Order in the Cosmos
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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. -
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. -
Apollonius of Pergaconics. Books One - Seven
APOLLONIUS OF PERGACONICS. BOOKS ONE - SEVEN INTRODUCTION A. Apollonius at Perga Apollonius was born at Perga (Περγα) on the Southern coast of Asia Mi- nor, near the modern Turkish city of Bursa. Little is known about his life before he arrived in Alexandria, where he studied. Certain information about Apollonius’ life in Asia Minor can be obtained from his preface to Book 2 of Conics. The name “Apollonius”(Apollonius) means “devoted to Apollo”, similarly to “Artemius” or “Demetrius” meaning “devoted to Artemis or Demeter”. In the mentioned preface Apollonius writes to Eudemus of Pergamum that he sends him one of the books of Conics via his son also named Apollonius. The coincidence shows that this name was traditional in the family, and in all prob- ability Apollonius’ ancestors were priests of Apollo. Asia Minor during many centuries was for Indo-European tribes a bridge to Europe from their pre-fatherland south of the Caspian Sea. The Indo-European nation living in Asia Minor in 2nd and the beginning of the 1st millennia B.C. was usually called Hittites. Hittites are mentioned in the Bible and in Egyptian papyri. A military leader serving under the Biblical king David was the Hittite Uriah. His wife Bath- sheba, after his death, became the wife of king David and the mother of king Solomon. Hittites had a cuneiform writing analogous to the Babylonian one and hi- eroglyphs analogous to Egyptian ones. The Czech historian Bedrich Hrozny (1879-1952) who has deciphered Hittite cuneiform writing had established that the Hittite language belonged to the Western group of Indo-European languages [Hro]. -
The Almagest
Alma College The Alma, MI 48801 Almagest The bi-weekly newsletter of the Department of Mathematics and Computer Science. Your trusted source for news. Volume 9 No. 4 October 24, 2016 Math & C.S. Colloquium pportionment is a mathematical way to round A integers proportionally. Although well known to determine how many seats each state receives in the U.S. House of Representatives, apportionment methods are also used in the U.S. presidential primaries and the general election. In this talk, Dr. Michael Jones will Why Call it “The Almagest?” examine the geometry of two types of paradoxical behavior ctually, the name of our newsletter was that may occur in these A borrowed from an astronomical handbook settings, using real data when published around 150 A.D. The author was appropriate. We’ll also touch on some recent Claudius Ptolemy, an Egyptian astronomer, mathe- proposed laws and how they would affect the matician, and geographer of Greek descent. paradoxical behavior. Dr. Jones is an Associate Almagest came in thirteen volumes and proclaimed Editor at the American Mathe-matical Society's Mathematical Reviews in Ann Arbor, MI. that the universe was geocentric—the Earth was the middle of the universe. That, however, is not “The Mathematics of Apportionment in what most interests a mathematician about U.S. Presidential Primaries and the Almagest. Of more importance to us is the lost mathematical work that it displays. General Election” Presenter: Dr. Michael Jones Hipparchus was a Greek astronomer and mathema- Date: Tuesday, November 1st tician whose work dates to about three centuries Time: 4:00 prior to Ptolemy’s. -
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. -
The Adaptation of Babylonian Methods in Greek Numerical Astronomy
FIgure 1. A Babylonian tablet (B.M. 37236) listing undated phases of Mars according to the System A scheme. By permission of the Trustees of the British Museum. This content downloaded from 128.122.149.96 on Thu, 04 Jul 2019 12:50:19 UTC All use subject to https://about.jstor.org/terms The Adaptation of Babylonian Methods in Greek Numerical Astronomy By Alexander Jones* THE DISTINCTION CUSTOMARILY MADE between the two chief astro- nomical traditions of antiquity is that Greek astronomy was geometrical, whereas Babylonian astronomy was arithmetical. That is to say, the Babylonian astronomers of the last five centuries B.C. devised elaborate combinations of arithmetical sequences to predict the apparent motions of the heavenly bodies, while the Greeks persistently tried to explain the same phenomena by hypothe- sizing kinematic models compounded out of circular motions. This description is substantially correct so far as it goes, but it conceals a great difference on the Greek side between the methods of, say, Eudoxus in the fourth century B.C. and those of Ptolemy in the second century of our era. Both tried to account for the observed behavior of the stars, sun, moon, and planets by means of combinations of circular motions. But Eudoxus seems to have studied the properties of his models purely through the resources of geometry. The only numerical parameters associated with his concentric spheres in our ancient sources are crude periods of synodic and longitudinal revolution, that is to say, data imposed on the models rather than deduced from them.1 By contrast, Ptolemy's approach in the Alma- 2 gest is thoroughly numerical. -
