Theory and Didactic in Olympiodorus and the Alexandrian School: A

Total Page:16

File Type:pdf, Size:1020Kb

Theory and Didactic in Olympiodorus and the Alexandrian School: A Mnemosyne (2021) 341-353 brill.com/mnem Review Article ∵ Theory and Didactic in Olympiodorus and the Alexandrian School A Discussion of Two New Translations Albert Joosse Dept. of Philosophy and Religious Studies, Utrecht University, Utrecht, The Netherlands [email protected] Received July 2020 | Accepted July 2020 Abstract This review article considers two recent Italian and English translations of works by Olympiodorus of Alexandria and his immediate successors (sixth century ce). These translations make accessible to a wider audience a number of works that help us un- derstand a transitional period in the history of thought. This review takes a closer look at some of the substantive views expressed by the translators and evaluates editorial and translation choices. We should beware of exaggerating the differences between these sixth-century philosophers, this review argues, while recognizing that there may be considerable distance between what they thought and what the surviving texts show. Keywords Olympiodorus – Elias – David – commentary – prolegomena © Albert Joosse, 2020 | doi:10.1163/1568525X-bja10065 This is an open access article distributed under the terms of the CC BY 4.0Downloaded license. from Brill.com10/05/2021 12:21:50PM via free access 342 Joosse Francesca Filippi. Olimpiodoro d’Alessandria. Tutti i commentari a Platone. Introduzione, traduzione, testo greco a fronte e note. (2 vols). Sankt Augustin, Academia Verlag, 2017. lxxviii, 390; lxxvi, 504 pp. Pr. € 65,00. ISBN 9783896656841; 9783896656858. Sebastian Gertz. Elias and David. ‘Introductions to Philosophy’ with Olympiodorus: ‘Introduction to Logic’. London, Bloomsbury, 2018. viii, 257 pp. Pr. £ 85,00. ISBN 9781350051744. 1 Entering a Transitional Period Francesca Filippi’s two-volume Italian translation with notes of Olympiodorus’ Platonic works and Sebastian Gertz’ English translation of three introductory works from sixth-century Alexandria help make this transitory period in the history of philosophy more accessible. The transition is still insufficiently understood. It is a transition to philosophical traditions—Armenian, Syriac, Byzantine, Arabic—that require more investigation. And while the philosoph- ical era from which it derives has received intensifying scrutiny, the relations of sixth-century philosophy and earlier thinkers remain debated. This time of transition itself, however, also needs to be examined for its own character.1 Filippi’s and Gertz’ work helps this effort. Filippi (hereafter: F.) translates Olympiodorus’ commentaries on the Platonic dialogues First Alcibiades, Gorgias, and Phaedo, as well as the Prolegomena to Plato’s Philosophy, which she claims should be credited to Olympiodorus. Gertz (hereafter: G.) translates Elias’ and David’s respective Introductions to Philosophy (as he translates the Prolegomena) and Olympiodorus’ Introduction to Logic (Prolegomena logica). Both authors have contributed to the study of late ancient Neoplatonism in earlier work, F. with a monograph on Proclus’ commentary on the First Alcibiades (2012), G. with his book on Olympiodorus’ and Damascius’ commentaries on the Phaedo (2011). In addition to its value as a translation, F.’s work also develops a substantive view of Olympiodorus’ place in the history of philosophy that is a welcome contribution to the dis- cussion among Neoplatonic scholars. G.’s volume, an addition to the Ancient Commentators on Aristotle series, has no such aim but nevertheless gives us a good sense of the importance to the Alexandrians of the business of introduc- ing students to ancient thought. 1 For an argument that stresses the status aparte of the sixth century see Perkams 2017, 22-28. MnemosyneDownloaded from74 (2021)Brill.com10/05/2021 341-353 12:21:50PM via free access Olympiodorus and the Alexandrian School 343 2 Olympiodorus: The Last Neoplatonist? Introducing the œuvre of Olympiodorus, F. proposes to read it as testimony of a phase of consolidation and expansion in the Neoplatonic school. She surveys negative valuations of the philosophical quality of Olympiodorus’ œuvre and more recent insistence on the importance of the didactic reasons behind a less speculative and ontological orientation of his commentaries. According to F., recent studies share two features: a concern to defend Olympiodorus from the criticisms of previous generations