The Library of Alexandria
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Lecture 9 Hellenistic Kingdoms Chronology
Lecture 9 Hellenistic Kingdoms Chronology: Please see the timeline and browse this website: http://www.metmuseum.org/toah/hd/haht/hd_haht.htm Star Terms: Geog. Terms: Ptolemy II Philadelphos Alexandria (Egypt) Apollonius of Rhodes Pergamon (Pergamum) The Museon of Alexandria Antioch The Pharos Lighthouse Red Sea Idylls of Theocritus A. Altar of Zeus (Pergamon, Turkey), c. 175 BCE Attalos I and the Gauls/ gigantomachy/ Pergamon in Asia Minor/high relief/ violent movement Numismatics/ “In the Great Altar of Zeus erected at Pergamon, the Hellenistic taste for emotion, energetic movement, and exaggerated musculature is translated into relief sculpture. The two friezes on the altar celebrated the city and its superiority over the Gauls, who were a constant threat to the Pergamenes. Inside the structure, a small frieze depicted the legendary founding of Pergamon. In 181 BCE Eumenes II had the enormous altar “built on a hill above the city to commemorate the victory of Rome and her allies over Antiochos III the Great of Syria at the Battle of Magnesia (189 BCE) a victory that had given Eumenes much of the Seleucid Empire. A large part of the sculptural decoration has been recovered, and the entire west front of the monument, with the great flight of stairs leading to its entrance, has been reconstructed in Berlin, speaking to the colonial trend of archaeological imperialism of the late 19th century. Lecture 9 Hellenistic Kingdoms B. Dying Gaul, Roman copy of a bronze original from Pergamon, c. 230-220 BCE, marble theatrical moving, and noble representations of an enemy/ pathos/ physical depiction of Celts/Gauls This sculpture is from a monument commemorating the victory in 230 BCE of Attalos I (ruled 241-197 BCE) over the Gauls, a Celtic people who invaded from the north. -
Greeks Doing Algebra
Greeks Doing Algebra There is a long-standing consensus in the history of mathematics that geometry came from ancient Greece, algebra came from medieval Persia, and the two sciences did not meet until seventeenth-century France (e.g. Bell 1945). Scholars agree that the Greek mathematicians had no methods comparable to algebra before Diophantus (3rd c. CE) or, many hold, even after him (e.g. Szabó 1969, Unguru and Rowe 1981, Grattan-Guinness 1996, Vitrac 2005. For a survey of arguments see Blåsjö 2016). The problems that we would solve with algebra, the Greeks, especially the authors of the canonical and most often studied works (such as Euclid and Apollonius of Perga), approached with spatial geometry or not at all. This paper argues, however, that the methods which uniquely characterize algebra, such as information compression, quantitative abstraction, and the use of unknowns, do in fact feature in Greek mathematical works prior to Diophantus. We simply have to look beyond the looming figures of Hellenistic geometry. In this paper, we shall examine three instructive cases of algebraic problem-solving methods in Greek mathematical works before Diophantus: The Sand-reckoner of Archimedes, the Metrica of Hero of Alexandria, and the Almagest of Ptolemy. In the Sand-reckoner, Archimedes develops a system for expressing extremely large numbers, in which the base unit is a myriad myriad. His process is indefinitely repeatable, and theoretically scalable to express a number of any size. Simple though it sounds to us, this bit of information compression, by which a cumbersome quantity is set to one in order to simplify notation and computation, is a common feature of modern mathematics but was almost alien to the Greeks. -
Champ Math Study Guide Indesign
Champions of Mathematics — Study Guide — Questions and Activities Page 1 Copyright © 2001 by Master Books, Inc. All rights reserved. This publication may be reproduced for educational purposes only. BY JOHN HUDSON TINER To get the most out of this book, the following is recommended: Each chapter has questions, discussion ideas, research topics, and suggestions for further reading to improve students’ reading, writing, and thinking skills. The study guide shows the relationship of events in Champions of Mathematics to other fields of learning. The book becomes a springboard for exploration in other fields. Students who enjoy literature, history, art, or other subjects will find interesting activities in their fields of