Index Rerum Et Nominum Antiquorum

Total Page:16

File Type:pdf, Size:1020Kb

Index Rerum Et Nominum Antiquorum INDEX RERUM ET NOMINUM ANTIQUORUM For nomina antiqua see also index locorum potiorum. The numbers again refer to the location in the footnotes (abbreviated n, e.g. 47n156 means p. 47 note 156), in the complementary notes (abbreviated en, e.g. 129cn225 means p. 129 complementary note 225), and in the text (just the page number). The cross-references in the notes may also be of some help. Aelius Donatus see Donatus Archimedes 6n13, 13, 24, 24n81, Aelius Theon 56n185, 122cn5 37n127, 40, 41,41nl37, 43, 44,45- Aetius 47n156, 129cn225 8,45n148,48n158,48n159,53, atnov tlj~ £mypacplj~ see 53n177, 62n206,92, 103, 103n349, isagogical questions (title) 103n353, 113, 115, 115n382, 116, Albinus 12, 71, 72n250 117 Alcinous 99, 99n337, 107n364, Archytas of Tarentum 119n397 111, 112, 114, 120n400 Aristaeus mathematicus 10, Alexander of Aphrodisias 11n31, 21, 64 23n79, 107n364, 108n365, 111-2, Aristarchus of Samos 14 111-2n374, 112n375, 114, 126cn89 Aristotle 4nl0, 12, 13n39, 33n118, Alexander of Lycopolis on 34, 43,46,47, 47nl56, 48, 52, Demiurge 108, 108n365 56n185, 66n226, 67n227, 67n228, Alexander Polyhistor 1 02n343 68n229, 82n290,83n295,86-7,95, 0./..oyov see line(s) 103n353, 109, 111, 112n375, 114, Ammonius Hermiae 13, 20, 115-6, 118, 119, 123cn11, 124- 21n68,43,43n143,45,48,56,88, 5cn67, 131cn357 88n313,92, 129cn260, 130cn308 Aristoxeneans 73n255 avayvrocrt~, avaytvcOOKElV, see arithmetic 9n25, 19, 22, 24n80, reading (study) 29, 57, 61nl96, 79, 82-91, 83n295, an-Nayrizi see Anaritius 118, 120n403 an-Nadim see at N arithmology 19, 90 ava/..oy{a see proportion arrangement see isagogical ques- analysis 9-14, 9n26, 10n27, 11n34, tions 16, 36n122, 62-3, 62n204, 62n207, &ppT]tOV see line(s) 64n218, 64n219, 65, 123cn26 apxaiot see ancients avanaA.tv /..ucn~ 123cn26 amiq>Eta see isagogical questions Anaritius 25n84, 26, 26n90, (unclarity) 125cn77, 126cn89 Asclepius of Tralles 20, 88-9 ancients 1n3, 20-1, 22, 23, 23n76, astrolabe 88n313, 129cn260 30, 42, 51, 86-7, 117-9, 117n389, astrology 1, 15, 68n229, 71-5, 119n396 7ln246, 72n251, 76n261, 78-9, 96- ante opus/ in ipso opere 61, 79 8 Anthemius of Trailes 31 Astronomer, Great 17-20, 17n50, Antiphon the Sophist 46 18n54,90 Apollinarius mathematicus 15 Astronomer, Little 16-20, 17n50, Apollonius of Perga 3n8, 7, 7n19, 17n51, 18n54 9n26, 10, 10n27, 10n29, 11, 13, acrtpOVOJ.lOU!J.EVa 20n66 13n39, 21, 24, 24n81, 32,33n117, astronomy 1, lnl, 1n3, 2, 6, 14- 36-40, 36nl22, 37nl27, 38nl28, 20, 18n54, 20n66, 22,23n79, 39n131, 39n132, 40-3, 41n137, 24n80, 29, 54, 63, 65-71, 66n223, 41n139, 44,47, 48, 62, 64, 65,92, 66n226,68n229,69n234, 71n246, 95, 123cn26 72, 73, 76-8, 76n261, 83, 83n295, Apuleius 106 84,88n313,90,92,93, 