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Simon Stevin
II THE PRINCIPAL WORKS OF SIMON STEVIN E D IT E D BY ERNST CRONE, E. J. DIJKSTERHUIS, R. J. FORBES M. G. J. MINNAERT, A. PANNEKOEK A M ST E R D A M C. V. SW ETS & Z E IT L IN G E R J m THE PRINCIPAL WORKS OF SIMON STEVIN VOLUME II MATHEMATICS E D IT E D BY D. J. STRUIK PROFESSOR AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE (MASS.) A M S T E R D A M C. V. SW ETS & Z E IT L IN G E R 1958 The edition of this volume II of the principal works of SIMON STEVIN devoted to his mathematical publications, has been rendered possible through the financial aid of the Koninklijke. Nederlandse Akademie van Wetenschappen (Royal Netherlands Academy of Science) Printed by Jan de Lange, Deventer, Holland The following edition of the Principal Works of SIMON STEVIN has been brought about at the initiative of the Physics Section of the Koninklijke Nederlandse Akademie van Weten schappen (Royal Netherlands Academy of Sciences) by a committee consisting of the following members: ERNST CRONE, Chairman of the Netherlands Maritime Museum, Amsterdam E. J. DIJKSTERHUIS, Professor of the History of Science at the Universities of Leiden and Utrecht R. J. FORBES, Professor of the History of Science at the Municipal University of Amsterdam M. G. J. M INNAERT, Professor of Astronomy at the University of Utrecht A. PANNEKOEK, Former Professor of Astronomy at the Municipal University of Amsterdam The Dutch texts of STEVIN as well as the introductions and notes have been translated into English or revised by Miss C. -
Beginnings of Trigonometry
Beginnings of Trigonometry Trigonometry is an area of mathematics used for determining geometric quantities. Its name, first published in 1595 by B. Pitiscus, means "the study of trigons (triangles)" in Latin. Ancient Greek Mathematicians first used trigonometric functions with the chords of a circle. The first to publish these chords in 140 BC was Hipparchus, who is now called the founder of trigonometry. In AD 100, Menelaus, another Greek mathematician, published six lost books of tables of chords. Ptolemy, a Babylonian, also wrote a book of chords. Using chords, Ptolemy knew that sin(xy+= ) sin x cos y + cos x sin y and abc = = sinABC sin sin In his great astronomical handbook, The Almagest, Ptolemy provided a table of chords for steps of °, from 0° to 180°, that is accurate to 1/3600 of a unit. Ptolemy's degree of accuracy is due in part because the Hellenistic Greeks had adopted the Babylonian base- 60 (sexagesimal) numeration system. He also explained his method for constructing his table of chords, and in the course of the book he gave many examples of how to use the table to find unknown parts of triangles from known parts. Ptolemy provided what is now known as Menelaus's theorem for solving spherical triangles, as well, and for several centuries his trigonometry was the primary introduction to the subject for any astronomer. Sine first appeared in the work of Aryabhata, a Hindu. He used the word jya for sine. He also published the first sine tables. Brahmagupta, in 628, also published a table of sines for any angle. -
Copernicus and His Revolutions
Copernicus and his Revolutions Produced for the Cosmology and Cultures Project of the OBU Planetarium by Kerry Magruder August, 2005 2 Credits Written & Produced by: Kerry Magruder Narrator: Candace Magruder Copernicus: Kerry Magruder Cardinal Schönberg: Phil Kemp Andreas Osiander: J Harvey C. S. Lewis: Phil Kemp Johann Kepler: J Harvey Book Images courtesy: History of Science Collections, University of Oklahoma Libraries Photographs and travel slides courtesy: Duane H.D. Roller Archive, History of Science Collections, University of Oklahoma Libraries Digital photography by: Hannah Magruder Soundtrack composed and produced by: Eric Barfield Special thanks to... Peter Barker, Bernie Goldstein, Katherine Tredwell, Dennis Danielson, Mike Keas, JoAnn Palmeri, Hannah Magruder, Rachel Magruder, Susanna Magruder, Candace Magruder Produced with a grant from the American Council of Learned Societies 3 1. Contents 1. Contents________________________________________________3 2. Introduction _____________________________________________4 A. Summary ____________________________________________4 B. Synopsis ____________________________________________5 C. Instructor Notes_______________________________________7 3. Before the Show _________________________________________9 A. Vocabulary and Definitions _____________________________9 B. Pre-Test ____________________________________________10 4. Production Script________________________________________11 A. Production Notes_____________________________________11 B. Theater Preparation___________________________________13 -