and the tendency to measure Olympiodorus’ philosophical quality by the similarity between his works and those of his Athenian predecessors (vol. 1, xvii). However, she argues, this dou- ble agenda risks obscuring our view of Olympiodorus’ own contribution on his own terms. More specifically, she warns against the assumption to see a tight connection between theoretical similarity between Olympiodorus and Proclus and a similarity in their works, so that divergences from the Proclan model in the type of commentary Olympiodorus writes are signs of theoreti- cal divergence (vol. 1, xviii). But this, she argues, mistakes the logic of the de- velopment of the Neoplatonic school. In any school, we can discern a phase of theoretical innovation and one of consolidation and expansion. We should recognise Olympiodorus as a consolidator. In the phase of consolidation, the school seeks to fit the theoretical novelties into the cultural environment by in- tegrating what is compatible with them in other cultural traditions, by refuting what is incompatible with them, and by maximizing the explanatory power of the terms used in communicating these ideas. Had the socio-political circum- stances not been such as to put an end to pagan teaching in Alexandria, F. sub- mits, the sixth century would have constituted the high point of Neoplatonism in late antiquity (vol. 1, xix). In her discussion of the socio-political circumstances, which make them- selves felt particularly in the Gorgias commentary (vol. 2, xvi), F. weighs in on the debate on the event that we know as the closure of the Athenian Academy (vol. 1, xxiii-xxix) as well as on the conditions in Alexandria itself (vol. 1, xxix- xxxvi). On the Athenian side, F. considers to be mistaken the interpretation that ties the closure of the school mainly to the provincial authorities and that sees a pushback against magic and soothsaying behind the triad of ‘philoso- phy, astronomy and dice’ in the law, as reported by Malalas, that leads to the ban on philosophy in Athens (Chronicle 18.47).2 Banning dice would have been 2 The whole passage reads: Ἐπὶ δὲ τῆς ὑπατείας τοῦ αὐτοῦ Δεκίου ὁ αὐτὸς βασιλεὺς θεσπίσας πρόσ­ ταξιν ἔπεμψεν ἐν Ἀθήναις, κελεύσας μηδένα διδάσκειν φιλοσοφίαν μήτε ἀστρονομίαν [Thurn; νόμιμα Dindorf] ἐξηγεῖσθαι μήτε κόττον ἐν μιᾷ τῶν πόλεων γίνεσθαι (‘During the consulship of Mnemosyne 74 (2021) 341-353 Downloaded from Brill.com10/05/2021 12:21:50PM via free access 344 Joosse motivated by anti-gambling convictions anyway (as happened elsewhere and later). Moreover, F. argues, we should resist the preference for ἀστρονομία over νόμιμα that is necessary for this interpretation (as accepted by Thurn, Malalas’ most recent editor). There is much to say in favour of νόμιμα: it was part of Justinian’s push to be the sole legal authority that independent exegeses of the law were prohibited (F. ties this to closures of legal schools in Alexandria, Rome, Caesarea etc.). So it makes sense to think the Athenian law included the prohibition of νόμιμα ἐξηγεῖσθαι. Finally, Thurn’s reading, which is based on a parallel from a very different context (vol. 1, xxvii), does not deliver what is needed, F. argues. In the sixth century, ἀστρονομία and ἀστρολογία were kept separate (F. adduces Ol. In Mete. 19.20-27 Stüve as—convincing—evidence).3 For F., then, philosophical teaching was indeed the target of imperial legisla- tion. F. develops a plausible case,4 although not one most at home in a book on Olympiodorus. F.’s treatment of the situation of the Alexandrian school goes back a long way to describe the setup of the Alexandrian school in previous centuries (vol. 1, xxix-xxx), and even to reference the statements and works about Christians of Aelius Aristides, Celsus and Porphyry (vol. 1, xxx-xxxii). She rightly concen- trates on an event or arrangement that is likely to have had major implications for philosophers in the following decades: with pagan philosophers caught in the spotlight of an imperial investigation in the late 480s, Olympiodorus’ teacher Ammonius and the bishop of Alexandria (Petrus Mongus, most likely) came to an agreement that allowed Ammonius to continue teaching. F. de- scribes two rival reconstructions of events: on the one hand, the theory that Ammonius adapted his teaching to make it unobjectionable to the Christians, and on the other hand the theory that Ammonius collaborated and to a degree betrayed his former colleagues. F. argues that in the absence of more evidence we should accept a synthesis of both interpretations. This