interest. Parents will find that the questions and activities enhance their investments in the Champion books because children of different age levels can use them. The questions with answers are designed for younger readers. Questions are objective and depend solely on the text of the book itself. The questions are arranged in the same order as the content of each chapter. A student can enjoy the book and quickly check his or her understanding and comprehension by the challenge of answering the questions. The activities are designed to serve as supplemental material for older students. The activities require greater knowledge and research skills. An older student (or the same student three or four years later) can read the book and do the activities in depth. CHAPTER 1 QUESTIONS 1. A B C D — Pythagoras was born on an island in the (A. Aegean Sea B. Atlantic Ocean C. Caribbean Sea D. -
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. -
15 Famous Greek Mathematicians and Their Contributions 1. Euclid
15 Famous Greek Mathematicians and Their Contributions 1. Euclid He was also known as Euclid of Alexandria and referred as the father of geometry deduced the Euclidean geometry. The name has it all, which in Greek means “renowned, glorious”. He worked his entire life in the field of mathematics and made revolutionary contributions to geometry. 2. Pythagoras The famous ‘Pythagoras theorem’, yes the same one we have struggled through in our childhood during our challenging math classes. This genius achieved in his contributions in mathematics and become the father of the theorem of Pythagoras. Born is Samos, Greece and fled off to Egypt and maybe India. This great mathematician is most prominently known for, what else but, for his Pythagoras theorem. 3. Archimedes Archimedes is yet another great talent from the land of the Greek. He thrived for gaining knowledge in mathematical education and made various contributions. He is best known for antiquity and the invention of compound pulleys and screw pump. 4. Thales of Miletus He was the first individual to whom a mathematical discovery was attributed. He’s best known for his work in calculating the heights of pyramids and the distance of the ships from the shore using geometry. 5. Aristotle Aristotle had a diverse knowledge over various areas including mathematics, geology, physics, metaphysics, biology, medicine and psychology. He was a pupil of Plato therefore it’s not a surprise that he had a vast knowledge and made contributions towards Platonism. Tutored Alexander the Great and established a library which aided in the production of hundreds of books. -
Alexander's Empire
4 Alexander’s Empire MAIN IDEA WHY IT MATTERS NOW TERMS & NAMES EMPIRE BUILDING Alexander the Alexander’s empire extended • Philip II •Alexander Great conquered Persia and Egypt across an area that today consists •Macedonia the Great and extended his empire to the of many nations and diverse • Darius III Indus River in northwest India. cultures. SETTING THE STAGE The Peloponnesian War severely weakened several Greek city-states. This caused a rapid decline in their military and economic power. In the nearby kingdom of Macedonia, King Philip II took note. Philip dreamed of taking control of Greece and then moving against Persia to seize its vast wealth. Philip also hoped to avenge the Persian invasion of Greece in 480 B.C. TAKING NOTES Philip Builds Macedonian Power Outlining Use an outline to organize main ideas The kingdom of Macedonia, located just north of Greece, about the growth of had rough terrain and a cold climate. The Macedonians were Alexander's empire. a hardy people who lived in mountain villages rather than city-states. Most Macedonian nobles thought of themselves Alexander's Empire as Greeks. The Greeks, however, looked down on the I. Philip Builds Macedonian Power Macedonians as uncivilized foreigners who had no great A. philosophers, sculptors, or writers. The Macedonians did have one very B. important resource—their shrewd and fearless kings. II. Alexander Conquers Persia Philip’s Army In 359 B.C., Philip II became king of Macedonia. Though only 23 years old, he quickly proved to be a brilliant general and a ruthless politician. Philip transformed the rugged peasants under his command into a well-trained professional army. -
Ancient Civilizations