Al-Kindi, a Ninth-Century Physician, Philosopher, And
AL-KINDI, A NINTH-CENTURY PHYSICIAN, PHILOSOPHER, AND SCHOLAR by SAMI HAMARNEH FROM 9-12 December, I962, the Ministry of Guidance in Iraq celebrated the thousandth anniversary of one of the greatest intellectual figures of ninth century Baghdad, Abui Yuisuf Ya'qiib ibn Ishaq al-Kind? (Latin Alkindus).1 However, in the aftermath ofthis commendable effort, no adequate coverage of al-Kindl as a physician-philosopher ofardent scholarship has, to my knowledge, been undertaken. This paper, therefore, is intended to shed light on his intel- lectual contributions within the framework of the environment and time in which he lived. My proposals and conclusions are mainly based upon a study of al-Kindi's extant scientific and philosophical writings, and on scattered information in the literature of the period. These historical records reveal that al-Kindi was the only man in medieval Islam to be called 'the philosopher of the Arabs'.2 This honorary title was apparently conferred upon him as early as the tenth century if not during his lifetime in the ninth. He lived in the Abbasids' capital during a time of high achievement. As one of the rare intellectual geniuses of the century, he con- tributed substantially to this great literary, philosophic, and scientific activity, which included all the then known branches of human knowledge. Very little is known for certain about the personal life of al-Kind?. Several references in the literary legacy ofIslam, however, have assisted in the attempt to speculate intelligently about the man. Most historians of the period confirm the fact that al-Kindl was of pure Arab stock and a rightful descendant of Kindah (or Kindat al-Muliuk), originally a royal south-Arabian tribe3. -
The Arabic-Latin Translators – Natural Science and Philosophy
CHARLES BURNETT List of Publications Books, and articles over 100 pages long Articles and pamphlets, arranged thematically, and in chronological order within each topic The Arabic-Latin Translators – Natural Science and Philosophy – Astronomy and Astrology - Medicine and Psychology – Magic and Divination – Arithmetic and Geometry – Anglo- Norman Science and Learning in the Twelfth Century – Peter Abelard and the French Schools – Music – Contacts between the West and the Far East – Miscellaneous – Reviews (selection) List of editions of Latin texts in books and articles above (Please note that some diacritical markings are missing) Books, and articles over 100 pages long: 1. Hermann of Carinthia, De essentiis, critical edition, translation and commentary, Leiden, 1982, 385 pp. (reviews in Speculum, 1984, pp. 911–3, Cahiers de civilisation médiévale, 28, 1985, p. 685, Mittellateinisches Jahrbuch, 20, 1985, pp. 287–90, Deutsches Archiv, 41, 1985, p. 255, Rivista di storia della filosofia, 2, 1984, pp. 349–51, Bulletin de théologie ancienne et médiévale, 14, 1989, p. 695). 2. ‘A Checklist of the Manuscripts Containing Writings of Peter Abelard and Heloise and Other Works Closely Associated with Abelard and his School’, Revue d’histoire des textes, 14–15, 1984–5, pp. 183–302 (with David Luscombe and Julia Barrow). 3. Pseudo-Bede, De mundi celestis terrestrisque constitutione: a Treatise on the Universe and the Soul, edition, translation and commentary, Warburg Institute Surveys and Texts 10, London, 1985. 88 pp. (reviews in Isis, 77, 1986, pp. 182–3, Revue d’histoire ecclésiastique, 81, 1986, p. 742, Ambix, 33, 1986, p. 155, Journal of the History of Astronomy, 19, 1988, pp. -
The Reappearance of Sapphic Fragments in the Italian Renaissance
