISCO MACMILLAN & CO., LIMITED LONDON BOMBAY CALCUTTA MELBOURNE THE MACMILLAN CO. OF CANADA, LTD. TORONTO A HISTORY OF ELEMENTARY MATHEMATICS WITH HINTS ON METHODS OF TEACHING BY FLORIAN CAJORI, PH.D. PROFESSOR OF MATHEMATICS IN COLORADO COLLEGE REVISED AND ENLARGED EDITION THE MACMILLAN COMPANY LONDON : MACMILLAN & CO., LTD. 1917 All rights reserved Engineering Library COPYRIGHT, 1896 AND 1917, BY THE MACMILLAN COMPANY. Set up and electrotyped September, 1896. Reprinted August, 1897; March, 1905; October, 1907; August, 1910; February, 1914. Revised and enlarged edition, February, 1917. o ^ PREFACE TO THE FIRST EDITION "THE education of the child must accord both in mode and arrangement with the education of mankind as consid- ered in other the of historically ; or, words, genesis knowledge in the individual must follow the same course as the genesis of knowledge in the race. To M. Comte we believe society owes the enunciation of this doctrine a doctrine which we may accept without committing ourselves to his theory of 1 the genesis of knowledge, either in its causes or its order." If this principle, held also by Pestalozzi and Froebel, be correct, then it would seem as if the knowledge of the history of a science must be an effectual aid in teaching that science. Be this doctrine true or false, certainly the experience of many instructors establishes the importance 2 of mathematical history in teaching. With the hope of being of some assistance to my fellow-teachers, I have pre- pared this book and have interlined my narrative with occasional remarks and suggestions on methods of teaching. -
Women in Early Pythagoreanism
Women in Early Pythagoreanism Caterina Pellò Faculty of Classics University of Cambridge Clare Hall February 2018 This dissertation is submitted for the degree of Doctor of Philosophy Alla nonna Ninni, che mi ha insegnato a leggere e scrivere Abstract Women in Early Pythagoreanism Caterina Pellò The sixth-century-BCE Pythagorean communities included both male and female members. This thesis focuses on the Pythagorean women and aims to explore what reasons lie behind the prominence of women in Pythagoreanism and what roles women played in early Pythagorean societies and thought. In the first chapter, I analyse the social conditions of women in Southern Italy, where the first Pythagorean communities were founded. In the second chapter, I compare Pythagorean societies with ancient Greek political clubs and religious sects. Compared to mainland Greece, South Italian women enjoyed higher legal and socio-political status. Similarly, religious groups included female initiates, assigning them authoritative roles. Consequently, the fact that the Pythagoreans founded their communities in Croton and further afield, and that in some respects these communities resembled ancient sects helps to explain why they opened their doors to the female gender to begin with. The third chapter discusses Pythagoras’ teachings to and about women. Pythagorean doctrines did not exclusively affect the followers’ way of thinking and public activities, but also their private way of living. Thus, they also regulated key aspects of the female everyday life, such as marriage and motherhood. I argue that the Pythagorean women entered the communities as wives, mothers and daughters. Nonetheless, some of them were able to gain authority over their fellow Pythagoreans and engage in intellectual activities, thus overcoming the female traditional domestic roles. -
The Project Gutenberg Ebook #31061: a History of Mathematics