114,115, Aratus 15n46, 38nl28 116, 118, 120n403, 129cn260 Arcadius 80 Athanasius 108, 108n366, 130cn319 INDEX RERUM ET NOMINUM ANTIQUORUM 169 Attalus of Pergamum 7, 36, 125~cn77, 126cn89, 127cn108 38n128,39n132,40 on Hippocrates 15-6, 128cn217 Attalus of Rhodes 38n128 onJohn 56 Atticus platonicus 101n340, 105, on Nicomachus 19, 87-9, 106 88n310 authenticity see isagogical questions on Ptolemy 3, 3n8, 8, 17, 18, Autolycus of Pitane 14, 15, 69n234 19, 25, 65n222, 76-81, 76n261, 76n263, 76n264, 78n267,93, ~acnA.tu~ 96, 128-9cn225 Apuleius (Demiurge) 106 on the Alcibiades maior 41n136 Atticus (Demiurge I on the Golden Verses 56 naiJ.~acnA.tu~) 106 on the Timaeus 47, 48, 103, 109, Numenius (First God) 107 109n368, 113, 114-5, 117, 120 Origen the Christian on Virgil 62 (Demiurge) 105, 107, commentary tradition 2, 6-20, 107n364 8n24, 13n39, 22-6, 43n142, Philoponus (Demiurge) 47n157, 61n200, 77, 80n278, 107n364 82n287, 87-9, 87-8n310, 89-91, ps.Plato 105, 106, 107n364 103, 128cn217, 12~9cn225 see also Demiurge comments in margine 10n27, biography see vita 13, 13n39, 25, 42, 43 Boethius 13n39, 82n287, 89 see also Quintilian's formula; ante opus Calcidius 99n337 conics calculation 6, 24n80, 69n234 Apollonius 36-40 canon (see also corpus) 5, 10n27, Archimedes 37n127, 41 56 Eutocius 40-3 of Analysis 12, 13, 16 Hypatia 43n142 of Astronomy 16 Serenus 3n8, 43n142 of Plato's works 5, 12, 13 Con on of Samos 40 of Plotinus' treatises 12n38, 30 contents see isagogical questions canonics 22n72, 24n80, 29, 62, 63, (theme) 73n255, 83,83n295,90, 120n403 corpus of writings 4, 5, 10n27, 12, Cassiodorus 17-8, 19 12n37, 13, 14, 15, 15n45, 16, catalogue see vita 16n47, 17, 18, 20, 26, 28,56,93 Charmadas 5 see also canon Chrysippus of Soloi 23n79, creative see interpretation 86n305, 128cn192 Cicero 7n21, 18, 109n368 Damascius 19, 61n196, 114n380, circle 46, 48, 64, 102, 102n343, 129cn260 102n345, 111, 112n375 dates 2-3, 12, 13 clarification, clarity see isagogical of analytical corpus 13 questions of Anon. in Nicom. 89n318 classification see isagogical of Anon. in Ptol. 17n48 questions (arrangement) of astronomical corpus 53-4 Cleomedes 23n79, 24n81 of Conica 36 Commentaries 1 of Aelius Theon 122cn5 on Apollonius 3, 3n8, 13, 36, of Apollonius 2, 36n122, 41, 48 40-3, 43n142 ofEutocius 3, 43n143 on Archimedes 3, 13, 40, 44-8, of Geminus 23n79 45n148 of Heron 2, 49, 50 on Aristotle 47, 48, 109, 111-2, of Pappus 3, 101 115, 116, 126cn89 ofPtolemy 2 on astronomical works 14-20, of Serenus 3n8 17n51 ofTheodosius 14n42 on Euclid 2n7, 3, 8, 11n33, 23- ofTheon 3 35, 23n78, 24-5n84, 25n85, datum see OEOOIJ.EYOY 27n98, 31-5, 32n114, 34n120, David the Invincible 68n229 36, 42, 50, 55, 61-5, 64n219, dedicatee(s) 8n21, 36, 37, 38n128, 72n250,77, 92, 93, 99, 99n336, 40,44n145,66, 71 .