1 The reappearance of sapphic fragments in the Italian Renaissance 2 3 4 In this article the survival of the sapphic fragments of the ancient times in Renaissance period is 5 examined. More specifically the reappearance of the sapphic verses is presented concerning the first 6 publications (editio princeps) and the most widespread texts of ancient authors during West 7 Renaissance. These texts were the primary sources, on which the later publications of the sapphic 8 work were based, while they also had a great influence on the reception of the ancient poet by the 9 Renaissance writers. 10 11 Key words: classical tradition in the Italian Renaissance; reception of Sappho; survival of the 12 sapphic poetry during the Renaissance 13 14 Introduction: In ancient times, Sappho's poetry was an object of admiration, and many ancient 15 sources refer to her as the Tenth Muse (Hallett 1979: 447) or ‘the poetess’, as Homer was ‘the poet’ 16 (Parker 1993: 312). Also, the Alexandrian grammarians included Sappho in the canon of the nine 17 lyric poets (ibid: 340). It seems, however, that already in the 9th century A.D. the poems of Sappho 18 have been disappeared: around 1550, Jerome Cardan reports that Gregory of Nazianzus had 19 publicly destroyed Sappho's works, while at the end of the 16th century, Joseph Justus Scaliger 20 claims that her poems were burnt in Rome and Constantinople in 1073 by order of Pope Gregory 21 VII (Reynolds 2001: 81). Similar information is also recorded by other writers1. In fact, Sappho's 22 works were probably lost since people stopped to copy them in the period that the parchment 23 replaced the papyrus (ibid: 18). -
Preprint N°494
2019 Preprint N°494 The Reception of Cosmography in Vienna: Georg von Peuerbach, Johannes Regiomontanus, and Sebastian Binderlius Thomas Horst Published in the context of the project “The Sphere—Knowledge System Evolution and the Shared Scientific Identity of Europe” https://sphaera.mpiwg-berlin.mpg.de The Reception of Cosmography in Vienna: Georg von Peuerbach, Johannes Regiomontanus, and Sebastian Binderlius1 Abstract In this paper, the importance of the cosmographical activities of the Vienna astronomical “school” for the reception of the Tractatus de Sphaera is analyzed. First, the biographies of two main representatives of the Vienna mathematical/astronomical circle are presented: the Austrian astronomers, mathematicians, and instrument makers Georg von Peuerbach (1423– 1461) and his student Johannes Müller von Königsberg (Regiomontanus, 1436–1476). Their studies influenced the cosmographical teaching at the University of Vienna enormously for the next century and are relevant to understanding what followed; therefore, the prosopo- graphical introductions of these Vienna scholars have been included here, even if neither can be considered a real author of the Sphaera. Moreover, taking the examples of an impressive sixteenth-century miscellany (Austrian Na- tional Library, Cod. ser. nov. 4265, including the recently rediscovered cosmography by Sebastian Binderlius, compiled around 1518), the diversity of different cosmographical studies in the capital of the Habsburg Empire at the turning point between the Middle Ages and the early modern period is demonstrated. Handwritten comments in the Vienna edition of De sphaera (1518) also show how big the influence of Sacrobosco’s work remained as a didactical tool at the universities in the first decades of the sixteenth century—and how cosmographical knowledge was transformed and structured in early modern Europe by the editors and readers of the Sphaera. -
Translations from Arabic (Astronomy/Astrology) : the Formation of Terminology