The Project Gutenberg EBook of A History of Mathematics, by Florian Cajori This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: A History of Mathematics Author: Florian Cajori Release Date: January 24, 2010 [EBook #31061] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK A HISTORY OF MATHEMATICS *** Produced by Andrew D. Hwang, Peter Vachuska, Carl Hudkins and the Online Distributed Proofreading Team at http://www.pgdp.net transcriber's note Figures may have been moved with respect to the surrounding text. Minor typographical corrections and presentational changes have been made without comment. This PDF file is formatted for screen viewing, but may be easily formatted for printing. Please consult the preamble of the LATEX source file for instructions. A HISTORY OF MATHEMATICS A HISTORY OF MATHEMATICS BY FLORIAN CAJORI, Ph.D. Formerly Professor of Applied Mathematics in the Tulane University of Louisiana; now Professor of Physics in Colorado College \I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history."|J. W. L. Glaisher New York THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., Ltd. 1909 All rights reserved Copyright, 1893, By MACMILLAN AND CO. Set up and electrotyped January, 1894. Reprinted March, 1895; October, 1897; November, 1901; January, 1906; July, 1909. Norwood Pre&: J. S. Cushing & Co.|Berwick & Smith. -
Bibliography
Bibliography A. Aaboe, Episodes from the Early History of Mathematics (Random House, New York, 1964) A.D. Aczel, Fermat’s Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem (Four Walls Eight Windows, New York, 1996) D. Adamson, Blaise Pascal: Mathematician, Physicist, and Thinker About God (St. Martin’s Press, New York, 1995) R.P. Agarwal, H. Agarwal, S.K. Sen, Birth, Growth and Computation of Pi to ten trillion digits. Adv. Differ. Equat. 2013, 100 (2013) A.A. Al-Daffa’, The Muslim Contribution to Mathematics (Humanities Press, Atlantic Highlands, 1977) A.A. Al-Daffa’, J.J. Stroyls, Studies in the Exact Sciences in Medieval Islam (Wiley, New York, 1984) E.J. Aiton, Leibniz: A Biography (A. Hilger, Bristol, Boston, 1984) R.E. Allen, Greek Philosophy: Thales to Aristotle (The Free Press, New York, 1966) G.J. Allman, Greek Geometry from Thales to Euclid (Arno Press, New York, 1976) E.N. da C. Andrade, Sir Issac Newton, His Life and Work (Doubleday & Co., New York, 1954) W.S. Anglin, Mathematics: A Concise History and Philosophy (Springer, New York, 1994) W.S. Anglin, The Queen of Mathematics (Kluwer, Dordrecht, 1995) H.D. Anthony, Sir Isaac Newton (Abelard-Schuman, New York, 1960) H.G. Apostle, Aristotle’s Philosophy of Mathematics (The University of Chicago Press, Chicago, 1952) R.C. Archibald, Outline of the history of mathematics.Am. Math. Monthly 56 (1949) B. Artmann, Euclid: The Creation of Mathematics (Springer, New York, 1999) C.N. Srinivasa Ayyangar, The History of Ancient Indian Mathematics (World Press Private Ltd., Calcutta, 1967) A.K. Bag, Mathematics in Ancient and Medieval India (Chaukhambha Orientalia, Varanasi, 1979) W.W.R. -
Wisdom» –Neopythagoreans and Others?
AIMS Mathematics, 1(2): 77-95 DOI: 10.3934/Math.2016.2.77 Received: 29 March 2016 Accepted: 8 April 2016 Published: 17 May 2016 http://www.aimspress.com/journal/Math Research article Which kind of mathematics was known and referred to by those who wanted to integrate mathematics in «Wisdom» –Neopythagoreans and others? Jens Høyrup* Section for philosophy and Science Studies, Roskilde University, Denmark * Correspondence: Email: [email protected]. Abstract: Plato, so the story goes, held mathematics in high esteem, and those philosopher-kings that ought to rule his republic should have a thorough foundation in mathematics. This may well be true – but an observation made by Aristotle suggests that the mathematics which Plato intends is not the one based on theorems and proofs which we normally identify with “Greek mathematics”. Most other ancient writers who speak of mathematics as a road toward Wisdom also appear to be blissfully ignorant of the mathematics of Euclid, Archimedes, Apollonios, etc. – though not necessarily of their names. The aim of the paper is to identify the kinds of mathematics which were available as external sources for this current (on the whole leaving out of consideration Liberal-Arts mathematics as not properly external). A number of borrowings can be traced to various practitioners' traditions – but always as bits borrowed out of context. Keywords: Ancient Greek mathematics; Neopythagoreans; Plato; Practitioners' mathematics; Recreational mathematics; Side-and-diagonal-numbers algorithm Contents Remarks about Plato