Recommended publications
  • Mathematicians
    MATHEMATICIANS [MATHEMATICIANS] Authors: Oliver Knill: 2000 Literature: Started from a list of names with birthdates grabbed from mactutor in 2000. Abbe [Abbe] Abbe Ernst (1840-1909) Abel [Abel] Abel Niels Henrik (1802-1829) Norwegian mathematician. Significant contributions to algebra and anal- ysis, in particular the study of groups and series. Famous for proving the insolubility of the quintic equation at the age of 19. AbrahamMax [AbrahamMax] Abraham Max (1875-1922) Ackermann [Ackermann] Ackermann Wilhelm (1896-1962) AdamsFrank [AdamsFrank] Adams J Frank (1930-1989) Adams [Adams] Adams John Couch (1819-1892) Adelard [Adelard] Adelard of Bath (1075-1160) Adler [Adler] Adler August (1863-1923) Adrain [Adrain] Adrain Robert (1775-1843) Aepinus [Aepinus] Aepinus Franz (1724-1802) Agnesi [Agnesi] Agnesi Maria (1718-1799) Ahlfors [Ahlfors] Ahlfors Lars (1907-1996) Finnish mathematician working in complex analysis, was also professor at Harvard from 1946, retiring in 1977. Ahlfors won both the Fields medal in 1936 and the Wolf prize in 1981. Ahmes [Ahmes] Ahmes (1680BC-1620BC) Aida [Aida] Aida Yasuaki (1747-1817) Aiken [Aiken] Aiken Howard (1900-1973) Airy [Airy] Airy George (1801-1892) Aitken [Aitken] Aitken Alec (1895-1967) Ajima [Ajima] Ajima Naonobu (1732-1798) Akhiezer [Akhiezer] Akhiezer Naum Ilich (1901-1980) Albanese [Albanese] Albanese Giacomo (1890-1948) Albert [Albert] Albert of Saxony (1316-1390) AlbertAbraham [AlbertAbraham] Albert A Adrian (1905-1972) Alberti [Alberti] Alberti Leone (1404-1472) Albertus [Albertus] Albertus Magnus
    [Show full text]
  • 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]
  • Implementing Eratosthenes' Discovery in the Classroom: Educational
    Implementing Eratosthenes’ Discovery in the Classroom: Educational Difficulties Needing Attention Nicolas Decamp, C. de Hosson To cite this version: Nicolas Decamp, C. de Hosson. Implementing Eratosthenes’ Discovery in the Classroom: Educational Difficulties Needing Attention. Science and Education, Springer Verlag, 2012, 21 (6), pp.911-920. 10.1007/s11191-010-9286-3. hal-01663445 HAL Id: hal-01663445 https://hal.archives-ouvertes.fr/hal-01663445 Submitted on 18 Dec 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Sci & Educ DOI 10.1007/s11191-010-9286-3 Implementing Eratosthenes’ Discovery in the Classroom: Educational Difficulties Needing Attention Nicolas De´camp • Ce´cile de Hosson Ó Springer Science+Business Media B.V. 2010 Abstract This paper presents a critical analysis of the accepted educational use of the method performed by Eratosthenes to measure the circumference of Earth which is often considered as a relevant means of dealing with issues related to the nature of science and its history. This method relies on a number of assumptions among which the parallelism of sun rays. The assumption of sun rays parallelism (if it is accurate) does not appear spontaneous for students who consider sun rays to be divergent.
    [Show full text]
  • 9 · the Growth of an Empirical Cartography in Hellenistic Greece
    9 · The Growth of an Empirical Cartography in Hellenistic Greece PREPARED BY THE EDITORS FROM MATERIALS SUPPLIED BY GERMAINE AUJAe There is no complete break between the development of That such a change should occur is due both to po­ cartography in classical and in Hellenistic Greece. In litical and military factors and to cultural developments contrast to many periods in the ancient and medieval within Greek society as a whole. With respect to the world, we are able to reconstruct throughout the Greek latter, we can see how Greek cartography started to be period-and indeed into the Roman-a continuum in influenced by a new infrastructure for learning that had cartographic thought and practice. Certainly the a profound effect on the growth of formalized know­ achievements of the third century B.C. in Alexandria had ledge in general. Of particular importance for the history been prepared for and made possible by the scientific of the map was the growth of Alexandria as a major progress of the fourth century. Eudoxus, as we have seen, center of learning, far surpassing in this respect the had already formulated the geocentric hypothesis in Macedonian court at Pella. It was at Alexandria that mathematical models; and he had also translated his Euclid's famous school of geometry flourished in the concepts into celestial globes that may be regarded as reign of Ptolemy II Philadelphus (285-246 B.C.). And it anticipating the sphairopoiia. 1 By the beginning of the was at Alexandria that this Ptolemy, son of Ptolemy I Hellenistic period there had been developed not only the Soter, a companion of Alexander, had founded the li­ various celestial globes, but also systems of concentric brary, soon to become famous throughout the Mediter­ spheres, together with maps of the inhabited world that ranean world.