Ancient civilizations Mediterranean EUROPE & MEDITERRANEAN COASTS / ANTALYA TO ATHENS Cruise 8 DAYS /7 NIGHTS ◆ EXTEND YOUR STAY IN A CLUB MED RESORT: Gregolimano CRUISE ON THE CLUB MED 2 Welcome aboard Club Med 2, for a unique experience that provides a gateway to the world. Elegance and comfort are the essence of this magnificent 5-masted sailing ship EUROPE & MEDITERRANEAN COASTS / ANTALYA TO ATHENS Mediterranean Ancient civilizations Cruise ◆ From 29/08/2020 to 05/09/2020 - 8 days / 7 ◆ EXTEND YOUR STAY IN A CLUB MED RESORT: Gnirgehgtsolimano Your cruise Days Stages Arrival Departure Nautical Hall 1. Saturday ANTALYA .. 20:00 CLOSED 2. Sunday PAPHOS 12:00 19:00 CLOSED 3. Monday ALEXANDRIA 13:00 CLOSED 4. Tuesday ALEXANDRIA .. 21:00 CLOSED 5. Wednesday RHODES 21:00 CLOSED 6. Thursday RHODES .. 19:00 CLOSED 7. Friday SANTORINI 08:00 19:00 CLOSED 8. Saturday ATHENS 08:00 CLOSED Day 1 : Boarding from 16h to 19h Day 8 : Landing from 9h to 11h Date of publication: 10/03/2020 The information contained in this document is valid on this date, and is subject to change. For full, up-to-date information, contact your travel agent or the Club Med website. The images are non contractual, and serve only as an indication. 2 EUROPE & MEDITERRANEAN COASTS / ANTALYA TO ATHENS Mediterranean Ancient civilizations Cruise ◆ From 29/08/2020 to 05/09/2020 - 8 days / 7 ◆ EXTEND YOUR STAY IN A CLUB MED RESORT: Gnirgehgtsolimano Itinerary of your cruise Nicknamed the "Turkish Riviera", this seaside resort, which is the most popular in the country, is home to an old city which contains fine Day 1 - Saturday Antalya examples of local architecture, beautifully carved woodwork, mosques, etc. -
The Ptolemies: an Unloved and Unknown Dynasty. Contributions to a Different Perspective and Approach
THE PTOLEMIES: AN UNLOVED AND UNKNOWN DYNASTY. CONTRIBUTIONS TO A DIFFERENT PERSPECTIVE AND APPROACH JOSÉ DAS CANDEIAS SALES Universidade Aberta. Centro de História (University of Lisbon). Abstract: The fifteen Ptolemies that sat on the throne of Egypt between 305 B.C. (the date of assumption of basileia by Ptolemy I) and 30 B.C. (death of Cleopatra VII) are in most cases little known and, even in its most recognised bibliography, their work has been somewhat overlooked, unappreciated. Although boisterous and sometimes unloved, with the tumultuous and dissolute lives, their unbridled and unrepressed ambitions, the intrigues, the betrayals, the fratricides and the crimes that the members of this dynasty encouraged and practiced, the Ptolemies changed the Egyptian life in some aspects and were responsible for the last Pharaonic monuments which were left us, some of them still considered true masterpieces of Egyptian greatness. The Ptolemaic Period was indeed a paradoxical moment in the History of ancient Egypt, as it was with a genetically foreign dynasty (traditions, language, religion and culture) that the country, with its capital in Alexandria, met a considerable economic prosperity, a significant political and military power and an intense intellectual activity, and finally became part of the world and Mediterranean culture. The fifteen Ptolemies that succeeded to the throne of Egypt between 305 B.C. (date of assumption of basileia by Ptolemy I) and 30 B.C. (death of Cleopatra VII), after Alexander’s death and the division of his empire, are, in most cases, very poorly understood by the public and even in the literature on the topic. -
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. -
Bridges Conference Paper
Bridges 2018 Conference Proceedings Landmarks in Algebra Quilt Elaine Krajenke Ellison Sarasota, Florida, USA; [email protected]; www.mathematicalquilts.com Abstract The Landmarks in Algebra quilt was an effort to include as many cultures that contributed significantly to the development of algebra as we know it today. Each section of the quilt illustrates a culture or a mathematician that made important advances in the development of algebra. Space did not allow more than four cultures, even though other nationalities made contributions. Babylonian mathematicians, Greek mathematicians, Indian mathematicians, and Persian mathematicians are highlighted for their important work. Figure 1: The Landmarks in Algebra quilt, 82 inches by 40 inches. First Panel: Plimpton 322 The first panel of the quilt illustrates the Plimpton 322 tablet. The Plimpton 322 tablet inspired me to design a quilt based on algebra. Recent historical research by Eleanor Robson, an Oriental Scholar at the University