DOCSLIB.ORG

Bernardino Baldi's in Mechanica Aristotelis Problemata Exercitationes

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Bernardino Baldi's in Mechanica Aristotelis Problemata Exercitationes Bernardino Baldi’s In mechanica Aristotelis problemata exercitationes ii Max Planck Research Library for the History and Development of Knowledge Series Editors Jürgen Renn, Robert Schlögl, Bernard F. Schutz. Edition Open Access Development Team Lindy Divarci, Beatrice Gabriel, Jörg Kantel, Matthias Schemmel, and Kai Surendorf, headed by Peter Damerow. Scientific Board Markus Antonietti, Ian Baldwin, Antonio Becchi, Fabio Bevilacqua, William G. Boltz, Jens Braarvik, Horst Bredekamp, Jed Z. Buchwald, Olivier Darrigol, Thomas Duve, Mike Edmunds, Yehuda Elkana, Fynn Ole Engler, Robert K. Englund, Mordechai Feingold, Rivka Feldhay, Gideon Freudenthal, Paolo Galluzzi, Kostas Gavroglu, Mark Geller, Domenico Giulini, Günther Görz, Gerd Graßhoff, James Hough, Manfred Laubich- ler, Glenn Most, Pier Daniele Napolitani, Alessandro Nova, Hermann Parzinger, Dan Potts, Circe Silva da Silva, Ana Simões, Richard Stephen- son, Mark Stitt, Noel M. Swerdlow, Liba Taub, Martin Vingron, Scott Walter, Norton Wise, Gerhard Wolf, Rüdiger Wolfrum, Zhang Baichun. Sources 3 Edition Open Access 2011 Bernardino Baldi’s In mechanica Aristotelis problemata exercitationes Elio Nenci Communicated by Jürgen Renn and Antonio Becchi Edition Open Access 2011 Max Planck Research Library for the History and Development of Knowledge Sources 3 Communicated by Jürgen Renn and Antonio Becchi Translated from Italian into English by Adriano Carugo Copyedited by Lindy Divarci ISBN 978-3-86931-961-2 First published 2011 Printed in Germany by epubli, Oranienstraße 183, 10999 Berlin http://www.epubli.de Edition Open Access http://www.edition-open-access.de Published under Creative Commons by-nc-sa 3.0 Germany Licence http://creativecommons.org/licenses/by-nc-sa/3.0/de/ The Deutsche Nationalbibliothek lists this publication in the Deutsche Na- tionalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de. The images of the facsimile part are produced by the Digitization Center of the Bavarian State Library, Munich from an original of the library’s rare book collection, call number Res/4 A.hydr.79 v The Max Planck Research Library for the History and Development of Knowledge comprises three subseries, Studies, Proceedings, and Sources. They present research results and the relevant sources in a new format that combines the advantages of traditional publications and the digital medium. Available both as printed books and as online open access publi- cations they present original scientific work submitted under the scholarly responsibility of members of the Scientific Board and their academic peers. The volumes of the three subseries and their electronic counterparts are directed at scholars and students of various disciplines, and at a broader public interested in how science shapes our world. They provide rapid access to knowledge at low cost. Moreover, by combining print with digital publication, the series offer a new way of publishing research in flux and of studying historical topics or current issues in relation to primary materials that are otherwise not easily available. The initiative is presently supported by research departments of three Max Planck Institutes, the MPI for the History of Science, the Fritz Haber Institute of the MPG, and the MPI for Gravitational Physics (Albert Ein- stein Institute). This is in line with the Berlin Declaration on Open Access to Knowledge in the Sciences and Humanities, launched by the Max Planck Society in 2003. The volumes of the Studies series are dedicated to a key subject in the history and development of knowledge, bringing together perspectives from different fields and combining source-based empirical research with theoretically guided approaches. Studies typically present working group volumes with integrative approaches to problems ranging from the global- ization of knowledge to the nature of spatial thinking. The volumes of the Proceedings series present the results of scientific meetings on current issues and support further cooperation on these issues with an electronic platform. The volumes of the Sources series typically presents a primary source – relevant for the history and development of knowledge – in facsimile, transcription, or translation. The original sources are complemented by an introduction and by commentaries reflecting original scholarly work. The sources reproduced in this series may be rare books, manuscripts, documents or other materials that are not readily accessible in libraries and archives. On the basis of scholarly expertise the publication of the three se- ries brings together traditional books produced by print-on-demand tech- niques with modern information technology. Based on and extending the functionalities of the existing open access repository ECHO (European vi Cultural Heritage Online), this initiative aims at a model for an unprece- dented, web-based scientific working environment integrating access to information with interactive features. Contents Part 1: On this Book 1 1 The Author................................................ 