Translations from Arabic (Astronomy/Astrology) : The Formation of Terminology In the history of science the notion of “Arabic science” - or, in our context, “Arabic astronomy” - is a well-known term, mostly in connection with its influ ence on the development of Western science in the Middle Ages. This term, however, needs some comment, both for the terms “astronomy” and “Arabic”. First: the Arabs were the inhabitants of the Arabian Peninsula, mostly bedouins, largely isolated from the scientific developments in the Near Eastern regions cultivating the sciences. On the other hand, these Arabs observed the natural phenomena for many centuries. They observed the stars and their behav iour through the year and derived from them rules for fixing the seasons and periods of rain and drought etc. and used the stars for orientation in their migra tions by night. All this was sort of a popular knowledge of the sky and popular star lore. After the spread of Islam through the countries of the Middle East the Arabs gradually became acquainted with the sciences cultivated in the Byzan tine and Iranian regions. In the eighth century translations of astrological and astronomical works began to be made from Persian, Indian and Greek into Arabic, and from now on started what has become so well-known as “Arabic astronomy”, i.e. the “scientific” astronomy, in contrast to the old-Arabic folk astronomy. While the translation movement continued into the tenth century, from the first half of the ninth century on “Arabic” astronomers, having studied the translated materials, began to develop their own, “Arabic”, scientific, and no longer popular, astronomy. -
The Copernican System
The Copernican system Jan P. Hogendijk Dept of Mathematics, Utrecht University 8 june 2011 1 Prelude: the 15th century Copernicus: biography Copernicus’ new system: Main Points Copernicus’ new system: Dirty Details The reception of the new system 2 Renaissance Invention of Printing by Johannes Gutenberg (Mainz), ca. 1450: typesetting with movable type, printing press, paper. 3 Most important astronomer of the 15th century Johannes Muller¨ of K¨onigsberg (Bavaria), or Regiomontanus (1436-1476) 4 Biography of Regiomontanus (1436-1476) 1448: Entered University of Leipzig. 1460: Met cardinal Bessarion (from Trebizond), travelled with him to Italy. 1463: completed Epitome of the Almagest (of Ptolemy) [printed 1492]. ca. 1461: made observations of eclipses, etc. which diverged from the predictions by e.g. the Alfonsine tables. 5 Quotation from Regiomontanus (1464) “I cannot [but] wonder at the indolence of common astronomers of our age, who, just as credulous women, receive as something divine and immutable whatever they come upon in books, either of tables of their instructions, for they believe in writers and make no effort to find the truth.” Regiomontanus wanted to restore and “update” Ptolemaic astronomy in order to predict astronomical phenomena accurately. 1471: he founded printing press in Nurnberg,¨ producing mathematical and astronomical works with great accuracy. 6 Product of Regiomontanus’ Press (1472) Novae Theoricae Planetarum, Georg von Peuerbach (1423-1461) 7 Example of Regiomontanus’ own predictions solar and lunar eclipses, 1489, 1490 8 Nicolas Copernicus (1473-1543): biography 1473 Torun (Poland) - 1543 Frauenburg = Frombork (now in Poland, near coast and Russian border) Studied at the University of Krakow. Worked in service of the Catholic Church until his death. -
Michael C. Weber the ADOPTION of AL-Farabl's "MATHEMATICAL
Michael C. Weber THE ADOPTION OF AL-FARABl'S "MATHEMATICAL SCIENCES" IN THE MEDIEVAL WEST: A Study in Cross-Cultural Borrowing It is a truism recognised in all modern textbooks in both Western and World Civilisation that the medieval Islamic civilisation transferred the accomplishments of Greek science to the Latin West. As is well known, this was largely accomplished in Christian Spain after the Re conquista (i. e., after 1085) and slightly later in Sicily. Cross-cultural borrowing of this type was, as William McNeill said, "one of the prin ciple stimuli to innovation" in the receiving civilisation. I Prior to the twelfth-century translations of Greek and Arabic texts, the Carolingian heritage in "scientific study" was of a derivative and secondary char acter, more likely to cite Virgil or Macrobius as authorities than any scientific writer of Anti-quity.2 This was particularly evident in the sciences of the quadrivium, given that "All quadrivium studies lan guished in the Latin world [of late antiquity] and geometry was the most neglected subject of the four."3 As the centuries passed, the situa tion grew even worse, primarily as the result of there being very few ancient works available to