DOCSLIB.ORG

9780521792974 Index.Pdf

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
9780521792974 Index.Pdf Cambridge University Press 0521792975 - Surveying Instruments of Greece and Rome M. J. T. Lewis Index More information INDEX Note: page references to figures are in italic. Abdaraxos Ammonius , , Acrocorinth , , , amphitheatres Adrastus , , , , Anaximander Aegina , , Andrias Aflimun (Philo) , , , Anna Comnena , , , Africanus, Julius , –, –, , , Anonymus Byzantinus –, –, – –, , – Agatharchides , Antikythera mechanism , , , Agesistratus Antioch in Pisidia aqueduct agrimensor , , , , Antioch on Orontes aqueduct , akaina Apollodorus of Athens , , –, Alatri aqueduct , , , Albano, lake emissary , , , , Apollodorus of Damascus , , Apollonius of Perge , , Alexander of Aphrodisias , , , Apollonius, engineer Apuleius Alexandreion aqueduct aqueducts , , , , Alexandria , , arcades on , astronomy at , , bridges on , , –, , latitude of , , , , , builders of , , mechanics at , , , cascades on , Museum of , , discharge of science at , , gradients on , –, –, , surveying at , , , – passim, –, algebra , , –, , inverted siphons on , , , , alidade , , , , –, , alignment by dead reckoning –, pipelines on –, , , , , – by extrapolation , reverse gradients on , , , by geometrical construction –, , , –, – surveying of , –, , , by interpolation , , –, –, – passim by successive approximation –, surveying errors on –, –, – alpharion , and see under name of city served Alps , , , Aquileia sundial © Cambridge University Press www.cambridge.org Cambridge University Press 0521792975 - Surveying Instruments of Greece and Rome M. J. T. Lewis Index More information INDEX Arabic, reference letters in, , surveying in , –, , , , terminology in, , , , Bahr Yusuf canal translations into –, , , , balance –, , , arachne , Balbus , , , , , – Archimedes al-Battani on astronomy, – beacons –, , on circumference of earth, – Beirut aqueduct on geometry, , , , bematistai on mechanics, , –, –, , L. Betilienus Varus , – on water surface, , , , al-Biruni reference letters, – Bisitun (Bagistanos) Aristarchus Bithynia , , , Aristotle , , , , Biton , –, , , , , Aristyllus Bohemond , Arrian , Bologna aqueduct , –, , , Artemidorus , – Ashurbanipal boning boards , , , asl, aslu Brescia astrolabe , Assyria , , bridges , asteriskos , and see aqueducts and river, width of astrabister, astraphister Briord tunnel , astrolabe, armillary –, , , , Byzantium, astronomy in , –, –, surveying in , , , plane , –, , , – technology in , name synonymous with dioptra – Caesarea shadow square on , aqueduct , astrology , , , , Caligula , astronomical instruments , –, , Cambyses II , canals , , , –, , , and see names of instruments Canterbury , astronomy , , –, –, –, Cardan suspension Atabyrios , Carhaix aqueduct , Athenaeus Mechanicus , , , Carpus of Antioch –, , , – Cassiodorus , , Athens , , , , , catapults , , , , , aqueduct , , , , centuriation – Attalus, astronomer , , , Chagnon tunnel , Attalus II – chains, measuring –, –, augeion Chaireas son of Damon Avienus Chichester , , , – China , , , –, –, Babylon, science in –, –, –, Chios , , chord tables , , © Cambridge University Press www.cambridge.org Cambridge University Press 0521792975 - Surveying Instruments of Greece and Rome M. J. T. Lewis Index More information INDEX chorobates –, , , , , diaugeion Cicero , Dicaearchus –, –, , , circle, division of , –, –, , Cleomedes , , , , –, , Diodorus Siculus , , Dionysius – Cleon dioptra, as sighting tube – clocks , , , , , Hero’s –, –, –, Clodius Septiminus , – Hipparchan (four-cubit) , , , , clouds, height of , , Cologne aqueduct standard – passim, , –, Commodus , –, , –, Constantine VII Porphyrogennetos chronology of –, , Constantinople , , degree scale on , , , , aqueduct , material of hippodrome , , – not used in West? , , Contrebia Belaisca inscription reconstruction of –, – Copais tunnel , , size of cords, measuring , –, , , stand of –, –, , Corinth , universal joint on , aqueduct direction (bearing) , –, – canal , –, – and see orientation corniculi dodecahedrons – Corpus Agrimensorum , –, , Dorchester, aqueduct , , Dyrrhachium (Durazzo) , Crates of Mallos , Cremna aqueduct earth, circumference of , , , – Crimea curvature of , cross-staff (Jacob’s staff) , , ecliptic circle , , so-called, for right angles , coordinates Ctesias obliquity of , Ctesibius , , plane of cultellatio Egypt , , , , cuniculi –, , , science in , – Cyrus I , surveying in –, –, –, , – Dagon aqueduct Ephesus aqueduct Darius I , , equator, plane of , decempeda equatorial armillary degree, value of –, –, , coordinates , , and see circle, division of Eratosthenes , , , – Demetrius Poliorcetes on circumference of earth , –, diabetes , , – diagrams in treatises , , , , , on mountain heights –, , , , – © Cambridge University Press www.cambridge.org Cambridge University Press 0521792975 - Surveying Instruments of Greece and Rome M. J. T. Lewis Index More information INDEX Ermine Street , , Greece, influence of on Roman surveying Etruscans, surveying by , , , –, , grids , –, tunnels of , , –, , , groma , , –, –, – – passim Euclid , , , , , gromaticus , Eudoxus , , , , gruma, see groma Eumenes II Eupalinus , , , , , halysis exercises, surveying , , –, , hamma harbours , Ezekiel Heliodorus , , Heraclea, Italy Faventinus , Hero of Alexandria passim and Fayum, groma from , , asteriskos , –, – irrigation of – dioptra –, –, –, , –, , ferramentum , , –, – – Festus , , hodometer –, – Firdausi levelling , , , – Fontvieille tunnel other procedures , , , , Forma Urbis Romae , –, – Foss Way Herod the Great Frontinus , , , , – Herodes Atticus Fucino, lake emissary Herodotus , , , , Hieronymus of Cardia , Gadara aqueducts Hipparchus and astronomy , , –, Galen , , Gamaliel II, Rabbi , , , and circumference of earth –, Gardon, river , , , , , Gartree Road and see dioptra gears , , –, , –, Hippodamus of Miletus, Geminus , , , , , , Hippolytus Geneva aqueduct Hisdai, Rabbi , geometry , , –, , , , hodometer , –, , , –, Gerbert d’Aurillac Humeima aqueduct gnoma, gnome Hyginus Gromaticus , , , , gnomon (shadow stick) , , – for orientation , , Hypsicles for sun altitude , –, –, , Ibn al-‘Awwam , , , –, Goths Ibn al-Nadim , C. Gracchus Ibn al-Saffar , gradients xviii Ibn Lujun and see aqueducts India , , © Cambridge University Press www.cambridge.org Cambridge University Press 0521792975 - Surveying Instruments of Greece and Rome M. J. T. Lewis Index More information INDEX Iran, see Persia Leicester Iraq , , aqueduct irrigation , , length, units of xviii–xx, –, , –, channels , , , , , in Egypt , –, Lepcis Magna aqueduct in Mesopotamia lepta Islam, surveying in , , , – level, gunner’s surveying instruments in , , , Hero’s water , , –, , – plumb-line (A-frame, builder’s) , – Isthmus, see Corinth Egyptian , , Ivrea, relief of groma from , Greek –, , , , Islamic , Jacob’s staff, see cross–staff Roman , Joshua, patriarch spirit , Joshua ben Hananiah, Rabbi , U-tube – Julian of Ascalon water , , –, , , , Julius Caesar , and see individual names of levels Justinian , levelling , –, –, , –, Juvenal – with dioptra , , , , –, , Kaikos, river – and see Pergamon, aqueducts with libra – kamal with water , , , – Kamateros, John , , – Levi ben Gerson , al-Karaji, date of source of – libella , on dioptra , –, , , , libra , , , –, , on levelling , , –, , , reconstruction of –, – – librator , , on staff , , , libritor – on suspended sighting tube , , limes, German , –, –, Lincoln , , on tunnel surveying , , , aqueduct , –, linee karchesion , , Little St Bernard Pass Karun, river Liu Hui Kharga oasis , London , , , , – al-Khuwarizmi and see New River koilia Lorch Kyllene, Mount , , , , , Lupitus lychnia , Lyon aqueducts , , , Lambaesis , , Laodicea ad Lycum aqueduct Main, river latitudes –, , –, al-Mamun, caliph , © Cambridge University Press www.cambridge.org Cambridge University Press 0521792975 - Surveying Instruments of Greece and Rome M. J. T. Lewis Index More information INDEX Mappae Clavicula , , , – Necho , maps , , –, – Nemi, lake emissary , , , , Agrippa’s , , –, of Rome Nero , Ptolemys’s , , New River , , Marcellus, M. Claudius , , Nicomedes Marinus of Tyre , , Nicomedia, Bithynia , , markers –, , , , , Nile, river –, , , – and see stakes Nile–Red Sea canal –, , – Marseille , , Nîmes aqueduct , –, , , Martianus Capella , , , Masha’allah Nineveh aqueduct , mathematics , , Nipsus, M. Junius , , , , measurement of distances , –, , – , , , Nonius Datus , , – and see chains, cords, pacing and rods ‘measuring rod’, astronomical –, Oenoanda aqueduct Medway, river – Ogilby, John mensor , , Olympiodorus , meridian , , , , , , Olympus, Mount , –, , , plane of , meridional altitudes , orientation , , –, , –, armillary (ring) , , , and see direction merkhet , Mesopotamia , , pacing , , , meteoroscope , , , , paddle wheel , Meton Palladius , , , mezupit – Pangaeus mines Middle Ages, surveying in , Pappus , , , , milestones , , parallactic instrument , , Miletus , , Parthenon –, Miltenberg-Altstadt Paul of Alexandria , mining , , , , , Paul, Saint Mithridates VI Pelion, Mount , mizan , –, , –, –, Pergamon , , Moeris, lake , aqueducts , , , , , , mountains, heights of , , , , , – nursery of surveying , , murjiqal Periander , Mynas Codex , , , –, Persia , , –, , Mytilene aqueduct tunnels and surveying in , , , –, Narbonne aqueduct
Load more

Recommended publications
  • Mathematical Discourse in Philosophical Authors: Examples from Theon of Smyrna and Cleomedes on Mathematical Astronomy
    Mathematical discourse in philosophical authors: Examples from Theon of Smyrna and Cleomedes on mathematical astronomy Nathan Sidoli Introduction Ancient philosophers and other intellectuals often mention the work of mathematicians, al- though the latter rarely return the favor.1 The most obvious reason for this stems from the im- personal nature of mathematical discourse, which tends to eschew any discussion of personal, or lived, experience. There seems to be more at stake than this, however, because when math- ematicians do mention names they almost always belong to the small group of people who are known to us as mathematicians, or who are known to us through their mathematical works.2 In order to be accepted as a member of the group of mathematicians, one must not only have mastered various technical concepts and methods, but must also have learned how to express oneself in a stylized form of Greek prose that has often struck the uninitiated as peculiar.3 Be- cause of the specialized nature of this type of intellectual activity, in order to gain real mastery it was probably necessary to have studied it from youth, or to have had the time to apply oneself uninterruptedly.4 Hence, the private nature of ancient education meant that there were many educated individuals who had not mastered, or perhaps even been much exposed to, aspects of ancient mathematical thought and practice that we would regard as rather elementary (Cribiore 2001; Sidoli 2015). Starting from at least the late Hellenistic period, and especially during the Imperial and Late- Ancient periods, some authors sought to address this situation in a variety of different ways— such as discussing technical topics in more elementary modes, rewriting mathematical argu- ments so as to be intelligible to a broader audience, or incorporating mathematical material di- rectly into philosophical curricula.
