Aestimatio: Critical Reviews in the History of Science
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Enthymema XXIII 2019 the Technê of Aratus' Leptê Acrostich
Enthymema XXIII 2019 The Technê of Aratus’ Leptê Acrostich Jan Kwapisz University of Warsaw Abstract – This paper sets out to re-approach the famous leptê acrostich in Aratus’ Phaenomena (783-87) by confronting it with other early Greek acrostichs and the discourse of technê and sophia, which has been shown to play an important role in a gamut of Greek literary texts, including texts very much relevant for the study of Aratus’ acrostich. In particular, there is a tantalizing connection between the acrostich in Aratus’ poem that poeticized Eudoxus’ astronomical work and the so- called Ars Eudoxi, a (pseudo-)Eudoxian acrostich sphragis from a second-century BC papyrus. Keywords – Aratus; Eudoxus; Ars Eudoxi; Acrostichs; Hellenistic Poetry; Technê; Sophia. Kwapisz, Jan. “The Technê of Aratus’ Leptê Acrostich.” Enthymema, no. XXIII, 2019, pp. 374-89. http://dx.doi.org/10.13130/2037-2426/11934 https://riviste.unimi.it/index.php/enthymema Creative Commons Attribution 4.0 Unported License ISSN 2037-2426 The Technê of Aratus’ Leptê Acrostich* Jan Kwapisz University of Warsaw To the memory of Cristiano Castelletti (1971-2017) Λεπτὴ μὲν καθαρή τε περὶ τρίτον ἦμαρ ἐοῦσα εὔδιός κ’ εἴη, λεπτὴ δὲ καὶ εὖ μάλ’ ἐρευθὴς πνευματίη· παχίων δὲ καὶ ἀμβλείῃσι κεραίαις 785 τέτρατον ἐκ τριτάτοιο φόως ἀμενηνὸν ἔχουσα ἠὲ νότου ἀμβλύνετ’ ἢ ὕδατος ἐγγὺς ἐόντος. (Arat. 783-87) If [the Moon is] slender and clear about the third day, she will bode fair weather; if slender and very red, wind; if the crescent is thickish, with blunted horns, having a feeble fourth-day light after the third day, either it is blurred by a southerly or because rain is in the offing. -
Glossary Glossary
Glossary Glossary Albedo A measure of an object’s reflectivity. A pure white reflecting surface has an albedo of 1.0 (100%). A pitch-black, nonreflecting surface has an albedo of 0.0. The Moon is a fairly dark object with a combined albedo of 0.07 (reflecting 7% of the sunlight that falls upon it). The albedo range of the lunar maria is between 0.05 and 0.08. The brighter highlands have an albedo range from 0.09 to 0.15. Anorthosite Rocks rich in the mineral feldspar, making up much of the Moon’s bright highland regions. Aperture The diameter of a telescope’s objective lens or primary mirror. Apogee The point in the Moon’s orbit where it is furthest from the Earth. At apogee, the Moon can reach a maximum distance of 406,700 km from the Earth. Apollo The manned lunar program of the United States. Between July 1969 and December 1972, six Apollo missions landed on the Moon, allowing a total of 12 astronauts to explore its surface. Asteroid A minor planet. A large solid body of rock in orbit around the Sun. Banded crater A crater that displays dusky linear tracts on its inner walls and/or floor. 250 Basalt A dark, fine-grained volcanic rock, low in silicon, with a low viscosity. Basaltic material fills many of the Moon’s major basins, especially on the near side. Glossary Basin A very large circular impact structure (usually comprising multiple concentric rings) that usually displays some degree of flooding with lava. The largest and most conspicuous lava- flooded basins on the Moon are found on the near side, and most are filled to their outer edges with mare basalts. -
Alexander Jones Calendrica I: New Callippic Dates
ALEXANDER JONES CALENDRICA I: NEW CALLIPPIC DATES aus: Zeitschrift für Papyrologie und Epigraphik 129 (2000) 141–158 © Dr. Rudolf Habelt GmbH, Bonn 141 CALENDRICA I: NEW CALLIPPIC DATES 1. Introduction. Callippic dates are familiar to students of Greek chronology, even though up to the present they have been known to occur only in a single source, Ptolemy’s Almagest (c. A.D. 150).1 Ptolemy’s Callippic dates appear in the context of discussions of astronomical observations ranging from the early third century B.C. to the third quarter of the second century B.C. In the present article I will present new attestations of Callippic dates which extend the period of the known use of this system by almost two centuries, into the middle of the first century A.D. I also take the opportunity to attempt a fresh examination of what we can deduce about the Callippic calendar and its history, a topic that has lately been the subject of quite divergent treatments. The distinguishing mark of a Callippic date is the specification of the year by a numbered “period according to Callippus” and a year number within that period. Each Callippic period comprised 76 years, and year 1 of Callippic Period 1 began about midsummer of 330 B.C. It is an obvious, and very reasonable, supposition that this convention for counting years was instituted by Callippus, the fourth- century astronomer whose revisions of Eudoxus’ planetary theory are mentioned by Aristotle in Metaphysics Λ 1073b32–38, and who also is prominent among the authorities cited in astronomical weather calendars (parapegmata).2 The point of the cycles is that 76 years contain exactly four so-called Metonic cycles of 19 years. -
