Ptolemy's Tetrabiblos, Or Quadripartite
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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. -
What Are Primary Directions? 1
The Basics: What are Primary Directions? 1 1 The Basics: What are Primary Directions? The technique known today as primary directions is one of the most ancient and renowned methods of astrological forecasting. It is also, as I hope to show in this book, one of the most powerful. From classical antiquity throughout the Middle Ages and Renaissance, and even into the twentieth century, all the great names of western astrology have worked with primary directions.1 It was the predictive technique of Dorotheus and Ptolemy, of Māshāʾallāh and Abū Maʿshar, of Regiomontanus and Placidus, of Morin de Villefranche and William Lilly. To understand the traditional astrologers, we must understand primary directions. The primary motion The word primary refers not only to the pre-eminence of the technique, but to the primary motion on which it is based. This is simply the daily rotation of the earth around its axis, appearing to us as the rotation of the sky – complete with planets, stars, and the signs of the zodiac – around our place of observation.2 In approximately 24 hours not only the Sun, but every planet and zodiacal degree will rise in the east, culminate in the south (for an observer in the northern hemisphere), set in the west, and finally travel unseen across its lowest point in the north (the anti-culmination below the horizon) to the place where it will rise again. A planet or point in the zodiac rising at the eastern horizon is said to be conjunct the ascendant. When culminating, it is similarly conjunct the midheaven or medium caeli (MC); when setting, conjunct the descendant; and when anti-culminating, conjunct the lower midheaven or imum caeli (IC). -
Strategies of Defending Astrology: a Continuing Tradition
Strategies of Defending Astrology: A Continuing Tradition by Teri Gee A thesis submitted in conformity with the requirements for the degree of Doctorate of Philosophy Institute for the History and Philosophy of Science and Technology University of Toronto © Copyright by Teri Gee (2012) Strategies of Defending Astrology: A Continuing Tradition Teri Gee Doctorate of Philosophy Institute for the History and Philosophy of Science and Technology University of Toronto 2012 Abstract Astrology is a science which has had an uncertain status throughout its history, from its beginnings in Greco-Roman Antiquity to the medieval Islamic world and Christian Europe which led to frequent debates about its validity and what kind of a place it should have, if any, in various cultures. Written in the second century A.D., Ptolemy’s Tetrabiblos is not the earliest surviving text on astrology. However, the complex defense given in the Tetrabiblos will be treated as an important starting point because it changed the way astrology would be justified in Christian and Muslim works and the influence Ptolemy’s presentation had on later works represents a continuation of the method introduced in the Tetrabiblos. Abû Ma‘shar’s Kitâb al- Madkhal al-kabîr ilâ ‘ilm ahk. âm al-nujûm, written in the ninth century, was the most thorough surviving defense from the Islamic world. Roger Bacon’s Opus maius, although not focused solely on advocating astrology, nevertheless, does contain a significant defense which has definite links to the works of both Abû Ma‘shar and Ptolemy. As such, he demonstrates another stage in the development of astrology. -
PHIL 339 Intro Phil of Science, UO Philosophy Dept, Winter 2018
1 PHIL 339 Intro Phil of Science, UO Philosophy Dept, Winter 2018 Albert Einstein, Marie Curie, Benjamin Franklin,Watson & Crick, Rosalind Franklin, Galileo Galilei, Dr. Linus Pauling, William Crawford Eddy, James Watt Maria Goeppert-Mayer, Charles Darwin, James Clerk Maxwell, Archimedes, Lise Meitner, Sigmund Freud, Irène Joliot-Curie Gregor Johann Mendel,Chien-Shiung Wu,Barbara McClintock, Neil DeGrasse Tyson. All Contents ©2017 Photo Researchers, Inc., 307 Fifth Avenue, New York, NY , 10016 212-758-3420 800-833- 9033 Science Source® is a registered trademark of Photo Researchers, Inc. / 2 PHIL 339 Intro Phil of Science, UO Philosophy Dept, Winter 2018 Course Data PHIL 339 Intro Phil of Science >2 4.00 cr. Grading Options: Optional for all students Instructor: Prof. N. Zack, Office: 239 SCH Phone: (541) 346-1547 Office Hours: WTh -2-3 See CRN for CommentsPrereqs/Comments: Prereq: one philosophy course (waiver available) *Note: This is a 2-hr course twice a week and discussion is built in. There will breaks and variations in subject matter to keep it interesting. OVERVIEW/DESCRIPTION (See also APPENDICES A-D AFTER SYLLABUS) Philosophy of Science is unique to philosophy. It raises questions about facts, theories, reality, explanation, and truth not often addressed by scientists or other humanistic scholars. This course will provide the basics of Philosophy of Science with concrete examples as science now applies to contemporary subjects such as Climate Change, Feminism, and Race. Students will have an opportunity to choose their own branches of inquiry for end-of-term reports. Work will consist of reading, discussion, and 4 3-page papers. -