    [Show full text]
  • The Geodetic Sciences in Byzantium
    The geodetic sciences in Byzantium Dimitrios A. Rossikopoulos Department of Geodesy and Surveying, Aristotle University of Thessaloniki [email protected] Abstract: Many historians of science consider that geodeasia, a term used by Aristotle meaning "surveying", was not particularly flourishing in Byzantium. However, like “lo- gistiki” (practical arithmetic), it has never ceased to be taught, not only at public universi- ties and ecclesiastical schools, as well as by private tutors. Besides that these two fields had to do with problems of daily life, Byzantines considered them necessary prerequisite for someone who wished to study philosophy. So, they did not only confine themselves to copying and saving the ancient texts, but they also wrote new ones, where they were ana- lyzing their empirical discoveries and their technological achievements. This is the subject of this paper, a retrospect of the numerous manuscripts of the Byzantine period that refer to the development of geodesy both in teaching and practices of surveying, as well as to mat- ters relating to the views about the shape of the earth, the cartography, the positioning in travels and generally the sciences of mapping. Keywords: Geodesy, geodesy in Byzantium, history of geodesy, history of surveying, history of mathematics. Περίληψη: Πολλοί ιστορικοί των επιστημών θεωρούν ότι η γεωδαισία, όρος που χρησι- μοποίησε ο Αριστοτέλης για να ορίσει την πρακτική γεωμετρία, την τοπογραφία, δεν είχε ιδιαίτερη άνθιση στο Βυζάντιο. Ωστόσο, όπως και η “λογιστική”, δεν έπαψε ποτέ να διδά- σκεται όχι μόνο στα κοσμικά πανεπιστήμια, αλλά και στις εκκλησιαστικές σχολές, καθώς επίσης και από ιδιώτες δασκάλους. Πέρα από το ότι οι δύο αυτοί κλάδοι είχαν να κάνουν με προβλήματα της καθημερινής ζωής των ανθρώπων, οι βυζαντινοί θεωρούσαν την διδα- σκαλία τους απαραίτητη προϋπόθεση ώστε να μπορεί κανείς να παρακολουθήσει μαθήμα- τα φιλοσοφίας.
    [Show full text]
  • Gifts from the Greeks
    Gifts from the Greeks 1. Philosophy: The ancient Greeks were the first to try to explain the world around them without resorting to things like magic myth or religion. Philosophy starts with the great Greek thinkers such as Aristotle, and it is something that shapes our world to this day. 2. Astronomy: Some of the most important discoveries of Ancient Greece in the field of astrology can be summarized in: the naming of the different planets, planet deriving from Greek word that means wonderer; the idea that the Earth rotates around its axis; the idea that the Earth is part of a heliocentric system, which means that the Earth, along with all the other planets revolve around a static Sun; the first 3D model of the movement of the planets; the categorization of the stars, organizing them into constellations; and a highly accurate assumption about the circumference of the Earth based on the angle of shadows in different parts of the World. 3. Mathematics: Geometry and its rules were invented by Euclid. Euclidian geometry is the first we come in contact as we go to school. Almost all the basic knowledge that we have about mathematics is a result of the discoveries of Ancient Greece. 4. Botany: Aristotle was one of the first botanists in the world. He collected information about most of the plants that were known in the world at that time. One of his students, Theophrastus, who is also considered one of the inventors of this new field, categorized, and named all these plants. 5. Biology: This vast topic was studied by some of the greatest minds of Ancient Greece, including Aristotle, Hypocrites or Dioscorides.