The Magic of the Atwood Sphere
The magic of the Atwood Sphere Exactly a century ago, on June Dr. Jean-Michel Faidit 5, 1913, a “celestial sphere demon- Astronomical Society of France stration” by Professor Wallace W. Montpellier, France Atwood thrilled the populace of [email protected] Chicago. This machine, built to ac- commodate a dozen spectators, took up a concept popular in the eigh- teenth century: that of turning stel- lariums. The impact was consider- able. It sparked the genesis of modern planetariums, leading 10 years lat- er to an invention by Bauersfeld, engineer of the Zeiss Company, the Deutsche Museum in Munich. Since ancient times, mankind has sought to represent the sky and the stars. Two trends emerged. First, stars and constellations were easy, especially drawn on maps or globes. This was the case, for example, in Egypt with the Zodiac of Dendera or in the Greco-Ro- man world with the statue of Atlas support- ing the sky, like that of the Farnese Atlas at the National Archaeological Museum of Na- ples. But things were more complicated when it came to include the sun, moon, planets, and their apparent motions. Ingenious mecha- nisms were developed early as the Antiky- thera mechanism, found at the bottom of the Aegean Sea in 1900 and currently an exhibi- tion until July at the Conservatoire National des Arts et Métiers in Paris. During two millennia, the human mind and ingenuity worked constantly develop- ing and combining these two approaches us- ing a variety of media: astrolabes, quadrants, armillary spheres, astronomical clocks, co- pernican orreries and celestial globes, cul- minating with the famous Coronelli globes offered to Louis XIV. -
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. -
Theme 4: from the Greeks to the Renaissance: the Earth in Space
Theme 4: From the Greeks to the Renaissance: the Earth in Space 4.1 Greek Astronomy Unlike the Babylonian astronomers, who developed algorithms to fit the astronomical data they recorded but made no attempt to construct a real model of the solar system, the Greeks were inveterate model builders. Some of their models—for example, the Pythagorean idea that the Earth orbits a celestial fire, which is not, as might be expected, the Sun, but instead is some metaphysical body concealed from us by a dark “counter-Earth” which always lies between us and the fire—were neither clearly motivated nor obviously testable. However, others were more recognisably “scientific” in the modern sense: they were motivated by the desire to describe observed phenomena, and were discarded or modified when they failed to provide good descriptions. In this sense, Greek astronomy marks the birth of astronomy as a true scientific discipline. The challenges to any potential model of the movement of the Sun, Moon and planets are as follows: • Neither the Sun nor the Moon moves across the night sky with uniform angular velocity. The Babylonians recognised this, and allowed for the variation in their mathematical des- criptions of these quantities. The Greeks wanted a physical picture which would account for the variation. • The seasons are not of uniform length. The Greeks defined the seasons in the standard astronomical sense, delimited by equinoxes and solstices, and realised quite early (Euctemon, around 430 BC) that these were not all the same length. This is, of course, related to the non-uniform motion of the Sun mentioned above. -
Aristarchus of Samos and Graeco-Babylonian Astronomy George Huxley