    [Show full text]
  • A Short History of Greek Mathematics
    Cambridge Library Co ll e C t i o n Books of enduring scholarly value Classics From the Renaissance to the nineteenth century, Latin and Greek were compulsory subjects in almost all European universities, and most early modern scholars published their research and conducted international correspondence in Latin. Latin had continued in use in Western Europe long after the fall of the Roman empire as the lingua franca of the educated classes and of law, diplomacy, religion and university teaching. The flight of Greek scholars to the West after the fall of Constantinople in 1453 gave impetus to the study of ancient Greek literature and the Greek New Testament. Eventually, just as nineteenth-century reforms of university curricula were beginning to erode this ascendancy, developments in textual criticism and linguistic analysis, and new ways of studying ancient societies, especially archaeology, led to renewed enthusiasm for the Classics. This collection offers works of criticism, interpretation and synthesis by the outstanding scholars of the nineteenth century. A Short History of Greek Mathematics James Gow’s Short History of Greek Mathematics (1884) provided the first full account of the subject available in English, and it today remains a clear and thorough guide to early arithmetic and geometry. Beginning with the origins of the numerical system and proceeding through the theorems of Pythagoras, Euclid, Archimedes and many others, the Short History offers in-depth analysis and useful translations of individual texts as well as a broad historical overview of the development of mathematics. Parts I and II concern Greek arithmetic, including the origin of alphabetic numerals and the nomenclature for operations; Part III constitutes a complete history of Greek geometry, from its earliest precursors in Egypt and Babylon through to the innovations of the Ionic, Sophistic, and Academic schools and their followers.
    [Show full text]
  • The Two Earths of Eratosthenes Author(S): Christián Carlos Carman and James Evans Source: Isis, Vol
    University of Puget Sound Sound Ideas All Faculty Scholarship Faculty Scholarship 3-2015 The woT Earths of Eratosthenes James Evans University of Puget Sound, [email protected] Christián Carlos Carman Buenos Aires, Argentina Follow this and additional works at: http://soundideas.pugetsound.edu/faculty_pubs Citation Christián C. Carman and James Evans, “The wT o Earths of Eratosthenes,” Isis 106 (2015), 1-16. This Article is brought to you for free and open access by the Faculty Scholarship at Sound Ideas. It has been accepted for inclusion in All Faculty Scholarship by an authorized administrator of Sound Ideas. For more information, please contact [email protected]. The Two Earths of Eratosthenes Author(s): Christián Carlos Carman and James Evans Source: Isis, Vol. 106, No. 1 (March 2015), pp. 1-16 Published by: The University of Chicago Press on behalf of The History of Science Society Stable URL: http://www.jstor.org/stable/10.1086/681034 . Accessed: 08/12/2015 15:41 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The University of Chicago Press and The History of Science Society are collaborating with JSTOR to digitize, preserve and extend access to Isis.
    [Show full text]
  • Antipodes: in Search of the Southern Continent Is a New History of an Ancient Geography
    ANTIPODES In Search of the Southern Continent AVAN JUDD STALLARD Antipodes: In Search of the Southern Continent is a new history of an ancient geography. It reassesses the evidence for why Europeans believed a massive southern continent existed, About the author and why they advocated for its Avan Judd Stallard is an discovery. When ships were equal historian, writer of fiction, and to ambitions, explorers set out to editor based in Wimbledon, find and claim Terra Australis— United Kingdom. As an said to be as large, rich and historian he is concerned with varied as all the northern lands both the messy detail of what combined. happened in the past and with Antipodes charts these how scholars “create” history. voyages—voyages both through Broad interests in philosophy, the imagination and across the psychology, biological sciences, high seas—in pursuit of the and philology are underpinned mythical Terra Australis. In doing by an abiding curiosity about so, the question is asked: how method and epistemology— could so many fail to see the how we get to knowledge and realities they encountered? And what we purport to do with how is it a mythical land held the it. Stallard sees great benefit gaze of an era famed for breaking in big picture history and the free the shackles of superstition? synthesis of existing corpuses of That Terra Australis did knowledge and is a proponent of not exist didn’t stop explorers greater consilience between the pursuing the continent to its sciences and humanities. Antarctic obsolescence, unwilling He lives with his wife, and to abandon the promise of such dog Javier.
