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Typesetting Classical Greek Philology Could Not find Anything Really Suitable for Her
276 TUGboat, Volume 23 (2002), No. 3/4 professor of classical Greek in a nearby classical high Philology school, was complaining that she could not typeset her class tests in Greek, as she could do in Latin. I stated that with LATEX she should not have any The teubner LATEX package: difficulty, but when I started searching on CTAN,I Typesetting classical Greek philology could not find anything really suitable for her. At Claudio Beccari that time I found only the excellent Greek fonts de- signed by Silvio Levy [1] in 1987 but for a variety of Abstract reasons I did not find them satisfactory for the New The teubner package provides support for typeset- Font Selection Scheme that had been introduced in LAT X in 1994. ting classical Greek philological texts with LATEX, E including textual and rhythmic verse. The special Thus, starting from Levy’s fonts, I designed signs and glyphs made available by this package may many other different families, series, and shapes, also be useful for typesetting philological texts with and added new glyphs. This eventually resulted in other alphabets. my CB Greek fonts that now have been available on CTAN for some years. Many Greek users and schol- 1 Introduction ars began to use them, giving me valuable feedback In this paper a relatively large package is described regarding corrections some shapes, and, even more that allows the setting into type of philological texts, important, making them more useful for the com- particularly those written about Greek literature or munity of people who typeset in Greek — both in poetry. -
Positional Notation Or Trigonometry [2, 13]
The Greatest Mathematical Discovery? David H. Bailey∗ Jonathan M. Borweiny April 24, 2011 1 Introduction Question: What mathematical discovery more than 1500 years ago: • Is one of the greatest, if not the greatest, single discovery in the field of mathematics? • Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? • Was fiercely resisted in Europe for hundreds of years after its discovery? • Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, to- gether with the basic arithmetic computational schemes, which were discov- ered in India prior to 500 CE. ∗Bailey: Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. Email: [email protected]. This work was supported by the Director, Office of Computational and Technology Research, Division of Mathematical, Information, and Computational Sciences of the U.S. Department of Energy, under contract number DE-AC02-05CH11231. yCentre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, NSW 2308, Australia. Email: [email protected]. 1 2 Why? As the 19th century mathematician Pierre-Simon Laplace explained: It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very sim- plicity and the great ease which it has lent to all computations put our arithmetic in the first rank of useful inventions; and we shall appre- ciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity. -
Archimedes' Principle
General Physics Lab Handbook by D.D.Venable, A.P.Batra, T.Hubsch, D.Walton & M.Kamal Archimedes’ Principle 1. Theory We are aware that some objects oat on some uids, submerged to diering extents: ice cubes oat in water almost completely submerged, while corks oat almost completely on the surface. Even the objects that sink appear to weigh less when they are submerged in the uid than when they are not. These eects are due to the existence of an upward ‘buoyant force’ that will act on the submerged object. This force is caused by the pressure in the uid being increased with depth below the surface, so that the pressure near the bottom of the object is greater than the pressure near the top. The dierence of these pressures results in the eective ‘buoyant force’, which is described by the Archimedes’ principle. According to this principle, the buoyant force FB on an object completely or partially submerged in a uid is equal to the weight of the uid that the (submerged part of the) object displaces: FB = mf g = f Vg . (1) where f is the density of the uid, mf and V are respectively mass and the volume of the displaced uid (which is equal to the volume of the submerged part of the object) and g is the gravitational acceleration constant. 2. Experiment Object: Use Archimedes’ principle to measure the densities of a given solid and a provided liquid. Apparatus: Solid (metal) and liquid (oil) samples, beaker, thread, balance, weights, stand, micrometer, calipers, PASCO Science Workshop Interface, Force Sensors and a Macintosh Computer. -