Arfstarchus of Samos and Graeco-Babylonian Astronomy Huxley, George Greek, Roman and Byzantine Studies; Summer 1964; 5, 2; ProQuest pg. 123 Aristarchus of Samos and Graeco-Babylonian Astronomy George Huxley N THE HALF CENTURY following the death of Alexander the Great the I history of astronomy amongst the Greeks is dominated by Aris tarchus the Samian, who is best known for his theory of the earth's revolution about the sun. His life cannot be dated exactly, but it is clear that he was already of mature age by 280 B.C., for Ptolemy states that "the men around Aristarchus," that is to say his pupils, observed the summer solstice in that year, the 50th of the first Callippic period [Ptolemy, Almagest 3.1]. He was a pupil of Strato the Lampsacene, who succeeded Theophrastus as head of the Lyceum in ca. 288/7 B.C. [Apollodorus 244 F 40] and remained in that post for eighteen years till his death not later than 269 B.C. [Apollodorus 244 F 350]. The date of the publication of Aristarchus's heliocentric theory is not known, but the doctrine was attacked by Cleanthes the Stoic land so must have been well known by 232 B.C., when Cleanthes died; but the helio centric hypothesis may have been formulated much earlier than that. Vitruvius spoke highly of the versatility of Aristarchus in geometry, astronomy, and music [De Architectura 1.1.16], and ascribes to him the invention of two kinds of sundial-the hemispherical uKac/>T} and the disc in the plane [9.8.1].2 He perhaps made use of these improved instruments in his observations of the solstices. -
The Phenomena and Diosemeia of Aratus
LIBRARY OF CONGRESS 0002035357^ Qass-TA 3 87 3 " Book- A £ 4 164-8 THE PHENOMENA AND DIOSEMEIA A RAT US $3r(ntetr at tije SEniDersttj $ress. 4 \ : THE PHENOMENA AND DIOSEMEIA OF ARATUS, TRANSLATED INTO ENGLISH VERSE, WITH NOTES, BY JOHN LAMB, D.D. MASTER OF CORPUS CHRISTI COLLEGE, CAMBRIDGE, AND DEAN OF BRISTOL. UavO' 'Hyrjcnava^ re kcli 'Epfiimros ra Kar aldprjv Tetpea, Kai 7roXXot ravra cpaivo/xeva Bt/3Xois iyKaredevTO' aixoaKOTTioL §' dcpapaprow AAAA TO AEIITOAOrOY 2KHHTPON APAT02 EXEI. LONDON JOHN W. PARKER, WEST STRAND. M.DCCC.XLVIII. Page 40, line 200, for Cythia read Cynthia. THE LIFE OF ARATUS, WHEN Cilicia, in the days of Cicero*, boasted of being the birth-place of the Poet Aratus, there was reserved for her a far higher honour, the giving birth to one of the noblest of mankind, if true nobility consist in the power of benefiting the human race, and in the exercise of that power to the greatest extent by the most unexampled self-denial. Soli, the native city of Aratus, was not far distant from Tarsus, the birth-place of St Paul; and the fame of the heathen Poet has been considerably enhanced by a passage from his writings having been quoted by his countryman, the christian Apostle. One biographer indeed states that Aratus was a native of Tarsus, and he is occasionally called Tarsensis; but the more probable opinion is, that he was born at Soli, and he is commonly called Solensis. The date of his birth is about 260 years before the Christian sera. The names of his parents were Athedonorus and Letophila, they were persons of some conse- * Cicero was Proconsul of Cilicia a. -
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Cicero Among the Stars: Natural Philosophy and Astral Culture at Rome Ashley Ariel Simone Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy under the Executive Committee of the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2020 © 2020 Ashley A. Simone All Rights Reserved ABSTRACT Cicero Among the Stars: Natural Philosophy and Astral Culture at Rome Ashley Ariel Simone This dissertation examines Cicero’s contribution to the rise of astronomy and astrology in the literary and cultural milieu of the late Republic and early Empire. Chapter One, “Rome’s Star Poet,” examines how Cicero conceives of world building through words to connect Rome to the stars with the Latin language. Through a close study of the Aratea, I consider how Cicero’s pioneering of Latin astronomical language influenced other writers, especially his contemporaries Lucretius and Catullus. In Chapter Two, “The Stars and the Statesman,” I examine Cicero’s attitudes towards politics. By analyzing Scipio’s Dream and astronomy in De re publica, I show how Cicero uses cosmic models to yoke Rome to the stars. To understand the astral dimensions of Cicero’s philosophy, in Chapter Three, “Signs and Stars, Words and Worlds,” I provide a close reading of Cicero’s poetic quotations in context in the De natura deorum and De divinatione to show how Cicero puts the Aratean cosmos to the test in Academic fashion. Ultimately, I argue that Cicero profoundly shaped the Roman view of the stars and cemented the link between cosmos and empire. -
The Antikythera Shipwreck and Sinope's Culture During The
