The Antikythera Mechanism
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Archimedes of Syracuse
5 MARCH 2020 Engineering: Archimedes of Syracuse Professor Edith Hall Archimedes and Hiero II’s Syracuse Archimedes was and remains the most famous person from Syracuse, Sicily, in history. He belonged to the prosperous and sophisticated culture which the dominantly Greek population had built in the east of the island. The civilisation of the whole of ancient Sicily and South Italy was called by the Romans ‘Magna Graecia’ or ‘Great Greece’. The citis of Magna Graecia began to be annexed by the Roman Republic from 327 BCE, and most of Sicily was conquered by 272. But Syracuse, a large and magnificent kingdom, the size of Athens and a major player in the politics of the Mediterranean world throughout antiquity, succeeded in staying independent until 212. This was because its kings were allies of Rome in the face of the constant threat from Carthage. Archimedes was born into this free and vibrant port city in about 287 BCE, and as far as we know lived there all his life. When he was about twelve, the formidable Hiero II came to the throne, and there followed more than half a century of peace in the city, despite momentous power struggles going on as the Romans clashed with the Carthaginians and Greeks beyond Syracuse’s borders. Hiero encouraged arts and sciences, massively expanding the famous theatre. Archimedes’ background enabled him to fulfil his huge inborn intellectual talents to the full. His father was an astronomer named Pheidias. He was probably sent to study as a young man to Alexandria, home of the famous library, where he seems to have became close friend and correspondent of the great geographer and astonomer Eratosthenes, later to become Chief Librarian. -
A Centennial Celebration of Two Great Scholars: Heiberg's
A Centennial Celebration of Two Great Scholars: Heiberg’s Translation of the Lost Palimpsest of Archimedes—1907 Heath’s Publication on Euclid’s Elements—1908 Shirley B. Gray he 1998 auction of the “lost” palimp- tains four illuminated sest of Archimedes, followed by col- plates, presumably of laborative work centered at the Walters Matthew, Mark, Luke, Art Museum, the palimpsest’s newest and John. caretaker, remind Notices readers of Heiberg was emi- Tthe herculean contributions of two great classical nently qualified for scholars. Working one century ago, Johan Ludvig support from a foun- Heiberg and Sir Thomas Little Heath were busily dation. His stature as a engaged in virtually “running the table” of great scholar in the interna- mathematics bequeathed from antiquity. Only tional community was World War I and a depleted supply of manuscripts such that the University forced them to take a break. In 2008 we as math- of Oxford had awarded ematicians should honor their watershed efforts to him an honorary doc- make the cornerstones of our discipline available Johan Ludvig Heiberg. torate of literature in Photo courtesy of to even mathematically challenged readers. The Danish Royal Society. 1904. His background in languages and his pub- Heiberg lications were impressive. His first language was In 1906 the Carlsberg Foundation awarded 300 Danish but he frequently published in German. kroner to Johan Ludvig Heiberg (1854–1928), a He had publications in Latin as well as Arabic. But classical philologist at the University of Copenha- his true passion was classical Greek. In his first gen, to journey to Constantinople (present day Is- position as a schoolmaster and principal, Heiberg tanbul) to investigate a palimpsest that previously insisted that his students learn Greek and Greek had been in the library of the Metochion, i.e., the mathematics—in Greek. -
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. -
The Dark Shades of the Antikythera Mechanism
Journal of Radioanalytical and Nuclear Chemistry https://doi.org/10.1007/s10967-018-6255-9 (0123456789().,-volV)(0123456789().,-volV) The dark shades of the Antikythera Mechanism 1 2 3 Aristeidis Voulgaris • Christophoros Mouratidis • Andreas Vossinakis Received: 19 June 2018 Ó Akade´miai Kiado´, Budapest, Hungary 2018 Abstract In this work we analyze the dark shades which are evident on the AMRP X-ray positive Computed Tomographies and Radiographies of the Antikythera Mechanism ancient prototype. During 2000 years under the sea, the Mechanism bronze parts were totally corroded. The decreased X-ray absorption of the corroded bronze, allowed the CTs capture even in the thick large side of Fragment A. During the photometric analysis of the CTs, apart from corroded bronze, at least two other different (corroded) metal materials were detected, which were used by the ancient manufacturer during the construction of the Antikythera Mechanism. From our analysis and correlating with the mechanical evidence resulting by the use of our functional reconstruction models of the Antikythera Mechanism, we conclude that the existing design of the Antikythera Mechanism is probably the first of such a sophisticated design of the ancient manufacturer. Keywords Metals of Antikythera Mechanism Á Bronze corrosion Á Atacamite X-ray absorption Introduction Mechanism via the 2D X-ray and Thulium 170 radiation began by C. Karakalos of National Centre of Scientific The Antikythera Mechanism was found in 1901, in a Research ‘‘Demokritos’’ (Greece), in the 1970s. Karakalos shipwreck at 50 m depth, on a gulf of Antikythera island, took several film radiographies @160 keV [3]. The first Greece, by Symian sponge divers. -