General Index
General Index Italic page numbers refer to illustrations. Authors are listed in ical Index. Manuscripts, maps, and charts are usually listed by this index only when their ideas or works are discussed; full title and author; occasionally they are listed under the city and listings of works as cited in this volume are in the Bibliograph- institution in which they are held. CAbbas I, Shah, 47, 63, 65, 67, 409 on South Asian world maps, 393 and Kacba, 191 "Jahangir Embracing Shah (Abbas" Abywn (Abiyun) al-Batriq (Apion the in Kitab-i balJriye, 232-33, 278-79 (painting), 408, 410, 515 Patriarch), 26 in Kitab ~urat ai-arc!, 169 cAbd ai-Karim al-Mi~ri, 54, 65 Accuracy in Nuzhat al-mushtaq, 169 cAbd al-Rabman Efendi, 68 of Arabic measurements of length of on Piri Re)is's world map, 270, 271 cAbd al-Rabman ibn Burhan al-Maw~ili, 54 degree, 181 in Ptolemy's Geography, 169 cAbdolazlz ibn CAbdolgani el-Erzincani, 225 of Bharat Kala Bhavan globe, 397 al-Qazwlni's world maps, 144 Abdur Rahim, map by, 411, 412, 413 of al-BlrunI's calculation of Ghazna's on South Asian world maps, 393, 394, 400 Abraham ben Meir ibn Ezra, 60 longitude, 188 in view of world landmass as bird, 90-91 Abu, Mount, Rajasthan of al-BlrunI's celestial mapping, 37 in Walters Deniz atlast, pl.23 on Jain triptych, 460 of globes in paintings, 409 n.36 Agapius (Mabbub) religious map of, 482-83 of al-Idrisi's sectional maps, 163 Kitab al- ~nwan, 17 Abo al-cAbbas Abmad ibn Abi cAbdallah of Islamic celestial globes, 46-47 Agnese, Battista, 279, 280, 282, 282-83 Mu\:lammad of Kitab-i ba/Jriye, 231, 233 Agnicayana, 308-9, 309 Kitab al-durar wa-al-yawaqft fi 11m of map of north-central India, 421, 422 Agra, 378 n.145, 403, 436, 448, 476-77 al-ra~d wa-al-mawaqft (Book of of maps in Gentil's atlas of Mughal Agrawala, V. -
Claudius Ptolemy: Tetrabiblos
CLAUDIUS PTOLEMY: TETRABIBLOS OR THE QUADRIPARTITE MATHEMATICAL TREATISE FOUR BOOKS OF THE INFLUENCE OF THE STARS TRANSLATED FROM THE GREEK PARAPHRASE OF PROCLUS BY J. M. ASHMAND London, Davis and Dickson [1822] This version courtesy of http://www.classicalastrologer.com/ Revised 04-09-2008 Foreword It is fair to say that Claudius Ptolemy made the greatest single contribution to the preservation and transmission of astrological and astronomical knowledge of the Classical and Ancient world. No study of Traditional Astrology can ignore the importance and influence of this encyclopaedic work. It speaks not only of the stars, but of a distinct cosmology that prevailed until the 18th century. It is easy to jeer at someone who thinks the earth is the cosmic centre and refers to it as existing in a sublunary sphere. However, our current knowledge tells us that the universe is infinite. It seems to me that in an infinite universe, any given point must be the centre. Sometimes scientists are not so scientific. The fact is, it still applies to us for our purposes and even the most rational among us do not refer to sunrise as earth set. It practical terms, the Moon does have the most immediate effect on the Earth which is, after all, our point of reference. She turns the tides, influences vegetative growth and the menstrual cycle. What has become known as the Ptolemaic Universe, consisted of concentric circles emanating from Earth to the eighth sphere of the Fixed Stars, also known as the Empyrean. This cosmology is as spiritual as it is physical. -
Fortis-Bank-Sa-Nv-2003.Pdf