    [Show full text]
  • Aristarchus of Samos and Graeco-Babylonian Astronomy George Huxley
    Arfstarchus of Samos and Graeco-Babylonian Astronomy Huxley, George Greek, Roman and Byzantine Studies; Summer 1964; 5, 2; ProQuest pg. 123 Aristarchus of Samos and Graeco-Babylonian Astronomy George Huxley N THE HALF CENTURY following the death of Alexander the Great the I history of astronomy amongst the Greeks is dominated by Aris­ tarchus the Samian, who is best known for his theory of the earth's revolution about the sun. His life cannot be dated exactly, but it is clear that he was already of mature age by 280 B.C., for Ptolemy states that "the men around Aristarchus," that is to say his pupils, observed the summer solstice in that year, the 50th of the first Callippic period [Ptolemy, Almagest 3.1]. He was a pupil of Strato the Lampsacene, who succeeded Theophrastus as head of the Lyceum in ca. 288/7 B.C. [Apollodorus 244 F 40] and remained in that post for eighteen years till his death not later than 269 B.C. [Apollodorus 244 F 350]. The date of the publication of Aristarchus's heliocentric theory is not known, but the doctrine was attacked by Cleanthes the Stoic land so must have been well known by 232 B.C., when Cleanthes died; but the helio­ centric hypothesis may have been formulated much earlier than that. Vitruvius spoke highly of the versatility of Aristarchus in geometry, astronomy, and music [De Architectura 1.1.16], and ascribes to him the invention of two kinds of sundial-the hemispherical uKac/>T} and the disc in the plane [9.8.1].2 He perhaps made use of these improved instruments in his observations of the solstices.
    [Show full text]
  • The Cambridge History of Philosophy in Late Antiquity
    THE CAMBRIDGE HISTORY OF PHILOSOPHY IN LATE ANTIQUITY The Cambridge History of Philosophy in Late Antiquity comprises over forty specially commissioned essays by experts on the philosophy of the period 200–800 ce. Designed as a successor to The Cambridge History of Later Greek and Early Medieval Philosophy (ed. A. H. Armstrong), it takes into account some forty years of schol- arship since the publication of that volume. The contributors examine philosophy as it entered literature, science and religion, and offer new and extensive assess- ments of philosophers who until recently have been mostly ignored. The volume also includes a complete digest of all philosophical works known to have been written during this period. It will be an invaluable resource for all those interested in this rich and still emerging field. lloyd p. gerson is Professor of Philosophy at the University of Toronto. He is the author of numerous books including Ancient Epistemology (Cambridge, 2009), Aristotle and Other Platonists (2005)andKnowing Persons: A Study in Plato (2004), as well as the editor of The Cambridge Companion to Plotinus (1996). The Cambridge History of Philosophy in Late Antiquity Volume I edited by LLOYD P. GERSON cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao˜ Paulo, Delhi, Dubai, Tokyo, Mexico City Cambridge University Press The Edinburgh Building, Cambridge cb2 8ru,UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521876421 C Cambridge University Press 2010 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.
    [Show full text]
  • A Hellenistic Legacy: the Foundation for an ‘Unorthodox’ World View Within the Byzantine Tradition
    Kernos Revue internationale et pluridisciplinaire de religion grecque antique 1 | 1988 Varia A Hellenistic Legacy: The Foundation for an ‘Unorthodox’ World View within the Byzantine Tradition J.B. McMinn Electronic version URL: http://journals.openedition.org/kernos/83 DOI: 10.4000/kernos.83 ISSN: 2034-7871 Publisher Centre international d'étude de la religion grecque antique Printed version Date of publication: 1 January 1988 ISSN: 0776-3824 Electronic reference J.B. McMinn, « A Hellenistic Legacy: The Foundation for an ‘Unorthodox’ World View within the Byzantine Tradition », Kernos [Online], 1 | 1988, Online since 31 January 2011, connection on 01 May 2019. URL : http://journals.openedition.org/kernos/83 ; DOI : 10.4000/kernos.83 Kernos Kernos, 1(1988), p. 63-77. A helセenistャc LEGACY : THE FOUNDATION FOR AN 'UNORTHODOX' WORLD ,VIEW WITHIN BYZANTINE TRADITION (part one) On one historical point almost aU historians of Byzantine civilization are genera11y agreed, namely, that external changes in the East during the time of the Emperor Justinian pose the question of survival of late antiquity and its tradition in the new Byzantine world. In fact, they make the explicit c1aim that with the rise of the monastic movement, the anny reform, the c10sure of the universities, and the expansion of the Arabs, the influence of Hellenistic culture as a dominating force in Byzantine life cornes to an end1. And, as H.W. HAUSSIG, A History of Byzantine Civilization, trans".lM. Hussey, New York, 1971, p. 48-49, 74, 76-90, 115, 121-128, and 210-233. More than other historians, HAUSSIG (op. cit., p. 75) presses his point: «The age of Justinian is essentially the time of transition from the world of late antiquity [Hellenistic period] to that of Byzantium [...]».