3 2 The Context............................................... 7 3 The Book .................................................. 15 3.1 The General Principle: The Figure of the Circle . 16 3.2 The Balance: Questions 1–2, 9–10 and 20 . 17 3.3 The Lever: Questions 3, 21–22, 28 . 19 3.4 Problems Concerning Sailing: Questions 4–7 . 20 3.5 The Easy Movement of Bodies with Round Shapes: Question 8 . 23 3.6 The Simple Machines. The Axle in the Wheel, the Pulley and the Wedge: Questions 11, 13, 17–18. 25 3.7 The Sling: Question 12 . 27 3.8 The Breaking and Deformation of Materials. Pieces of Wood and Pebbles: Questions 14–16. 28 3.9 The Force of Percussion: Question 19. 29 3.10 The Composition of Motions: Questions 23–24 . 30 3.11 The Construction of Beds: Question 25 . 33 3.12 The Placement of Weights Carried on the Shoulders: Questions 26–27, 29 . 33 3.13 Rising from a Sitting Position: Question 30. 35 3.14 Problems Concerning Motion: Questions 31–34 . 36 3.15 The Motion of Bodies in Eddying Water: Question 35 . 37 3.16 Appendix: The Problem of the Two Mean Proportionals . 37 4 Online Sources ............................................ 39 4.1 The First Edition of the Treatise of Baldi . 39 4.2 Ancient and Renaissance Sources Concerning Mechanics Used by Baldi . 39 4.3 Other Works and Translations by Baldi . 39 4.4 Other Renaissance Sources . 40 Bibliography............................................... 41 Part 2: Facsimile 45 Part 1: On this Book Chapter 1 The Author Bernardino Baldi was born in Urbino on June 6, 1553. After studying an- cient languages, he joined the group of scholars around the famous mathe- matician Federico Commandino.1 For many years Commandino had been preparing editions of the most important works of ancient mathematicians, translating them into Latin and providing them with textual commen- taries. Baldi himself took part in this enterprise. In his Life of Com- mandino he recalls: “when I was young and dedicated to these studies, I drew many of these geometrical figures with great labor.”2 And again, in the preface to his Italian translation of Hero’s3 Automati (Automata) he wrote: Hero wrote Spiritali (Pneumatics) as well as these Automati, and recently Federico Commandino translated Spiritali into Latin and illustrated it with figures.4 What Hero then wrote concerning Semoventi (Automata), fallen into oblivion since antiquity, was rescued and brought to light by me, at the sug- gestion of Commandino.5 Baldi studied under Commandino from 1570 to 1575, though between 1573 and 1575 he also attended the University of Padua to study medicine. But in Padua, as he himself states in one of his unpublished works, instead of dedicating himself to medical studies he followed the lectures on philos- ophy6 and those on classical literature given by Emanuel Margunios7 with whom he became friends. He also attended lectures on mathematics given by Pietro Catena,8 though without much benefit, as he himself states in his Cronica de’ matematici: 1Federico Commandino, 1509–1575. 2Baldi (1998, 518). 3Hero of Alexandria, first century CE. 4Commandino (1575). 5Baldi (1589, 9r). 6Genio, overo la misteriosa peregrinatione, Serrai (2002, 174–175). 7Emanuel Margunios, 1549–1602. 8Pietro Catena, 1501–1576. 4 1. The Author Pietro Catena (1573), Padua. He was giving lectures on math- ematics during the time I was at the University of Padua, and I attended his lectures on Aristotle’s Mechanics. He was old and facetious so that his classroom was filled with people who wanted to laugh rather than learn. He was not a man of great learning, and published just a small and simple work on the Sphere.9 Baldi’s most important work from that time was the Italian trans- lation of Hero’s Automati, which he had already finished, as can be seen from the dedication to the Venetian Giacomo Contarini:10 When Federico Commandino was still alive, I translated from the Greek text these two books of Hero’s Semoventi, thinking of publishing it at the time Commandino himself published Spiritali by the same ancient author. But other unexpected business as well as Commandino’s sudden death forced me to postpone the publication of the work.11 Soon after Commandino’s death, Baldi began to collect material for the composition of his work Vite de’ matematici (Lives of Mathemati- cians), while continuing his study of mathematics under the guidance of Guidobaldo del Monte.12 In 1580 he found a permanent position at the court of Guastalla, where he was employed as a court mathematician by Ferrante Gonzaga.13 The first biographer of Baldi, Fabrizio Scarloncino,14 states that in 1582 Baldi wrote a commentary on the Mechanical Prob- lems ascribed to Aristotle. This might have been the first draft of what was later published in the Exercitationes, which are presented here.15 During the next period of his life, Baldi produced many literary works as well as a series of studies on Vitruvius.16 About these works he wrote in his Life of Vitruvius: As to Scamilli impares,17 I wrote a little treatise where I re- jected the opinions of all those who wrote about it before me; 9Baldi (1707, 135–136).