The Two Earths of Eratosthenes Author(S): Christián Carlos Carman and James Evans Source: Isis, Vol
University of Puget Sound Sound Ideas All Faculty Scholarship Faculty Scholarship 3-2015 The woT Earths of Eratosthenes James Evans University of Puget Sound, [email protected] Christián Carlos Carman Buenos Aires, Argentina Follow this and additional works at: http://soundideas.pugetsound.edu/faculty_pubs Citation Christián C. Carman and James Evans, “The wT o Earths of Eratosthenes,” Isis 106 (2015), 1-16. This Article is brought to you for free and open access by the Faculty Scholarship at Sound Ideas. It has been accepted for inclusion in All Faculty Scholarship by an authorized administrator of Sound Ideas. For more information, please contact [email protected]. The Two Earths of Eratosthenes Author(s): Christián Carlos Carman and James Evans Source: Isis, Vol. 106, No. 1 (March 2015), pp. 1-16 Published by: The University of Chicago Press on behalf of The History of Science Society Stable URL: http://www.jstor.org/stable/10.1086/681034 . Accessed: 08/12/2015 15:41 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The University of Chicago Press and The History of Science Society are collaborating with JSTOR to digitize, preserve and extend access to Isis. -
A Modern Almagest an Updated Version of Ptolemy’S Model of the Solar System
A Modern Almagest An Updated Version of Ptolemy’s Model of the Solar System Richard Fitzpatrick Professor of Physics The University of Texas at Austin Contents 1 Introduction 5 1.1 Euclid’sElementsandPtolemy’sAlmagest . ......... 5 1.2 Ptolemy’sModeloftheSolarSystem . ..... 5 1.3 Copernicus’sModeloftheSolarSystem . ....... 10 1.4 Kepler’sModeloftheSolarSystem . ..... 11 1.5 PurposeofTreatise .................................. .. 12 2 Spherical Astronomy 15 2.1 CelestialSphere................................... ... 15 2.2 CelestialMotions ................................. .... 15 2.3 CelestialCoordinates .............................. ..... 15 2.4 EclipticCircle .................................... ... 17 2.5 EclipticCoordinates............................... ..... 18 2.6 SignsoftheZodiac ................................. ... 19 2.7 Ecliptic Declinations and Right Ascenesions. ........... 20 2.8 LocalHorizonandMeridian ............................ ... 20 2.9 HorizontalCoordinates.............................. .... 23 2.10 MeridianTransits .................................. ... 24 2.11 Principal Terrestrial Latitude Circles . ......... 25 2.12 EquinoxesandSolstices. ....... 25 2.13 TerrestrialClimes .................................. ... 26 2.14 EclipticAscensions .............................. ...... 27 2.15 AzimuthofEclipticAscensionPoint . .......... 29 2.16 EclipticAltitudeandOrientation. .......... 30 3 Dates 63 3.1 Introduction...................................... .. 63 3.2 Determination of Julian Day Numbers . .... 63 4 Geometric -
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. -
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 Origins of Mathematical Physics: New Light on an Old Question
PMI Ciência: Mitos, Histórias e Factos Arquímedes Referência: http://www.aip.org/pt/june00/origins.htm The Origins of Mathematical Physics: New Light on an Old Question A recently resurfaced tenth century manuscript, the Archimedes Palimpsest, includes the sole extant copy of Archimedes’s treatise, the Method. As scholars begin study, new insights into Archimedes are emerging. -- Reviel Netz Imagine that you have to start science from scratch. … the Archimedes manuscript has been overwritten Upon what disciplines should you draw? Philosophy, by a twelfth century prayer book. (Palimpsestos is the for instance, discusses the nature of time, space, and Greek word for rescraped, or overwritten, parchment.) reality. Religion, too, tries to make sense of the world Work is only just beginning on uncovering and as a whole; and so, sometimes, does literature. Several studying the original text. Many scholars in the field disciplines—for example, biology and medicine—deal hope we are near a much better understanding of with special and highly significant features of the Archimedes. I have looked at the palimpsest, and I world. Such are the most natural ways to begin believe this hope is well founded. In this article, I thinking about the world, and, in fact, most cultures delineate some of Archimedes’s originality, give an make sense of their world through a combination of example of the new information the Archimedes such intellectual resources. Mathematics, in Palimpsest may provide us, and I suggest, tentatively, comparison, appears like a non-starter. Here is a theory what Archimedes’s mathematical physics may have dealing with abstract objects, aiming at internal meant.