I. INTRODUCTION 3 II. PROPOSED PROFIT APPROPRIATION FOR THE PERIOD 4 DISTRIBUTION OF AN INTERIM DIVIDEND : REPORT OF THE ACCREDITED STATUTORY AUDITORS 6 III. AUDITORS: SPECIAL BRIEFS 8 IV. ARTICLE 523 OF COMPANY LAW 8 V. NOTES TO THE CONSOLIDATED BALANCE SHEET AND INCOME STATEMENT 9 VI. CONSOLIDATED BALANCE SHEET AND INCOME STATEMENT 15 REPORT OF THE ACCREDITED STATUTORY AUDITORS 83 VII. SHAREHOLDER BASE 85 VIII. MONTHLY HIGH AND LOW FOR FORTIS BANK SHARES ON THE WEEKLY AUCTIONS IN 2003 86 IX. BOARD OF DIRECTORS AND COUNCIL OF ACCREDITED STATUTORY AUDITORS FORTIS BANK 87 X. EXTERNAL POSTS HELD BY DIRECTORS AND EXECUTIVES THAT ARE SUBJECT TO A LEGAL DISCLOSURE REQUIREMENT 89 I. INTRODUCTION This document contains the annual report and the consolidated annual accounts of Fortis Bank as at 31 December 2003. The financial environment in which Fortis Bank operates was influenced in 2003 by an international unstable geopolitical situation combined with less than positive economic conditions and an improving, though still hesitant stock market climate. Despite a persistently challenging international economic environment, both Fortis and Fortis Bank once again succeeded during 2003 in streamlining and expanding operations beyond the domestic Benelux market; this had implications in terms of commercial organisation and operational and support activities. Fortis Bank continues to focus on its customer-first policy, vigorous cost control, efficiency improvement and the effective management of increased financial risks. Initiatives launched in previous years to prepare for the introduction and repercussions of the revision of the Basel Accord of 1988 regarding the capital adequacy standards of banks and the application of IAS/IFRS (International Accounting Standards / International Financial Reporting Standards) were further pursued in 2003; both changes will have a major impact on financial reporting. -
Kepler's Cosmological Synthesis
Kepler’s Cosmological Synthesis History of Science and Medicine Library VOLUME 39 Medieval and Early Modern Science Editors J. M. M. H. Thijssen, Radboud University Nijmegen C. H. Lüthy, Radboud University Nijmegen Editorial Consultants Joël Biard, University of Tours Simo Knuuttila, University of Helsinki Jürgen Renn, Max-Planck-Institute for the History of Science Theo Verbeek, University of Utrecht VOLUME 20 The titles published in this series are listed at brill.com/hsml Kepler’s Cosmological Synthesis Astrology, Mechanism and the Soul By Patrick J. Boner LEIDEN • BOSTON 2013 Cover illustration: Kepler’s Supernova, SN 1604, appears as a new star in the foot of Ophiuchus near the letter N. In: Johannes Kepler, De stella nova in pede Serpentarii, Prague: Paul Sessius, 1606, pp. 76–77. Courtesy of the Department of Rare Books and Manuscripts, Milton S. Eisenhower Library, Johns Hopkins University. Library of Congress Cataloging-in-Publication Data Boner, Patrick, author. Kepler’s cosmological synthesis: astrology, mechanism and the soul / by Patrick J. Boner. pages cm. — (History of science and medicine library, ISSN 1872-0684; volume 39; Medieval and early modern science; volume 20) Based on the author’s doctoral dissertation, University of Cambridge, 2007. Includes bibliographical references and index. ISBN 978-90-04-24608-9 (hardback: alk. paper) — ISBN 978-90-04-24609-6 (e-book) 1. Kepler, Johannes, 1571–1630—Philosophy. 2. Cosmology—History. 3. Astronomy—History. I. Title. II. Series: History of science and medicine library; v. 39. III. Series: History of science and medicine library. Medieval and early modern science; v. 20. QB36.K4.B638 2013 523.1092—dc23 2013013707 This publication has been typeset in the multilingual “Brill” typeface. -
UC San Diego UC San Diego Electronic Theses and Dissertations
UC San Diego UC San Diego Electronic Theses and Dissertations Title The science of the stars in Danzig from Rheticus to Hevelius / Permalink https://escholarship.org/uc/item/7n41x7fd Author Jensen, Derek Publication Date 2006 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA, SAN DIEGO THE SCIENCE OF THE STARS IN DANZIG FROM RHETICUS TO HEVELIUS A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in History (Science Studies) by Derek Jensen Committee in charge: Professor Robert S. Westman, Chair Professor Luce Giard Professor John Marino Professor Naomi Oreskes Professor Donald Rutherford 2006 The dissertation of Derek Jensen is approved, and it is acceptable in quality and form for publication on microfilm: _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ Chair University of California, San Diego 2006 iii FOR SARA iv TABLE OF CONTENTS Signature Page........................................................................................................... iii Dedication ................................................................................................................. iv Table of Contents ...................................................................................................... v List of Figures .......................................................................................................... -
October 2006