of Oxford, has shed new light on the ancient work of algebra [8]. The 4,000 year old Babylonian cuneiform tablet of Pythagorean Triples was purchased by George Arthur Plimpton in 1923 from Edgar J. Banks. Banks said the tablet came from a location near the ancient city of Larsa in Iraq [4]. Our first knowledge of mankind’s use of mathematics comes from the Egyptians and the Babylonians [1]. The Babylonian “texts” come to us in the form of clay tablets, usually about the size of a hand. The tablets were inscribed in cuneiform, a wedge-shaped writing owing its appearance to the stylus that was used to make it. Two types of mathematical tablets are generally found, table-texts and problem-texts [1]. -
Alexandria, Egypt, Before Alexander the Great: a Multidisciplinary Approach Yields Rich Discoveries
Alexandria, Egypt, before Alexander the Great: A multidisciplinary approach yields rich discoveries Jean-Daniel Stanley*, Geoarchaeology Program, Rm. E-206, drilling, photography, and television, along with refinement of Paleobiology, Smithsonian Institution National Museum of applicable high-resolution seismic methodologies and surveys Natural History (NMNH), Washington, D.C. 20013-7012, by research submarine and remote operated vehicle. Coastal USA; Richard W. Carlson*, Carnegie Institution of Washing- geoarchaeology reached a subdiscipline threshold ~25 years ton, Department of Terrestrial Magnetism, Washington, D.C. ago, at the time of publication of the multi-authored volume on 20015, USA; Gus Van Beek*, Anthropology, Smithsonian Insti- Quaternary coastlines and marine archaeology edited by Mas- tution NMNH, Washington, D.C., 20013-7012, USA; Thomas F. ters and Flemming (1983). Since then, the number of studies Jorstad*, Geoarchaeology Program, Rm. E-206, Paleobiology, that emphasize integration of varied geological and archaeo- Smithsonian Institution NMNH, Washington, D.C. 20013-7012, logical approaches in the marine realm has progressively risen. USA; Elizabeth A. Landau*, Geological Sciences, San Diego Of special note is the increased use of a classic geological State University, San Diego, California 92182-1020, USA methodology, sediment coring, to help resolve archaeological problems at sites that presently lie beneath the waves. This sub- ABSTRACT bottom technology has been applied with successful results in Historic records refer to Rhakotis as a settlement on Egypt’s most world oceans, especially in the Mediterranean (Morhange Mediterranean coast before Alexander the Great founded the et al., 2005; Marriner and Morhange, 2007; Stanley, 2007). famous Mediterranean port city of Alexandria in B.C. -
Eusebius' Exegesis Between Alexandria and Antioch
EUSEBIUS’ EXEGESIS BETWEEN ALEXANDRIA AND ANTIOCH: BEING A SCHOLAR IN CAESAREA (A TEST CASE FROM QUESTIONS TO STEPHANOS I) Claudio Zamagni* Eusebius’ Exegesis between Alexandria and Antioch Since the last comprehensive monograph on Eusebius by David Wal- lace-Hadrill, the exegesis of the bishop of Caesarea has been under- stood through his auspicious definition: Eusebius as an exegete has to be placed, like his city, between Antioch and Alexandria, halfway between the literal and the allegorical exegesis.1 Within such a frame- work, Carmel Sant has tried to settle a developing line in Eusebius’ career as an exegete. At its outset, under the influence of Pamphi- lus and Origen, Eusebius’ exegesis leans mainly toward the allegorical reading. Later, in the period between his appointment to the epis- copacy of Caesarea and the Council of Nicaea, there is a tendency to balance in Eusebius, and allegorical exegesis is perfectly offset by the ‘literal’ exegesis. Finally, in his last phase, which includes the * I am grateful to Aaron Johnson, University of Chicago, for his helpful suggestions about this paper and for his precious revision of my English. A big part of this essay is based on my dissertation, Les Questions et réponses sur les évangiles d’Eusèbe de Césarée. Étude et édition du résumé grec (Lausanne – Paris, 2003). 1 D.S. Wallace-Hadrill, Eusebius of Caesarea (London: Mowbray, 1960), 96–97 (American edition: Westminster, MD: Canterbury Press, 1961). These convictions are driven by an analysis of Eusebius’ philological and exegetical works related to the Bible (see ibid., pp. 59–99). This comprehension of Eusebius’ exegesis has also been recently confirmed by the remarkable study on the Commentary on Isaiah by M.J.