is somewhat disap- pointing, since the evidence for such a middle position is not better than for either of the rival theories. Whatever the circumstances, it seems likely that Olympiodorus was the last major pagan philosopher of ancient Alexandria, as F. firmly insists. In his own lectures, Olympiodorus took the presence of Christian students into account. He goes out of his way in his Gorgias commentary, for instance, to reassure Decius, the emperor issued a decree and sent it to Athens ordering that no one should teach philosophy nor interpret astronomy [/the laws] nor in any city should there be lots cast using dice’, tr. Watts, mod.). Note that, contrary to what F. implies, both νόμιμα and ἀστρονομίαν have MS support. 3 A similar passage: Simpl. in Ph. 293.10-15. 4 For an alternative interpretation see e.g. Watts 2006, 128-138. MnemosyneDownloaded from74 (2021)Brill.com10/05/2021 341-353 12:21:50PM via free access Olympiodorus and the Alexandrian School 345 them that they should not be disturbed when they hear of pagan myths. At no time, F. argues, did this detract from his commitment to pagan philosophy. But the very next generation of teachers was no longer pagan.
Recommended publications
  • The History of Egypt Under the Ptolemies
    UC-NRLF $C lb EbE THE HISTORY OF EGYPT THE PTOLEMIES. BY SAMUEL SHARPE. LONDON: EDWARD MOXON, DOVER STREET. 1838. 65 Printed by Arthur Taylor, Coleman Street. TO THE READER. The Author has given neither the arguments nor the whole of the authorities on which the sketch of the earlier history in the Introduction rests, as it would have had too much of the dryness of an antiquarian enquiry, and as he has already published them in his Early History of Egypt. In the rest of the book he has in every case pointed out in the margin the sources from which he has drawn his information. » Canonbury, 12th November, 1838. Works published by the same Author. The EARLY HISTORY of EGYPT, from the Old Testament, Herodotus, Manetho, and the Hieroglyphieal Inscriptions. EGYPTIAN INSCRIPTIONS, from the British Museum and other sources. Sixty Plates in folio. Rudiments of a VOCABULARY of EGYPTIAN HIEROGLYPHICS. M451 42 ERRATA. Page 103, line 23, for Syria read Macedonia. Page 104, line 4, for Syrians read Macedonians. CONTENTS. Introduction. Abraham : shepherd kings : Joseph : kings of Thebes : era ofMenophres, exodus of the Jews, Rameses the Great, buildings, conquests, popu- lation, mines: Shishank, B.C. 970: Solomon: kings of Tanis : Bocchoris of Sais : kings of Ethiopia, B. c. 730 .- kings ofSais : Africa is sailed round, Greek mercenaries and settlers, Solon and Pythagoras : Persian conquest, B.C. 525 .- Inarus rebels : Herodotus and Hellanicus : Amyrtaus, Nectanebo : Eudoxus, Chrysippus, and Plato : Alexander the Great : oasis of Ammon, native judges,
    [Show full text]
  • Water, Air and Fire at Work in Hero's Machines
    Water, air and fire at work in Hero’s machines Amelia Carolina Sparavigna Dipartimento di Fisica, Politecnico di Torino Corso Duca degli Abruzzi 24, Torino, Italy Known as the Michanikos, Hero of Alexandria is considered the inventor of the world's first steam engine and of many other sophisticated devices. Here we discuss three of them as described in his book “Pneumatica”. These machines, working with water, air and fire, are clear examples of the deep knowledge of fluid dynamics reached by the Hellenistic scientists. Hero of Alexandria, known as the Mechanicos, lived during the first century in the Roman Egypt [1]. He was probably a Greek mathematician and engineer who resided in the city of Alexandria. We know his work from some of writings and designs that have been arrived nowadays in their Greek original or in Arabic translations. From his own writings, it is possible to gather that he knew the works of Archimedes and of Philo the Byzantian, who was a contemporary of Ctesibius [2]. It is almost certain that Heron taught at the Museum, a college for combined philosophy and literary studies and a religious place of cult of Muses, that included the famous Library. For this reason, Hero claimed himself a pupil of Ctesibius, who was probably the first head of the Museum of Alexandria. Most of Hero’s writings appear as lecture notes for courses in mathematics, mechanics, physics and pneumatics [2]. In optics, Hero formulated the Principle of the Shortest Path of Light, principle telling that if a ray of light propagates from a point to another one within the same medium, the followed path is the shortest possible.