Archimedes Palimpsest a Brief History of the Palimpsest Tracing the Manuscript from Its Creation Until Its Reappearance Foundations...The Life of Archimedes
Archimedes Palimpsest A Brief History of the Palimpsest Tracing the manuscript from its creation until its reappearance Foundations...The Life of Archimedes Birth: About 287 BC in Syracuse, Sicily (At the time it was still an Independent Greek city-state) Death: 212 or 211 BC in Syracuse. His age is estimated to be between 75-76 at the time of death. Cause: Archimedes may have been killed by a Roman soldier who was unaware of who Archimedes was. This theory however, has no proof. However, the dates coincide with the time Syracuse was sacked by the Roman army. The Works of Archimedes Archimedes' Writings: • Balancing Planes • Quadrature of the Parabola • Sphere and Cylinder • Spiral Lines • Conoids and Spheroids • On Floating Bodies • Measurement of a Circle • The Sandreckoner • The Method of Mechanical Problems • The Stomachion The ABCs of Archimedes' work Archimedes' work is separated into three Codeces: Codex A: Codex B: • Balancing Planes • Balancing Planes • Quadrature of the Parabola • Quadrature of the Parabola • Sphere and Cylinder • On Floating Bodies • Spiral Lines Codex C: • Conoids and Spheroids • The Method of Mechanical • Measurement of a Circle Problems • The Sand-reckoner • Spiral Lines • The Stomachion • On Floating Bodies • Measurement of a Circle • Balancing Planes • Sphere and Cylinder The Reappearance of the Palimpsest Date: On Thursday, October 29, 1998 Location: Christie's Acution House, NY Selling price: $2.2 Million Research on Palimpsest was done by Walter's Art Museum in Baltimore, MD The Main Researchers Include: William Noel Mike Toth Reviel Netz Keith Knox Uwe Bergmann Codex A, B no more Codex A and B no longer exist. -
Archimedes and Liu Hui on Circles and Spheres Joseph W
www.ontologia.net/studies Ontology Studies 10, 2010 21-38 Archimedes and Liu Hui on Circles and Spheres Joseph W. Dauben Department of History Herbert H. Lehman College and Ph.D. Program in History The Graduate Center The City University of New York Reception date / Fecha de recepción: 27-05-2009 Acceptation date / Fecha de aceptación: 22-06-2009 Abstract This article describes the mystery of a long lost codex of Archimedes that resurfaced briefly at the turn of the last century by Johan Ludwig Heiberg. Long enough for the Danish historian of mathematics Heiberg to identify, photograph and eventually transcribe “The Method” and several other works by Archimedes of considerable mathematical interest. In 1879 Heiberg completed his dissertation, Quaestiones Archimedeae, devoted to Archimedes’ life, works, and transmission of his texts. Keywords: Archimedes, Ephodos, Method, Johan Ludwig Heiberg. Resumen. Arquímedes y Hui Liu en torno a círculos y esferas. Este artículo describe el misterio de un códice de Arquímedes perdido hace mucho tiempo que reapareció brevemente a principios del siglo pasado de la mano de Johan Ludwig Heiberg. Tiempo suficiente para que el historiador danés de las matemáticas Heiberg pudiese identificar, fotografiar y, finalmente, transcribir “El Método” y varias otras obras de Arquímedes de interés matemático considerable. En 1879 Heiberg completó su tesis doctoral, Quaestiones Archimedeae, dedicado a la vida de Arquímedes, las obras, y la transmisión de sus textos. Palabras clave: Arquímedes, ephodos, método, Johan Ludwig Heiberg. This story begins with a mystery—the mystery of a long lost codex of Archimedes that resurfaced briefly at the turn of the last century, long enough for the Danish historian of mathematics Johan Ludwig Heiberg to identify, photograph and eventually transcribe “The Method” and several other works by Archimedes of considerable mathematical 22 Ontology Studies 10, 2010 Joseph W. -
Order in the Cosmos
11/12/2015 Order in the Cosmos: how Babylonians and Greeks Shaped our World 1 11/12/2015 2 11/12/2015 Two distinct periods of flowering: • Old Babylonian astronomy: during and after First Babylonian dynasty (Hammurabi) 1830‐1531 BCE • New Babylonian/Chaldean astronomy: Neo‐Babylonian (Nebuchadnezzar) 626‐539 BCE Medo‐Persian 539‐331 BCE Seleucid 335‐141 BCE Parthian 129 BCE‐224 AD timeline Babylonian astronomy Evans 1998 3 11/12/2015 Babylonian Astronomers: ∏ most consistent, systematic and thorough astronomical observers of antiquity ∑ First to recognize periodicity astronomical phenomena (e.g. eclipses !), and apply mathematical techniques for predictions ∑ Systematically observed and recorded the heavens: ‐ Records spanning many centuries (> millennium) ‐ Archives of cuneiform tablets ‐ Famous Examples: Enuma Anu Enlil 68‐70 tablets Kassite period (1650‐1150) tablet 63: Venus tablet of Ammisaduga MUL.APIN 700 BCE oldest copy: 686 BCE • Several types of astronomical texts in Babylonian astronomy. • Four principal types: 1) astronomical diaries 2) goal year texts 3) ephemerides 4) procedure texts • Ephemerides: ‐ listing of positions of planets and their meaning (eg. extreme points retrograde path) ‐ predictive: positions based on calculations (based on scheme) ‐ ephemerides for Moon ‐ ephemerides for planets • Procedure texts: description of procedure(s) to calculate ephemerides 4 11/12/2015 Old text, probably Kassite period (1595‐1157 BCE) • Amajor series of 68 or 70 tablets • dealing with Babylonian astrology. • bulk is a substantial collection of omens, estimated to number between 6500 and 7000, • interpreting a wide variety of celestial and atmospheric phenomena in terms relevant to the king and state 2. If with it a cloudbank lies on the right of the sun: the trade in barley and straw will expand. -
Pos(Antikythera & SKA)018
Building the Cosmos in the Antikythera Mechanism Tony Freeth1 Antikythera Mechanism Research Project 10 Hereford Road, South Ealing, London W54 4SE, United Kingdom E-mail: [email protected] PoS(Antikythera & SKA)018 Abstract Ever since its discovery by Greek sponge divers in 1901, the Antikythera Mechanism has inspired fascination and fierce debate. In the early years no-one knew what it was. As a result of a hundred years of research, particularly by Albert Rehm, Derek de Solla Price, Michael Wright and, most recently, by members of the Antikythera Mechanism Research Project, there has been huge progress in understanding this geared astronomical calculating machine. With its astonishing lunar anomaly mechanism, it emerges as a landmark in the history of technology and one of the true wonders of the ancient world. The latest model includes a mechanical representation of the Cosmos that exactly matches an inscription on the back cover of the instrument. We believe that we are now close to the complete machine. From Antikythera to the Square Kilometre Array: Lessons from the Ancients, Kerastari, Greece 12-15 June 2012 1 Speaker Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it Building the Cosmos in the Antikythera Mechanism Tony Freeth 1. Ancient Astronomy Astronomy? Impossible to understand and madness to investigate... Sophocles Since astronomy is so difficult, I will try to keep everything as simple as possible! As all astronomers know well, the stars are fixed! When the ancients looked at the sky, they saw a number of astronomical bodies that moved relative to the stars. -
The Antikythera Mechanism, Rhodes, and Epeiros
The Antikythera Mechanism, Rhodes, and Epeiros Paul Iversen Introduction I am particularly honored to be asked to contribute to this Festschrift in honor of James Evans. For the last nine years I have been engaged in studying the Games Dial and the calendar on the Metonic Spiral of the Antikythera Mechanism,1 and in that time I have come to admire James’s willingness to look at all sides of the evidence, and the way in which he conducts his research in an atmosphere of collaborative and curious inquiry combined with mutual respect. It has long been suggested that the Antikythera Mechanism may have been built on the is- land of Rhodes,2 one of the few locations attested in ancient literary sources associated with the production of such celestial devices. This paper will strengthen the thesis of a Rhodian origin for the Mechanism by demonstrating that the as-of-2008-undeciphered set of games in Year 4 on the Games Dial were the Halieia of Rhodes, a relatively minor set of games that were, appro- priately for the Mechanism, in honor of the sun-god, Helios (spelled Halios by the Doric Greeks). This paper will also summarize an argument that the calendar on the Metonic Spiral cannot be that of Syracuse, and that it is, contrary to the assertions of a prominent scholar in Epirote stud- ies, consistent with the Epirote calendar. This, coupled with the appearance of the extremely minor Naan games on the Games Dial, suggests that the Mechanism also had some connection with Epeiros. The Games Dial and the Halieia of Rhodes The application in the fall of 2005 of micro-focus X-ray computed tomography on the 82 surviv- ing fragments of the Antikythera Mechanism led to the exciting discovery and subsequent publi- cation in 2008 of a dial on the Antikythera Mechanism listing various athletic games now known as the Olympiad Dial (but which I will call the Games or Halieiad Dial—more on that below), as well as a hitherto unknown Greek civil calendar on what is now called the Metonic Spiral.3 I begin with my own composite drawing of the Games Dial (Fig. -
The Draconic Gearing of the Antikythera Mechanism: Assembling the Fragment D, Its Role and Operation