    [Show full text]
  • Kytherian Newsletter November 2011
    Page 888 The KYTHERIAN, NOVEMBER 2011 ANCIENT GREEK TECHNOLOGY: THE ANTIKYTHERA MECHANISM Dr Amelia R Brown looks at ancient technology, and how it's affected modern technology The last two decades are generally described as an era of technology, characterised by the rapid development and global distribution of new technologies, especially in relation to transportation, by land or by sea. The ancient Greeks, however, are often described as overly traditional when it comes to technology, as they did not achieve modern levels of industrialisation. However the Antikythera Mechanism has been influential in changing opinions about ancient technology, as it is the most sophisticated geared machine to survive from Antiquity: a veritable primitive computer. Before its discovery on a shipwreck off the island of Antikythera in 1900, the existence of devices like it was hardly dreamed of, and in recent years it has been subjected to a battery of modern tests, though it is surely hiding secrets still (see Marchant's Decoding the Heavens. Three things seem clear, however, about ancient Greek technology, and about the Antikythera Mechanism. First, the Greeks knew how to work in bronze to a very high level of sophistication. Second, the Antikythera Mechanism derives from a context related to the city of Corinth, the origin for the names of the months on its dials, and the Greek city most famous for its bronze work. Finally, the mechanism was created to fulfil a perceived need in Greek society of its time, surely through incremental developments in technology, and NOT necessarily to fulfil the 'needs' which we perceive in our society today and which can be fulfilled by our technology.
    [Show full text]
  • Decoding the Antikythera Mechanism: Investigation of an Ancient Astronomical Calculator
    Decoding the Antikythera Mechanism: Investigation of an Ancient Astronomical Calculator 2 Supplementary Notes T. Freeth 1,2 , Y. Bitsakis 3,5 , X. Moussas 3, J.H. Seiradakis 4, A.Tselikas 5, E. Magkou 6, M. Zafeiropoulou 6, R. Hadland 7, D. Bate 7, A. Ramsey 7, M. Allen 7, A. Crawley 7, P. Hockley 7, T. Malzbender 8, D. Gelb 8, W. Ambrisco 9 and M.G. Edmunds 1 1 Cardiff University, School of Physics andAstronomy, Queens Buildings, The Parade, Cardiff CF24 3AA, UK. Mike Edmunds Mike.Edmunds @ astro.cf.ac.uk 2 Images First Ltd10 HerefordRoad, South Ealing, London W5 4SE, UK. Tony Freeth tony @ images- first.com 3 National & Kapodistrian University of Athens, Department of Astrophysics, Astronomy andMechanics, Panepistimiopolis, GR15783, Zographos, Greece. Xenophon Moussas, xmoussas @ phys.uoa.gr 4 Aristotle University of Thessaloniki, Department of Physics, Section of Astrophysics, Astronomy and Mechanics, GR-54124 Thessaloniki, Greece. John Seiradakis jhs @ astro.auth.gr 5 Centre for History andPalaeography, National Bank of Greece Cultural Foundation, P. Skouze 3, 10560 Athens, Greece. Yanis Bitsakis bitsakis @ gmail.com 6 National Archaeological Museum of Athens, 44 Patission Str, 106 82 Athens, Greece. 7 X-Tek Systems Ltd, Tring Business Centre, IcknieldWay, Tring, Herts HP23 4JX, UK. 8 Hewlett-PackardLaboratories, 1501 Page Mill Road, Palo Alto, CA 94304, USA. 9 Foxhollow Technologies Inc., 740 Bay Road, RedwoodCity, CA 94063, USA. Decoding the Antikythera Mechanism , published in Nature, Volume 444, Issue 7119, pp. 587-591 (2006). 1 Supplementary Information Guide There are three Supplementary Information sections: Supplementary Notes 1 (Fragments ) giving a key to fragment identification for Figure 1 of the main text andthe dimensions of the fragments.