    [Show full text]
  • The Mechanical Problems in the Corpus of Aristotle
    University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Faculty Publications, Classics and Religious Studies Department Classics and Religious Studies July 2007 The Mechanical Problems in the Corpus of Aristotle Thomas Nelson Winter University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/classicsfacpub Part of the Classics Commons Winter, Thomas Nelson, "The Mechanical Problems in the Corpus of Aristotle" (2007). Faculty Publications, Classics and Religious Studies Department. 68. https://digitalcommons.unl.edu/classicsfacpub/68 This Article is brought to you for free and open access by the Classics and Religious Studies at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Faculty Publications, Classics and Religious Studies Department by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Th e Mechanical Problems in the Corpus of Aristotle Th omas N. Winter Lincoln, Nebraska • 2007 Translator’s Preface. Who Wrote the Mechanical Problems in the Aristotelian Corpus? When I was translating the Mechanical Problems, which I did from the TLG Greek text, I was still in the fundamentalist authorship mode: that it survives in the corpus of Aristotle was then for me prima facie Th is paper will: evidence that Aristotle was the author. And at many places I found in- 1) off er the plainest evidence yet that it is not Aristotle, and — 1 dications that the date of the work was apt for Aristotle. But eventually, 2) name an author. I saw a join in Vitruvius, as in the brief summary below, “Who Wrote Th at it is not Aristotle does not, so far, rest on evidence.
    [Show full text]
  • From Ancient Greece to Byzantium
    Proceedings of the European Control Conference 2007 TuA07.4 Kos, Greece, July 2-5, 2007 Technology and Autonomous Mechanisms in the Mediterranean: From Ancient Greece to Byzantium K. P. Valavanis, G. J. Vachtsevanos, P. J. Antsaklis Abstract – The paper aims at presenting each period are then provided followed by technology and automation advances in the accomplishments in automatic control and the ancient Greek World, offering evidence that transition from the ancient Greek world to the Greco- feedback control as a discipline dates back more Roman era and the Byzantium. than twenty five centuries. II. CHRONOLOGICAL MAP OF SCIENCE & TECHNOLOGY I. INTRODUCTION It is worth noting that there was an initial phase of The paper objective is to present historical evidence imported influences in the development of ancient of achievements in science, technology and the Greek technology that reached the Greek states from making of automation in the ancient Greek world until the East (Persia, Babylon and Mesopotamia) and th the era of Byzantium and that the main driving force practiced by the Greeks up until the 6 century B.C. It behind Greek science [16] - [18] has been curiosity and was at the time of Thales of Miletus (circa 585 B.C.), desire for knowledge followed by the study of nature. when a very significant change occurred. A new and When focusing on the discipline of feedback control, exclusively Greek activity began to dominate any James Watt’s Flyball Governor (1769) may be inherited technology, called science. In subsequent considered as one of the earliest feedback control centuries, technology itself became more productive, devices of the modern era.