OCTOBER 2 0 0 6 �������������� http://www.universetoday.com �������������� TAMMY PLOTNER WITH JEFF BARBOUR 283 SUNDAY, OCTOBER 1 In 1897, the world’s largest refractor (40”) debuted at the University of Chica- go’s Yerkes Observatory. Also today in 1958, NASA was established by an act of Congress. More? In 1962, the 300-foot radio telescope of the National Ra- dio Astronomy Observatory (NRAO) went live at Green Bank, West Virginia. It held place as the world’s second largest radio scope until it collapsed in 1988. Tonight let’s visit with an old lunar favorite. Easily seen in binoculars, the hexagonal walled plain of Albategnius ap- pears near the terminator about one-third the way north of the south limb. Look north of Albategnius for even larger and more ancient Hipparchus giving an almost “figure 8” view in binoculars. Between Hipparchus and Albategnius to the east are mid-sized craters Halley and Hind. Note the curious ALBATEGNIUS AND HIPPARCHUS ON THE relationship between impact crater Klein on Albategnius’ southwestern wall and TERMINATOR CREDIT: ROGER WARNER that of crater Horrocks on the northeastern wall of Hipparchus. Now let’s power up and “crater hop”... Just northwest of Hipparchus’ wall are the beginnings of the Sinus Medii area. Look for the deep imprint of Seeliger - named for a Dutch astronomer. Due north of Hipparchus is Rhaeticus, and here’s where things really get interesting. If the terminator has progressed far enough, you might spot tiny Blagg and Bruce to its west, the rough location of the Surveyor 4 and Surveyor 6 landing area. -
The Age of Aquarius by Don Cerow, NCGR IV
The Age of Aquarius by Don Cerow, NCGR IV Welcome to the Age of Aquarius.* We are a generation that is perched on the dawn of a new epoch, a new vibration. The world is changing. Everything from politics to industry to our mortgages turns on a new pivot, and we are lucky enough to be able to witness the unfolding. There are those who feel as though the Age has already begun. Others believe that the Age is not yet here, and the called for changes have not yet fully unfolded. Both are correct. As we look around us, electricity fills the air. Lights, power, technology, refrigeration, computers, smart phones, microchips, and science are all manifestations of the New Age at work, of a brave new world already (up and running). But the use of fossil fuels, oil, coal, and natural gas, the inability of Congress to get things done due to party allegiances, the growing intensity of storms and the general weather patterns, are all indications Alpha Piscium and Omega Piscium are the stars thought by Don Cerow that the Age of Pisces is not yet over. to observationally “benchmark” the Age of Pisces. We are building to a crescendo with the warming of the planet being the Revelation 22:13 says, “I am the Alpha and the Omega, the First and the Last, the Beginning and the End.” When Revelation was written in the first century AD, the substantial catalyst that inaugurates “New Age” (Pisces) stretched out before them, describing what the future would hold. these changes. -
De Grote Dooi Zet In
De grote dooi zet in Karen Bies De Eerste Kamer heeft dit voorjaar de klimaatdoelen voor 2050 vastgesteld. Een energietransitie moet, maar welke maatregelen er komen en wie die gaat betalen, is niet duidelijk. ‘We kunnen niet op onze handen blijven zitten,’ zegt poolonderzoeker Maarten Loonen. Hij ziet op Spitsbergen de gletsjers afbrokkelen, de permafrost ontdooien. ‘Heel veel dat niet voorspeld was, is toch gebeurd. Dat maakt mij bang.’ ‘Op Spitsbergen, in een berg die altijd liep smeltwater van de ingang naar de letterlijk een rondje boven mijn hoofd. In bevroren is, zit sinds tien jaar een kamers toe. Het water bevroor en de drie het dorp Ny Ålesund zijn ‘s zomers 180 zadenbank. De zaden van een miljoen kilometer lange gang werd een ijsbaan. wetenschappers uit allerlei landen, die plantenrassen zijn daar in kamers Een ontwerpfout, zou je kunnen zeggen. elk hun eigen terrein onderzoeken. Ik ben ondergebracht. In geval van een grote Maar het laat ook zien dat we nog niet erheen gegaan voor de ganzen, verzamel oorlog of natuurramp zou deze ‘doomsday weten wat ons overkomt. Je probeert iets ook data over het gras, de poolvossen en vault’ het voedsel van de wereld veilig te bedenken dat alle rampen van de wereld de ijsberen. En omdat er zoveel verandert, stellen. Mocht de stroom in de ‘Svalbard overleeft. Nu al is het niet voldoende om doe ik nu ook de Noordse sternen en de Global Seed Vault’ uitvallen, dan duurt de klimaatverandering op Spitsbergen te insecten erbij.’ het 100 jaar eer de berg ontdooid is. De ondervangen.’ ingang zit op 70 meter hoogte.