Great Inventors of the Ancient World Preliminary Syllabus & Course Outline
CLA 46 Dr. Patrick Hunt Spring Quarter 2014 Stanford Continuing Studies http://www.patrickhunt.net Great Inventors Of the Ancient World Preliminary Syllabus & Course Outline A Note from the Instructor: Homo faber is a Latin description of humans as makers. Human technology has been a long process of adapting to circumstances with ingenuity, and while there has been gradual progress, sometimes technology takes a downturn when literacy and numeracy are lost over time or when humans forget how to maintain or make things work due to cataclysmic change. Reconstructing ancient technology is at times a reminder that progress is not always guaranteed, as when Classical civilization crumbled in the West, but the history of technology is a fascinating one. Global revolutions in technology occur in cycles, often when necessity pushes great minds to innovate or adapt existing tools, as happened when humans first started using stone tools and gradually improved them, often incrementally, over tens of thousands of years. In this third course examining the greats of the ancient world, we take a close look at inventions and their inventors (some of whom might be more legendary than actually known), such as vizier Imhotep of early dynastic Egypt, who is said to have built the first pyramid, and King Gudea of Lagash, who is credited with developing the Mesopotamian irrigation canals. Other somewhat better-known figures are Glaucus of Chios, a metallurgist sculptor who possibly invented welding; pioneering astronomer Aristarchus of Samos; engineering genius Archimedes of Siracusa; Hipparchus of Rhodes, who made celestial globes depicting the stars; Ctesibius of Alexandria, who invented hydraulic water organs; and Hero of Alexandria, who made steam engines. -
Squaring the Circle a Case Study in the History of Mathematics the Problem
Squaring the Circle A Case Study in the History of Mathematics The Problem Using only a compass and straightedge, construct for any given circle, a square with the same area as the circle. The general problem of constructing a square with the same area as a given figure is known as the Quadrature of that figure. So, we seek a quadrature of the circle. The Answer It has been known since 1822 that the quadrature of a circle with straightedge and compass is impossible. Notes: First of all we are not saying that a square of equal area does not exist. If the circle has area A, then a square with side √A clearly has the same area. Secondly, we are not saying that a quadrature of a circle is impossible, since it is possible, but not under the restriction of using only a straightedge and compass. Precursors It has been written, in many places, that the quadrature problem appears in one of the earliest extant mathematical sources, the Rhind Papyrus (~ 1650 B.C.). This is not really an accurate statement. If one means by the “quadrature of the circle” simply a quadrature by any means, then one is just asking for the determination of the area of a circle. This problem does appear in the Rhind Papyrus, but I consider it as just a precursor to the construction problem we are examining. The Rhind Papyrus The papyrus was found in Thebes (Luxor) in the ruins of a small building near the Ramesseum.1 It was purchased in 1858 in Egypt by the Scottish Egyptologist A. -
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. -
Chapter Two Democritus and the Different Limits to Divisibility
CHAPTER TWO DEMOCRITUS AND THE DIFFERENT LIMITS TO DIVISIBILITY § 0. Introduction In the previous chapter I tried to give an extensive analysis of the reasoning in and behind the first arguments in the history of philosophy in which problems of continuity and infinite divisibility emerged. The impact of these arguments must have been enormous. Designed to show that rationally speaking one was better off with an Eleatic universe without plurality and without motion, Zeno’s paradoxes were a challenge to everyone who wanted to salvage at least those two basic features of the world of common sense. On the other hand, sceptics, for whatever reason weary of common sense, could employ Zeno-style arguments to keep up the pressure. The most notable representative of the latter group is Gorgias, who in his book On not-being or On nature referred to ‘Zeno’s argument’, presumably in a demonstration that what is without body and does not have parts, is not. It is possible that this followed an earlier argument of his that whatever is one, must be without body.1 We recognize here what Aristotle calls Zeno’s principle, that what does not have bulk or size, is not. Also in the following we meet familiar Zenonian themes: Further, if it moves and shifts [as] one, what is, is divided, not being continuous, and there [it is] not something. Hence, if it moves everywhere, it is divided everywhere. But if that is the case, then everywhere it is not. For it is there deprived of being, he says, where it is divided, instead of ‘void’ using ‘being divided’.2 Gorgias is talking here about the situation that there is motion within what is. -