The Antikythera Shipwreck and Sinope’s Culture during the Mithridatic Wars Attilio Mastrocinque During the last years my curiosity has been kept alive by the research of Giovanni Pastore, a great expert in engineering, who has studied all the possibilities of an instrument, which was found in the shipwreck of Anti- kythera.1 This instrument is a box into which a series of 31 gear wheels have been placed in order to make astronomic calculations with a precision and of a complication that one had thought could only be attained in modern times.2 In the 1950’s D. de Solla Price studied this machine and reached the conclusion that it was a sort of clock, which had been adjusted in about 80 BC.3 He put forward the hypothesis that two boards existed on the main surfaces. On the first side pointers indicated the placement of both the Sun and the Moon in the Zodiac, and on the other side other astrological conjunc- tions were shown. The pointers were moved by means of a driving wheel or handle. Michael T. Wright has recently put forward new results for the instrument, noting that it was more complex than was previously thought, since it is not complete and we do not know how many pieces are missing.4 According to his reconstruction, the first side of the instrument was used to indicate the motion of the Sun, probably following the heliocentric theory of Aristarchos, and the motion of other planets. The opposite clock-face was perhaps a year calculator, which gave equivalences between the Egyptian year and other calendars and allowed the calculations of eclipses. -
Hipparchus's Table of Chords
ApPENDIX 1 Hipparchus's Table of Chords The construction of this table is based on the facts that the chords of 60° and 90° are known, that starting from chd 8 we can calculate chd(180° - 8) as shown by Figure Al.1, and that from chd S we can calculate chd ~8. The calculation of chd is goes as follows; see Figure Al.2. Let the angle AOB be 8. Place F so that CF = CB, place D so that DOA = i8, and place E so that DE is perpendicular to AC. Then ACD = iAOD = iBOD = DCB making the triangles BCD and DCF congruent. Therefore DF = BD = DA, and so EA = iAF. But CF = CB = chd(180° - 8), so we can calculate CF, which gives us AF and EA. Triangles AED and ADC are similar; therefore ADIAE = ACIDA, which implies that AD2 = AE·AC and enables us to calculate AD. AD is chd i8. We can now find the chords of 30°, 15°, 7~0, 45°, and 22~0. This gives us the chords of 150°, 165°, etc., and eventually we have the chords of all R P chord 8 = PQ, C chord (180 - 8) = QR, QR2 = PR2 _ PQ2. FIGURE A1.l. 235 236 Appendix 1. Hipparchus's Table of Chords Ci"=:...-----""----...........~A FIGURE A1.2. multiples of 71°. The table starts: 2210 10 8 2 30° 45° 522 chd 8 1,341 1,779 2,631 3,041 We find the chords of angles not listed and angles whose chords are not listed by linear interpolation. For example, the angle whose chord is 2,852 is ( 2,852 - 2,631 1)0 . -
The Aratus Latinus and Revised Aratus Latinus (Aratus Latinus Recensio Interpolata)
The Aratus latinus and Revised Aratus latinus (Aratus latinus recensio interpolata) Some time during the Alexandrian age, a number of related Greek texts started to appear alongside the original Greek version of the Phaenomena of Aratus to form a new astronomical corpus.1 These appended texts included some spurious prefaces, various versions of the life of the poet, one or two lists of constellations attributed to Eratosthenes and Hipparchus and discussions of the constellations as they appear on the sphere. This compilation also included abbreviated versions of the catasteristic myths associated with each constellation and descriptions of the shapes of the individual constellations with disposition of the stars within each figure. Some of these texts are associated with an astronomical treatise attributed to Eratosthenes (ca. 276 BC– ca. 195 BC), the details of which are described in the section on pseudo-Eratosthenes. The Alexandrian compilation seems to have been extremely popular across the Graeco-Roman world, appearing in several different formats with varying additions and subtractions and serving as the inspiration for numerous authors and poets in both languages. A definitive version of the Aratean corpus, with a set group of texts ordered in a particular fashion, appears to have come together some time between the beginning of the 2nd and end of the 3rd century AD. No complete version of this compilation, 1. The best scholarly work on this complicated subject can be found in MARTIN 1956, esp. pp. 69 ff. 1 which philologists usually refer to as ‘Φ’, has survived, but its contents have been largely reconstructed by combining a number of the later Greek and Latin fragments that formed a part or were derived from the original version of the original grouping of texts.