    [Show full text]
  • Table of Contents More Information
    Cambridge University Press 978-0-521-76376-9 - The Mechanical Hypothesis in Ancient Greek Natural Philosophy Sylvia Berryman Table of Contents More information Contents List of illustrations page vii Acknowledgements viii Introduction 1 1 Mechanics and the mechanical: some problems of terminology 9 The critics of prevailing usage 11 Some candidate definitions of the ‘mechanistic’ 15 2 ‘Mechanistic’ thought before mechanics? 21 Divine versus human technology 24 Working artifacts before the fourth century 29 Ancient atomism and the machine analogy 34 The ‘shortfalls’ of ancient technology 39 The ‘exclusion’ of ancient mechanics 43 3 Mechanics in the fourth century 54 The scope of ancient Greek mechanics 55 Archytas and the foundation of mechanics 87 Aristotle’s ‘mechanics’ of motion 97 Conclusion 104 4 The theory and practice of ancient Greek mechanics 105 The Aristotelian Mechanica 106 Ctesibius 115 Archimedes 117 Philo of Byzantium 123 v © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-76376-9 - The Mechanical Hypothesis in Ancient Greek Natural Philosophy Sylvia Berryman Table of Contents More information vi Contents Vitruvius 130 Hero of Alexandria 134 Pappus of Alexandria 143 Models of the heavens 146 5 Ancient Greek mechanics continued: the case of pneumatics 155 Pneumatic technology in the post-classical period 157 Ancient Greek pneumatic theory 165 The status of mechanics revisited: natural or artificial? 170 6 The philosophical reception of mechanics in antiquity 177 Mechanical theory in natural philosophy 179 The theory of pneumatics in natural philosophy 191 Pneumatics and medical theory 197 Working artifacts and the notion of a self-mover 201 Mechanical analogies for the functioning of organisms 205 Working artifacts in astronomy 216 Mechanical analogies in cosmology 220 Conclusion 231 Appendix: Ancient mechanics and the mechanical in the seventeenth century 236 Bibliography 250 Index of passages 274 General index 282 © Cambridge University Press www.cambridge.org.
    [Show full text]
  • Queen Arsinoë II, the Maritime Aphrodite and Early Ptolemaic Ruler Cult
    ΑΡΣΙΝΟΗ ΕΥΠΛΟΙΑ Queen Arsinoë II, the Maritime Aphrodite and Early Ptolemaic Ruler Cult Carlos Francis Robinson Bachelor of Arts (Hons. 1) A thesis submitted for the degree of Master of Philosophy at The University of Queensland in 2019 Historical and Philosophical Inquiry Abstract Queen Arsinoë II, the Maritime Aphrodite and Early Ptolemaic Ruler Cult By the early Hellenistic period a trend was emerging in which royal women were deified as Aphrodite. In a unique innovation, Queen Arsinoë II of Egypt (c. 316 – 270 BC) was deified as the maritime Aphrodite, and was associated with the cult titles Euploia, Akraia, and Galenaië. It was the important study of Robert (1966) which identified that the poets Posidippus and Callimachus were honouring Arsinoë II as the maritime Aphrodite. This thesis examines how this new third-century BC cult of ‘Arsinoë Aphrodite’ adopted aspects of Greek cults of the maritime Aphrodite, creating a new derivative cult. The main historical sources for this cult are the epigrams of Posidippus and Callimachus, including a relatively new epigram (Posidippus AB 39) published in 2001. This thesis demonstrates that the new cult of Arsinoë Aphrodite utilised existing traditions, such as: Aphrodite’s role as patron of fleets, the practice of dedications to Aphrodite by admirals, the use of invocations before sailing, and the practice of marine dedications such as shells. In this way the Ptolemies incorporated existing religious traditions into a new form of ruler cult. This study is the first attempt to trace the direct relationship between Ptolemaic ruler cult and existing traditions of the maritime Aphrodite, and deepens our understanding of the strategies of ruler cult adopted in the early Hellenistic period.
    [Show full text]
  • 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.