In Search of Fundamentals to Resist Ethnic Calamities and Maintain National Integrity
Scholarship Report – L. Picha Meiji Jingu & Shiseikan In Search of fundamentals to resist ethnic calamities and maintain national integrity Lefkothea Picha June-July 2013 1 Scholarship Report Meiji Jingu (明治神宮) & Shiseikan (至誠館) Contents Acknowledgements and impressions …………………………………… Page 3 a. Cultural trip at Izumo Taishia and Matsue city Introduction: Japan’s latest Tsunami versus Greek financial crisis reflecting national ethos…………………............................................................................ 6 Part 1 The Historic Horizon in Greece................................................... 7 a. Classical Period b. Persian wars c. Alexander’s the Great Empire d. Roman and Medieval Greece e. The Byzantine Period f. The Ottoman domination g. Commentary on the Byzantine epoch and Ottoman occupation h. World War II i. Greece after World War II j. Restoration of Democracy and Greek Politics in the era of Financial crisis Part 2 The liturgical and spiritual Greek ethos …………………………. 10 a. Greek mythology, the ancient Greek philosophy and Shinto b. Orthodox theology, Christian ethics and Shinto c. Purification process – Katharmos in ancient Greece, Christian Baptism and Misogi Part 3 Greek warriors’ ethos and Reflections on Bushido ..................... 14 a. Battle of Thermopylae (480 BC) b. Ancient Greek warriors armor c. Comparison of Spartan soldiers and Samurai d. The motto “freedom or death and the Greek anthem e. Monument of the unknown soldier and Yasukunii shrine f. Women warriors and their supportive role against invaders g. Reflections on Bushido and its importance in the modern era h. Personal training in Budo and relation with Shiseikan Part 4 Personal view on Greek nation’s metamorphosis………………… 20 a. From the illustrious ancestors to the cultural decay. Is catastrophy a chance to revive Greek nation? Lefkothea Picha 2 Scholarship Report Meiji Jingu (明治神宮) & Shiseikan (至誠館) Acknowledgments and impressions I would like to thank Araya Kancho for the scholarship received. -
Thales of Miletus Sources and Interpretations Miletli Thales Kaynaklar Ve Yorumlar
Thales of Miletus Sources and Interpretations Miletli Thales Kaynaklar ve Yorumlar David Pierce October , Matematics Department Mimar Sinan Fine Arts University Istanbul http://mat.msgsu.edu.tr/~dpierce/ Preface Here are notes of what I have been able to find or figure out about Thales of Miletus. They may be useful for anybody interested in Thales. They are not an essay, though they may lead to one. I focus mainly on the ancient sources that we have, and on the mathematics of Thales. I began this work in preparation to give one of several - minute talks at the Thales Meeting (Thales Buluşması) at the ruins of Miletus, now Milet, September , . The talks were in Turkish; the audience were from the general popu- lation. I chose for my title “Thales as the originator of the concept of proof” (Kanıt kavramının öncüsü olarak Thales). An English draft is in an appendix. The Thales Meeting was arranged by the Tourism Research Society (Turizm Araştırmaları Derneği, TURAD) and the office of the mayor of Didim. Part of Aydın province, the district of Didim encompasses the ancient cities of Priene and Miletus, along with the temple of Didyma. The temple was linked to Miletus, and Herodotus refers to it under the name of the family of priests, the Branchidae. I first visited Priene, Didyma, and Miletus in , when teaching at the Nesin Mathematics Village in Şirince, Selçuk, İzmir. The district of Selçuk contains also the ruins of Eph- esus, home town of Heraclitus. In , I drafted my Miletus talk in the Math Village. Since then, I have edited and added to these notes. -
Pre-Proto-Iranians of Afghanistan As Initiators of Sakta Tantrism: on the Scythian/Saka Affiliation of the Dasas, Nuristanis and Magadhans