    [Show full text]
  • Max Planck Institute for the History of Science Aristotle And
    MAX-PLANCK-INSTITUT FÜR WISSENSCHAFTSGESCHICHTE Max Planck Institute for the History of Science 2012 PREPRINT 422 TOPOI – Towards a Historical Epistemology of Space Pietro Daniel Omodeo, Irina Tupikova Aristotle and Ptolemy on Geocentrism: Diverging Argumentative Strategies and Epistemologies TOPOI – TOWARDS A HISTORICAL EPISTEMOLOGY OF SPACE The TOPOI project cluster of excellence brings together researchers who investigate the formation and transformation of space and knowledge in ancient civilizations and their later developments. The present preprint series presents the work of members and fellows of the research group Historical Epistemology of Space which is part of the TOPOI cluster. The group is based on a cooperation between the Humboldt University and the Max Planck Institute for the History of Science in Berlin and commenced work in September 2008. Contents 1 Introduction 1 2 Aristotle 5 2.1 Aristotle’s confrontation with the cosmologies of his prede- cessors . 6 2.2 Aristotle’s presentation of his own views . 9 3 Ptolemy 15 3.1 The heavens move like a sphere . 16 3.2 The Earth, taken as a whole, is sensibly spherical . 24 3.3 The Earth is in the middle of the heavens . 24 3.4 The Earth has the ratio of a point to the heavens . 32 3.5 The Earth does not have any motion from place to place . 33 4 Conclusions and perspectives 37 Chapter 1 Introduction This paper aims at a comparison of the different argumentative strategies employed by Aristotle and Ptolemy in their approaches to geocentrism through an analysis of their discussion of the centrality of the Earth in De caelo II, 13-14 and Almagest, I, 3-7.
    [Show full text]
  • Understanding the Antikythera Mechanism M.T
    Understanding the Antikythera Mechanism M.T. Wright Imperial College, London. Preprint of the written version of a lecture given at a conference held in Athens, 17th – 21st October 2005: 2o Διεθνές Συνέδριο Αρχαίας Ελληνικής Τεχνολογίας (2nd International Conference on Ancient Greek Technology). This paper is to be published in the Proceedings, of which the bibliographical details are to be announced, and is reproduced here with permission. The fragmentary Antikythera Mechanism, recovered from a shipwreck that is dateable to the 1st. century B.C., stands alone as evidence of the high level of attainment of the Hellenistic mechanic. A remarkably accomplished instrument of small size, it is justly celebrated as the earliest artefactual evidence for the use of toothed gearing. It is most widely known through the writing of the late Professor Derek Price1 and through secondary sources based on his work. Yet, as far as the instrument itself was concerned, Price’s treatment was inadequate and the Mechanism remained but poorly understood. A new reconstruction of the Antikythera Mechanism is now presented which, unlike all earlier reconstructions, accords with and accounts for very nearly all of the mechanical detail observed in the original fragments. It is based on a detailed survey of the original fragments carried out by the author at The National Archaeological Museum, Athens, in collaboration with the late Professor Allan Bromley (University of Sydney). Early results of this survey were presented at the First International Conference on Ancient Greek Technology (Thessaloniki, 1997).2 Price’s reconstruction was shown to be fundamentally flawed, but we could not then offer a more satisfactory alternative.