    [Show full text]
  • 6 X 10. Three Lines .P65
    Cambridge University Press 978-0-521-83746-0 - Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King Carl A. Huffman Index More information Select index of Greek words and phrases discussed in the text delf»v/delf, 64, 123, 125, 154 galnh, 66, 75, 491, 494–500, 504–05, 515 kanqa, 341 gr, 122–23 ll»triov, 194–95 gewmetrw, 567 nagka©wv, 396 gewmetrik, 232–33, 244 ndocov, 39–40 gewmetrik»v, 244 na©sqhtov, 449 nakmptw, 538 de»menoi, 217–18 naklw, 476–77 dicr»nou , 291 nakÅptw, 322 diagignÛskw, 58–59, 149–51 nalog©a, 179–81, 503, 529–37, 538; toÓ ­sou, diagnÛmen, xiv, 149 529–37 dignwsiv, 58–59, 149–51 nlogon, 179 digramma, 396, 566 namon, 291 d©aita, partn d©aitan , 300–01 nastrof, 123, 155 diallttw, 215 nepistmwn, 193–94 disthma, 166–67, 169, 181, 458 n»moiov, tn»moia , 436, 441–43 diatrib, 228–32 ntere©dw, 561 dunmenoi, 217–18 ntreisma, 297 dÅnamiv, 446 nt©lhyiv, 451 dusmcanov, 79, 348, 375, 379 nÛmalov, 513–15 nwmal»thv, 513 gg©gnomai, 539 »ristov, 511 e²dov, 93, 123, 226, 238, 250–51, 567; pqeia, 600, 603 (prÛtiston), 122 pantizw, 113, 156 e«kÛn, 601 planv, 542–43 kle©pw, 247 podeiktikäv, 375, 379 mp»diov, 335 p»deixiv, 71, 232, 237–38, mfusw, 113, 160 248–49 n aÉt, 222 podcomai, 503–04 nant©ov, 445 porov, 195 nargv, 71, 233, 236–37, 238, 246–47 pofrssw, 160 narm»zw, 351 riqmhtik, 240–44 xeur©skw, 193, 195, 196–200, 202 rmon©a, tperª tn rmon©an , 565 peiskwmzw, 314, 322 rc, 358, 500, 502, 598 piqumhtik»v, 93 rc kaª mhtr»poliv, 69 p©stamai, 196–200 %rcÅtav, 619 pistmwn, 193–94 stronomik»v, 244 pistthv, 389 aÎxh, 80, 386 pitelw, 72, 237–38, 247, 249 aÉt¼v fa, 55 pitmnw, 587 stÛ, 96 banausourg©a, 380 scatov oÉran»v, 87 638 © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83746-0 - Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King Carl A.
    [Show full text]
  • What the World Would Be Without Inventions?
    What the world would be without inventions? GREEK INVENTORS THROUGH TIME “The introduction of noble inventions seems to hold by far the most excellent place among human actions” ~ Francis Bacon 7 Greek inventors through time • Archimides • Euclid • Pythagoras • Thucydides • Ctesibius of Alexandria • Constantin Carathéodory • George Papanikolaou Archimides, the great mathematician and inventor of the “Archimides principle” GREEK INVENTORS I Archimedes of Syracuse (Ancient Greek: Ἀρχιμήδης [ar.kʰi.mɛː.dɛ̂ːs]; c . 287 – c. 212 BC) was a Greek mathematician, physicist, en gineer, inventor, and astronomer. He is regarded as one of the leading scientists in classical antiquity. Considered to be the greatest mathematician of ancient history, and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including: the area of a circle; the surface area and volume of a sphere; area of an ellipse; the area under a parabola; the volume of a segment of a paraboloid of revolution; the volume of a segment of a hyperboloid of revolution; and the area of a spiral. His other mathematical achievements include deriving an accurate approximation of pi; defining and investigating the spiral that now bears his name; and creating a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics, including an explanation of the principle of the lever. He is credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.