The Draconic gearing of the Antikythera Mechanism: Assembling the Fragment D, its role and operation A.Voulgaris1, C.Mouratidis2, A.Vossinakis3, G.Bokovos4 (Submitted 14 January 2020) 1Municipality of Thessaloniki, Directorate Culture and Tourism, Thessaloniki, GR-54625, Greece 2Hellenic Ministry of Education, Research and Religious Affairs, Kos, GR-85300, Greece 3Thessaloniki Astronomy Club, Thessaloniki, GR-54646, Greece 4Thessaloniki Science Center and Technology Museum-Planetarium, Thermi, GR-57001, Greece Abstract The unplaced Fragment D of the Antikythera Mechanism with an unknown operation was a mystery since the beginning of its discovery. The gear-r1, which was detected on the Fragment radiographies by C. Karakalos, is preserved in excellent condition, but this was not enough to correlate it to the existing gear trainings of the Mechanism. The suggestion that this gear could be a part of the hypothetical planet indication gearing is still a hypothesis since no mechanical evidence has been preserved. After the analysis of AMRP tomographies of Fragment D and its mechanical characteristics revealed that it could be part of the Draconic gearing. Although the Draconic cycle was well known during the Mechanism’s era as represents the fourth Lunar cycle, it seems that it is missing from the Antikythera Mechanism. The study of Fragment D was supported by the bronze reconstruction of the Draconic gearing by the authors. The adaptation of the Draconic gearing on the Antikythera Mechanism improves its functionality and gives answers on several questions. 1. Introduction. The Antikythera Mechanism, a geared machine based on the lunar cycles The Antikythera Mechanism a creation of an ingenious manufacturer of the Hellenistic era was a geared machine capable of performing complex astronomical calculations, mostly based on the lunar periodic cycles. -
Archimedes and the Palimpsest
http://www.mlahanas.de/Greeks/ArchimedesPal.htm Archimedes and the Palimpsest Michael Lahanas “The Method” was a work of Archimedes unknown in the Middle Ages, but the importance of which was realized after its discovery. Archimedes pioneered the use of infinitesimals, showing how by dividing a figure in an infinite number of infinitely small parts could be used to determine its area or volume. It was found in the so-called Archimedes Palimpsest. The ancient text was found in a rare 10th- century Byzantine Greek manuscript which is probably the oldest and most authentic copy of Archimedes’ major works to survive, and contains transcriptions of his writing on geometry and physics. The 174 pages of text was according to the Greek orthodox church stolen but the owners were descendants of a Frenchman who legally bought the volume in the 1920s. It was sold for $2 million at Christie’s. The manuscript was the only source for his treatise “On The Method of Mathematical Theorems” and the only known copy of the original Greek text of his work, “On Floating Bodies”. The manuscript also contains the text of his works “On The Measurement of the Circle”, “On the Sphere and the Cylinder”, “On Spiral Lines” and “On the Equilibrium of Planes”. The volume is a palimpsest, a manuscript in which pages have been written on twice. As writing material was expensive an original text could be washed off so the parchment could be reused. The upper layer of writing on the document to be auctioned contains instructions for religious rites but underneath it contains versions of Archimedes’ most celebrated Greek texts. -
The Antikythera Mechanism: the Ancient Computer That Mapped The
Sign In | Register Home Space The Antikythera Mechanism: the ancient Greek computer that mapped the stars Built over 2,000 years ago, the Antikythera mechanism calculated the movement of the Sun, Moon and planets using a system of dials and gears. 18th September, 2019 at 00:00 Imagine, in an age long before miniaturised electronics, a portable machine, the size and shape of a shoebox, that showed a moving picture of the cosmos, with the Sun, the Moon, and the planets orbiting at greatly accelerated speed, so that with a few twists of a knob, you could see where they would be in the sky on some chosen date years in the future or past. It sounds like something in a fantasy story, but the mysterious Antikythera Mechanism shows that these devices were indeed being built, over 2,000 years ago. Ad Try the Bike for 30 Days Exquisite devices like this were being crafted in a GTrey ethek w Bikorkesh forop 30 days, worry-free. somewhere in the eastern Mediterranean about 2,100 years ago or more. One of them met an unfortunate accident—for its owner, aLnEywARNay M, bOuRtE fortunate for us since from its shattered remains we can learn a great deal about ancient Greek science and its public face. The accident happened around 60 BC, off the island of Antikythera in the straits between Crete and the Peloponnese: a ship laden with bronze and marble statuary and other luxury objects, en route from the Aegean Sea to destinations in the western Mediterranean, was violently wrecked. ADVERTISING Replay inRead invented by Teads A team of Greek sponge divers discovered the shipwreck in 1900, and over the next year they salvaged what they could under the Greek government’s supervision.