    [Show full text]
  • Post-Euclid Greek Mathematics
    Archimedes Apollonius and the Conics How Apollonius described and classified the conic sections Some high points of Greek mathematics after Euclid Algebra Through History October 2019 Algebra Through History Greek Math Post Euclid Archimedes Apollonius and the Conics How Apollonius described and classified the conic sections Outline 1 Archimedes 2 Apollonius and the Conics 3 How Apollonius described and classified the conic sections Algebra Through History Greek Math Post Euclid Archimedes Apollonius and the Conics How Apollonius described and classified the conic sections Who was Archimedes? Lived ca. 287 - 212 BCE, mostly in Greek city of Syracuse in Sicily Studied many topics in what we would call mathematics, physics, engineering (less distinction between them at the time) We don’t know much about his actual life; much of his later reputation was based on somewhat dubious anecdotes, e.g. the “eureka moment,” inventions he was said to have produced to aid in defense of Syracuse during Roman siege in which he was killed, etc. Perhaps most telling: we do know he designed a tombstone for himself illustrating the discovery he wanted most to be remembered for (discussed by Plutarch, Cicero) Algebra Through History Greek Math Post Euclid Archimedes Apollonius and the Conics How Apollonius described and classified the conic sections Figure: Sphere inscribed in cylinder of equal radius 3Vsphere = 2Vcyl and Asphere = Acyl (lateral area) Algebra Through History Greek Math Post Euclid Archimedes Apollonius and the Conics How Apollonius described and classified the conic sections Surviving works On the Equilibrium of Planes (2 books) On Floating Bodies (2 books) Measurement of a Circle On Conoids and Spheroids On Spirals On the Sphere and Cylinder (2 books) Algebra Through History Greek Math Post Euclid Archimedes Apollonius and the Conics How Apollonius described and classified the conic sections Surviving works, cont.
    [Show full text]
  • By Salomon Bochner
    THE EMERGENCE OF ANALYSIS IN THE RENAISSANCE AND AFTER by Salomon Bochner CONTENTS 1. The Key Concepts of Analysis 11. The Force of Analysis 111. Functions IV. Real Numbers v. Space VI. Infinity VII. Continuity VIII. Post-analysis Number Theory and Algebra References I. THE KEY CONCEPTS OF ANALYSIS Analysis as an independent division of mathematics-and it is the largest division by far-is a "modern" creation. Greek antiquity did not have it, nor did the Middle Ages, except for occasional gropings, mostly faint ones. But in the sixteenth and seventeenth centuries, analysis began to sprout and rise in many contexts, and its influence began to spread into the farthest precincts of mathematics. All this started very suddenly, and it was as great a revolution as any then proliferating. The emergence of analysis in the Renaissance created a great divide in all of mathematics; there is a pre-analysis geometry and a post-analysis geome- try; a pre-analysis algebra and a post-analysis algebra; a pre-analysis num- ber thory and a post-analysis number theory, very much so; and, very im- portantly, a pre-analysis astronomy and a post-analysis astronomy. The first epochal manifestation of analysis-as analysis is conceived by us-was Johannes Kepler's proclamation of his Planetary Laws, especially the Law of Areas. There had been nothing like it before in an astronomy that had 12 RICE UNIVERSITY STUDIES been a mathematically controlled science for two millennia, not even in Co- pernicus, whatever his astronomical innovations may have been. Terminologically the Greeks did have analysis, in logic, in epistemology, and also in (late) mathematics, but for the most part in a contrasting paral- lelism with synthesis, and only rarely by itself.
    [Show full text]
  • Hippodamus of Miletus and the Character of the Athenian Dikastic Oath (Arist
    Hippodamus of Miletus and the Character of the Athenian Dikastic Oath (Arist. Pol. 2.8) Anders Dahl Sørensen 1. The debate over the Athenian dikastic oath Each year, those 6000 citizens of classical Athens who had been selected by lot to serve as citizen-judges (‘dikasts’) in the popular law courts swore an oath on the hill of Ardettos outside the city-walls, solemnly stating their commitment to a set of fun- damental principles that should guide their judicial decisions.1 The importance of this ‘dikastic oath’ for understanding the character of the Athenian legal system is not difficult to see. Given the crucial role of oaths in regulating human conduct in ancient societies, what the dikastic oath required the dikasts to do is likely to have shaped, not only the self-understanding, but also the judicial practice of the Athenian law courts. It is there- fore all the more unfortunate that the oath is not found in its entirety in any surviving ancient source.2 Max Fränkel’s classic reconstruction is elegant and has been widely accepted by scholars, but it is at bottom an intricate pastiche made up of bits and pieces drawn from a large number of citations of, and allusions to, the oath in Athenian law court speeches and in later 1 M. H. Hansen, Athenian Democracy in the Age of Demosthenes (Oxford/ Cam- bridge [Mass.] 1991) 181–183. 2 Scholars agree that the version cited in Dem. 24.149–151 is not authentic but probably an interpolated reconstruction by a later editor. See S. Johnstone, Disputes and Democracy.