Iranica Antiqua, vol. XXXVII, 2002 PRE-PROTO-IRANIANS OF AFGHANISTAN AS INITIATORS OF SAKTA TANTRISM: ON THE SCYTHIAN/SAKA AFFILIATION OF THE DASAS, NURISTANIS AND MAGADHANS BY Asko PARPOLA (Helsinki) 1. Introduction 1.1 Preliminary notice Professor C. C. Lamberg-Karlovsky is a scholar striving at integrated understanding of wide-ranging historical processes, extending from Mesopotamia and Elam to Central Asia and the Indus Valley (cf. Lamberg- Karlovsky 1985; 1996) and even further, to the Altai. The present study has similar ambitions and deals with much the same area, although the approach is from the opposite direction, north to south. I am grateful to Dan Potts for the opportunity to present the paper in Karl's Festschrift. It extends and complements another recent essay of mine, ‘From the dialects of Old Indo-Aryan to Proto-Indo-Aryan and Proto-Iranian', to appear in a volume in the memory of Sir Harold Bailey (Parpola in press a). To com- pensate for that wider framework which otherwise would be missing here, the main conclusions are summarized (with some further elaboration) below in section 1.2. Some fundamental ideas elaborated here were presented for the first time in 1988 in a paper entitled ‘The coming of the Aryans to Iran and India and the cultural and ethnic identity of the Dasas’ (Parpola 1988). Briefly stated, I suggested that the fortresses of the inimical Dasas raided by ¤gvedic Aryans in the Indo-Iranian borderlands have an archaeological counterpart in the Bronze Age ‘temple-fort’ of Dashly-3 in northern Afghanistan, and that those fortresses were the venue of the autumnal festival of the protoform of Durga, the feline-escorted Hindu goddess of war and victory, who appears to be of ancient Near Eastern origin. -
The Active Imperfect of the Verbs of the '2Nd Conjugation'
</SECTION<SECTION<LINK "pan-n*"> "art" "opt"> TITLE "Articles"> <TARGET "pan" DOCINFO AUTHOR "Nikolaos Pantelidis"TITLE "The active imperfect of the verbs of the ‘2nd conjugation’ in the Peloponnesian varieties of Modern Greek"SUBJECT "JGL, Volume 4"KEYWORDS "Modern Greek dialects, Peloponnesian varieties, imperfect, morphologization, leveling, violation of the trisyllabic window, loss of morpheme boundary, doubling of morphemes"SIZE HEIGHT "220"WIDTH "150"VOFFSET "4"> The active imperfect of the verbs of the ‘2nd conjugation’ in the Peloponnesian varieties of Modern Greek* Nikolaos Pantelidis Demokritus University of Thrace The present paper treats the different types of formation and the inflectional patterns of the active imperfect of the verbs that in traditional grammar are known as verbs of the ‘2nd conjugation’ in the Peloponnesian varieties of Modern Greek (except Tsakonian and Maniot), mainly from a diachronic point of view. A reconstruction of the processes that led to the current situa- tion is attempted and directions for further possible changes are suggested. The diachrony of the morphology of the imperfect of the ‘2nd conjugation’ in the Peloponnesian varieties involves developments such as morpho- logization of a phonological process and the evolution of number-oriented allomorphy at the level of aspectual markers, while at the same time offering interesting insights into the mechanisms and scope of morphological chang- es and the morphological structure of the Modern Greek verb. These devel- opments can also offer important -
The Greek Alphabet Sight and Sounds of the Greek Letters (Module B) the Letters and Pronunciation of the Greek Alphabet 2 Phonology (Part 2)
The Greek Alphabet Sight and Sounds of the Greek Letters (Module B) The Letters and Pronunciation of the Greek Alphabet 2 Phonology (Part 2) Lesson Two Overview 2.0 Introduction, 2-1 2.1 Ten Similar Letters, 2-2 2.2 Six Deceptive Greek Letters, 2-4 2.3 Nine Different Greek Letters, 2-8 2.4 History of the Greek Alphabet, 2-13 Study Guide, 2-20 2.0 Introduction Lesson One introduced the twenty-four letters of the Greek alphabet. Lesson Two continues to present the building blocks for learning Greek phonics by merging vowels and consonants into syllables. Furthermore, this lesson underscores the similarities and dissimilarities between the Greek and English alphabetical letters and their phonemes. Almost without exception, introductory Greek grammars launch into grammar and vocabulary without first firmly grounding a student in the Greek phonemic system. This approach is appropriate if a teacher is present. However, it is little help for those who are “going at it alone,” or a small group who are learning NTGreek without the aid of a teacher’s pronunciation. This grammar’s introductory lessons go to great lengths to present a full-orbed pronunciation of the Erasmian Greek phonemic system. Those who are new to the Greek language without an instructor’s guidance will welcome this help, and it will prepare them to read Greek and not simply to translate it into their language. The phonic sounds of the Greek language are required to be carefully learned. A saturation of these sounds may be accomplished by using the accompanying MP3 audio files.