medieval scholars on any of the sciences of the quadrivium. However, if we look at the guidelines for the "Divisions of the Sciences" and the lists of readings required for de grees in the thirteenth and fourteenth centuries, we see a renewed em phasis on the mathematical sciences. It is my contention that not only was the Arabic influence decisive for this innovation, but the particu lar path of influence in these sciences was the result of the translation and appropriation of curricular guides that had been written by Islamic scholars for their own students who wished to study ancient philoso phy and natural sciences, which they called the "Ancient" or "Foreign" sciences. -
Conrad Gessner Als Sprach- Und Literatur- Wissenschafter
Camenae n° 26 – novembre 2020 Urs B. LEU CONRAD GESSNER ALS SPRACH- UND LITERATUR- WISSENSCHAFTER Der Zürcher Universalgelehrte, Naturforscher und Arzt Conrad Gessner (1516–1565) hat kaum eigenständige Werke hinterlassen, die der neulateinischen Literatur zugezählt werden können, aber er hat verschiedene wichtige Beiträge zu den Sprachwissenschaften und zur Literaturgeschichte verfasst sowie zahlreiche Editionen antiker und byzantinischer Texte herausgegeben1. PHILOLOGISCHE PRÄGUNG Der Zürcher Reformator Huldrych Zwingli hat bekanntlich in der von ihm 1525 gegründeten Hohen Schule von Anfang an grossen Wert auf die Pflege der drei heiligen Sprachen (tres linguae sacrae) Hebräisch, Griechisch und Latein gelegt, in denen Jesus Christus am Kreuz auf Golgatha als König der Juden bezeichnet wurde wie es im Johannes- Evangelium, Kapitel 19, beschrieben wird: «Pilatus liess auch eine Tafel beschriften und sie oben am Kreuz anbringen. Darauf stand geschrieben: Jesus von Nazareth, der König der Juden. Diese Inschrift nun lasen viele Juden, denn die Stelle, wo Jesus gekreuzigt wurde, lag nahe bei der Stadt. Sie war in hebräischer, lateinischer und griechischer Sprache verfasst.» Zwingli betonte in seiner Schrift Wie Jugendliche aus gutem Haus zu erziehen ist die Wichtigkeit solider altsprachlicher Kenntnis vor allem für angehende Theologen: «Da ich es aber unternommen habe, diejenigen zu unterweisen, die schon die elementarsten Dinge erlernt haben, und da die lateinische Sprache überall bei allen bekannt ist, denke ich, dass diese keineswegs vernachlässigt -
The (Likely) Last Edition of Copernicus's Libri Revolutionum
Variants The Journal of the European Society for Textual Scholarship 14 | 2019 Varia The (likely) Last Edition of Copernicus’s Libri revolutionum André Goddu Electronic version URL: http://journals.openedition.org/variants/908 DOI: 10.4000/variants.908 ISSN: 1879-6095 Publisher European Society for Textual Scholarship Printed version Number of pages: 159-178 ISSN: 1573-3084 Electronic reference André Goddu, « The (likely) Last Edition of Copernicus’s Libri revolutionum », Variants [Online], 14 | 2019, Online since 10 July 2019, connection on 12 July 2019. URL : http://journals.openedition.org/ variants/908 ; DOI : 10.4000/variants.908 The authors The (likely) Last Edition of Copernicus’ Libri revolutionum André Goddu Review essay of Nicolas Copernic, De revolutionibus orbium coelestium, Des revolu- tions des orbes célestes. 3 volumes. Science et Humanisme, Collection published under the patronage of the Association Guillaume Budé (Paris: Les Belles Lettres, 2015). Vol. I: Introduction by Michel-Pierre Lerner and Alain-Philippe Segonds with the collaboration of Concetta Luna, Isabelle Pantin, and Denis Savoie, xxviii + 859 pp. Vol. II: Critical Edition and translation by Lerner, Segonds, and Jean-Pierre Verdet with the collaboration of Concetta Luna, viii + 537 pp. with French and Latin on facing pages and with the same page numbers. Vol. III: Notes, appendices, iconographic dossier, and general index by Lerner, Segonds, and Verdet with the collaboration of Luna, Savoie, and Michel Toulmonde, xviii + 783 pp. and 34 plates. T C’ , probably the last for the foresee- able future, represents the culmination of efforts that can be traced back to 1973. The two fundamental sources of De revolutionibus are Copernicus’s auto- graph copy which survived by sheer luck and the first edition published in Nuremberg in 1543.