    [Show full text]
  • Bibliography
    Bibliography A. Aaboe, Episodes from the Early History of Mathematics (Random House, New York, 1964) A.D. Aczel, Fermat’s Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem (Four Walls Eight Windows, New York, 1996) D. Adamson, Blaise Pascal: Mathematician, Physicist, and Thinker About God (St. Martin’s Press, New York, 1995) R.P. Agarwal, H. Agarwal, S.K. Sen, Birth, Growth and Computation of Pi to ten trillion digits. Adv. Differ. Equat. 2013, 100 (2013) A.A. Al-Daffa’, The Muslim Contribution to Mathematics (Humanities Press, Atlantic Highlands, 1977) A.A. Al-Daffa’, J.J. Stroyls, Studies in the Exact Sciences in Medieval Islam (Wiley, New York, 1984) E.J. Aiton, Leibniz: A Biography (A. Hilger, Bristol, Boston, 1984) R.E. Allen, Greek Philosophy: Thales to Aristotle (The Free Press, New York, 1966) G.J. Allman, Greek Geometry from Thales to Euclid (Arno Press, New York, 1976) E.N. da C. Andrade, Sir Issac Newton, His Life and Work (Doubleday & Co., New York, 1954) W.S. Anglin, Mathematics: A Concise History and Philosophy (Springer, New York, 1994) W.S. Anglin, The Queen of Mathematics (Kluwer, Dordrecht, 1995) H.D. Anthony, Sir Isaac Newton (Abelard-Schuman, New York, 1960) H.G. Apostle, Aristotle’s Philosophy of Mathematics (The University of Chicago Press, Chicago, 1952) R.C. Archibald, Outline of the history of mathematics.Am. Math. Monthly 56 (1949) B. Artmann, Euclid: The Creation of Mathematics (Springer, New York, 1999) C.N. Srinivasa Ayyangar, The History of Ancient Indian Mathematics (World Press Private Ltd., Calcutta, 1967) A.K. Bag, Mathematics in Ancient and Medieval India (Chaukhambha Orientalia, Varanasi, 1979) W.W.R.
    [Show full text]
  • Hipparchus's Table of Chords
    ApPENDIX 1 Hipparchus's Table of Chords The construction of this table is based on the facts that the chords of 60° and 90° are known, that starting from chd 8 we can calculate chd(180° - 8) as shown by Figure Al.1, and that from chd S we can calculate chd ~8. The calculation of chd is goes as follows; see Figure Al.2. Let the angle AOB be 8. Place F so that CF = CB, place D so that DOA = i8, and place E so that DE is perpendicular to AC. Then ACD = iAOD = iBOD = DCB making the triangles BCD and DCF congruent. Therefore DF = BD = DA, and so EA = iAF. But CF = CB = chd(180° - 8), so we can calculate CF, which gives us AF and EA. Triangles AED and ADC are similar; therefore ADIAE = ACIDA, which implies that AD2 = AE·AC and enables us to calculate AD. AD is chd i8. We can now find the chords of 30°, 15°, 7~0, 45°, and 22~0. This gives us the chords of 150°, 165°, etc., and eventually we have the chords of all R P chord 8 = PQ, C chord (180 - 8) = QR, QR2 = PR2 _ PQ2. FIGURE A1.l. 235 236 Appendix 1. Hipparchus's Table of Chords Ci"=:...-----""----...........~A FIGURE A1.2. multiples of 71°. The table starts: 2210 10 8 2 30° 45° 522 chd 8 1,341 1,779 2,631 3,041 We find the chords of angles not listed and angles whose chords are not listed by linear interpolation. For example, the angle whose chord is 2,852 is ( 2,852 - 2,631 1)0 .
    [Show full text]