    [Show full text]
  • Individuals Who Influenced Planning Before 1978 APA Identified 25 Individuals Who Significantly Influenced the Practice of Planning Before APA Was Established
    Individuals Who Influenced Planning Before 1978 APA identified 25 individuals who significantly influenced the practice of planning before APA was established. AICP already has designated more than half of them as National Planning Pioneers Hippodamus 5th century B.C. Hippodamus of Miletus was a Greek architect who introduced order and regularity into the planning of cities, which were intricate and confusing. For Pericles, he planned the arrangement of the harbor-town Peiraeus at Athens. When the Athenians founded Thurii in Italy, he accompanied the colony as architect. Later, in 408 B.C., he superintended the building of the new city of Rhodes. His schemes consisted of series of broad, straight streets, intersecting one another at right angles. Benjamin Banneker 1731-1806 Benjamin Banneker, one of the nation's best-known African American inventors, was born in Maryland, which was then a British colony. He was the grandson of a white indentured servant from England and a former slave. Always interested in mathematics and science, in 1753, Banneker was inspired to build his own clock out of wood based on his own designs and calculations. The clock kept accurate time until Banneker's house burned with all its contents in 1806. Banneker taught himself astronomy and advanced math from books and instruments borrowed from his neighbors, the Ellicotts, who shared his interest. He made astronomical and tide calculations and weather predictions for yearly almanacs, which he published from 1792 to 1797. Banneker's almanacs were compared favorably with Benjamin Franklin's Poor Richard 's Almanac. He sent a copy of the manuscript for his almanac to Thomas Jefferson, along with a letter in which he challenged Jefferson's ideas about the inferiority of blacks.
    [Show full text]
  • Greek City Planning in Theory and Practice
    CHAPTER ONE Greek City Planning in Theory and Practice E'VQEV évao'réaag 55y; Nowat'Qoog Geoeuhég, shrew 3:1; ZXEft'p e'xa‘u; a’wé‘ycfiv h@mm’zwv, ciqui 3; 727950; g?tacra'z «6A2; mi 35‘ezluaro 07x02); mi W703»; mince 625V mi €3a'wcm7" éfofifag. From here godlike Nausithoés had removed [the Phaiakians] and led a migration, and settled in Scheria, far away from men who eat bread, and driven a wall about the city, and built the houses, and made the temples of the gods, and allotted the holdings. (Homer, Odyssey 6.7—10, trans. Lattimore) In this earliest reference to Greek colonization, the basic elements of founding a new polis are already in place: the uninhabited land, the construction of fortifications and the temples of the gods, the division and allotment of agri— cultural land, and the building ofhouses, presumably on lots assigned to the c010— nists like the farmland. In its essence, the process remained basically the same for a thousand years. The goal of this chapter is not to provide a history of Greek city planning.1 Rather, it will consider a few literary accounts and historical cities which develop issues concerning the relations between polis and household, issues which relate to the understanding of the archaeological remains at Olynthus. These issues in- clude the composite nature of the citizen body in new cities and the consequent need to unify a diverse population, the correspondence between physical organi— zation and social structure, and the importance of the distribution of land as a mechanism for achieving unity and order.
    [Show full text]