    [Show full text]
  • Hess-2021-7.Pdf
    https://doi.org/10.5194/hess-2021-7 Preprint. Discussion started: 12 January 2021 c Author(s) 2021. CC BY 4.0 License. From mythology to science: the development of scientific hydrological concepts in the Greek antiquity and its relevance to modern hydrology Demetris Koutsoyiannis* and Nikos Mamassis Department of Water Resources and Environmental Engineering, School of Civil Engineering, National Technical 5 University of Athens, Heroon Polytechneiou 5, GR 157 80 Zographou, Greece * Corresponding author: [email protected] Abstract. Whilst hydrology is a Greek term, it has not been in use in the Classical literature but much later, during the Renaissance, in its Latin version, hydrologia. On the other hand, Greek natural philosophers created robust knowledge in related scientific areas, to which they gave names such as meteorology, climate and hydraulics. These terms are now in 10 common use internationally. Within these areas, Greek natural philosophers laid the foundation of hydrological concepts and the hydrological cycle in its entirety. Knowledge development was brought about by search for technological solutions to practical problems, as well as by scientific curiosity to explain natural phenomena. While initial explanations belong to the sphere of mythology, the rise of philosophy was accompanied by attempts to provide scientific descriptions of the phenomena. It appears that the first geophysical problem formulated in scientific terms was the explanation of the flood regime of the Nile, 15 then regarded as a paradox because of the spectacular difference from the river flow regime in Greece and other Mediterranean regions, i.e., the fact that the Nile flooding occurs in summer when in most of the Mediterranean the rainfall is very low.
    [Show full text]
  • Technē and Method in Ancient Artillery Construction: the Belopoeica of Philo of Byzantium
    Mark J. Schiefsky Technē and Method in Ancient Artillery Construction: The Belopoeica of Philo of Byzantium Abstract: In his Belopoeica, Philo of Byzantium presents artillery construction (belopoiikē) as a kind of expertise or technē that possesses a standardized meth- od for attaining success. I describe this method, which consists of a set of pro- cedures and rules that are systematically organized on the basis of general prin- ciples, and discuss Philo’s claim that its discovery depended crucially on experience (peira). In the second part of the Belopoeica Philo presents several designs for artillery engines that allegedly improve on the standard method. I discuss these designs, which draw on both natural philosophy and theoretical mechanics, and conclude with a brief attempt to place Philo’s picture of artillery construction as a technē involving both experience and theory in the context of roughly contemporary views of technē in philosophy and medicine. Introduction From the fourth century b.c. to the end of Antiquity, the discipline of artillery construction (belopoiikē) was one of the most important and highly developed types of professional expertise (technē) in the ancient Greco-Roman world.¹ Start- ing from the traditional bow, Greek engineers devised a wide array of mechanical shooting devices, weapons which had a significant impact on the course of his- tory. The development of this technology was fostered by royal patronage and carried out by communities of practitioners working in major cultural and polit- ical centers such as Alexandria and Rhodes. These practitioners had a high sense As is well known, the Greek term technē has no single English equivalent.
    [Show full text]
  • Ancient Greek Mathēmata from a Sociological Perspective
    Ancient Greek Mathēmata from a Sociological Perspective: A Quantitative Analysis Leonid Zhmud, Institute for the History of Science and Technology, St. Petersburg Alexei Kouprianov, National Research University–Higher School of Economics, St. Petersburg Abstract: This essay examines the quantitative aspects of Greco-Roman science, represented by a group of established disciplines that since the fourth century B.C.E. had been called mathēmata or mathēmatikai epistēmai. Among the mathēmata, which in antiquity normally comprised mathematics, mathematical astronomy, harmonics, mechanics, and optics, the essay also includes geography. Using a data set based on The Encyclopaedia of Ancient Natural Scientists, it considers a com- munity of mathēmatikoi (as they called themselves), or ancient scientists (as they are defined for the purposes of this essay), from a sociological point of view, fo- cusing on the size of the scientific population known to us and its disciplinary, temporal, and geographical distribution. A diachronic comparison of neighboring and partly overlapping communities—ancient scientists and philosophers—allows the pattern of their interrelationship to be traced. An examination of centers of sci- ence throughout ancient history reveals that there were five major sites—Athens, Al- exandria, Rhodes, Rome, and Byzantium/Constantinople—that appeared, in suc- cession, as leaders. These conclusions serve to reopen the issue of the place of mathēmata and mathēmatikoi in ancient society. he historiography of ancient Greek science is nearly as old as its subject. The earliest T known writings on the history of mathematics and astronomy belong to Eudemus of Rhodes, a pupil of Aristotle. When, after a long period of decline and oblivion in medieval Europe, the sciences were revived, it was ancient Greek science that became the primary sub- ject of Renaissance and early modern studies in the history of science.
    [Show full text]