Load more

Recommended publications
  • Hunting the White Elephant. When and How Did Galileo
    MAX-PLANCK-INSTITUT FÜR WISSENSCHAFTSGESCHICHTE Max Planck Institute for the History of Science PREPRINT 97 (1998) Jürgen Renn, Peter Damerow, Simone Rieger, and Michele Camerota Hunting the White Elephant When and how did Galileo discover the law of fall? ISSN 0948-9444 1 HUNTING THE WHITE ELEPHANT WHEN AND HOW DID GALILEO DISCOVER THE LAW OF FALL? Jürgen Renn, Peter Damerow, Simone Rieger, and Michele Camerota Mark Twain tells the story of a white elephant, a present of the king of Siam to Queen Victoria of England, who got somehow lost in New York on its way to England. An impressive army of highly qualified detectives swarmed out over the whole country to search for the lost treasure. And after short time an abundance of optimistic reports with precise observations were returned from the detectives giving evidence that the elephant must have been shortly before at that very place each detective had chosen for his investigations. Although no elephant could ever have been strolling around at the same time at such different places of a vast area and in spite of the fact that the elephant, wounded by a bullet, was lying dead the whole time in the cellar of the police headquarters, the detectives were highly praised by the public for their professional and effective execution of the task. (The Stolen White Elephant, Boston 1882) THE ARGUMENT In spite of having been the subject of more than a century of historical research, the question of when and how Galileo made his major discoveries is still answered insufficiently only. It is mostly assumed that he must have found the law of fall around the year 1604 and that only sev- 1 This paper makes use of the work of research projects of the Max Planck Institute for the History of Science in Berlin, some pursued jointly with the Biblioteca Nazionale Centrale in Florence, the Istituto e Museo di Storia della Scienza, and the Istituto Nazionale die Fisica Nucleare in Florence.
    [Show full text]
  • Galileo, Ignoramus: Mathematics Versus Philosophy in the Scientific Revolution
    Galileo, Ignoramus: Mathematics versus Philosophy in the Scientific Revolution Viktor Blåsjö Abstract I offer a revisionist interpretation of Galileo’s role in the history of science. My overarching thesis is that Galileo lacked technical ability in mathematics, and that this can be seen as directly explaining numerous aspects of his life’s work. I suggest that it is precisely because he was bad at mathematics that Galileo was keen on experiment and empiricism, and eagerly adopted the telescope. His reliance on these hands-on modes of research was not a pioneering contribution to scientific method, but a last resort of a mind ill equipped to make a contribution on mathematical grounds. Likewise, it is precisely because he was bad at mathematics that Galileo expounded at length about basic principles of scientific method. “Those who can’t do, teach.” The vision of science articulated by Galileo was less original than is commonly assumed. It had long been taken for granted by mathematicians, who, however, did not stop to pontificate about such things in philosophical prose because they were too busy doing advanced scientific work. Contents 4 Astronomy 38 4.1 Adoption of Copernicanism . 38 1 Introduction 2 4.2 Pre-telescopic heliocentrism . 40 4.3 Tycho Brahe’s system . 42 2 Mathematics 2 4.4 Against Tycho . 45 2.1 Cycloid . .2 4.5 The telescope . 46 2.2 Mathematicians versus philosophers . .4 4.6 Optics . 48 2.3 Professor . .7 4.7 Mountains on the moon . 49 2.4 Sector . .8 4.8 Double-star parallax . 50 2.5 Book of nature .
    [Show full text]
  • Geometry and Arithmetic in the Medieval Traditions of Euclid's
    Geometry and Arithmetic in the Medieval Traditions of Euclid's Elements: a View from Book II Leo Corry – Tel Aviv University Dedicated to my dear friend Sabetai Unguru on his 82th birthday Contents 1. Abstract .......................................................................................................... 1 2. Introduction .................................................................................................... 2 3. Euclid’s Elements - Book II and Geometric Algebra ............................................... 7 3.1. Elements Book II – An Overview ........................................................................................... 7 3.2. Geometric Algebra – An Overview ..................................................................................... 14 3.3. Visible and Invisible Figures ............................................................................................... 18 4. Book II in Late Antiquity and in Islam Mathematics ............................................. 22 4.1. Heron’s Commentary of the Elements ................................................................................ 22 4.2. Al-Khwārizmī and Abū Kāmil .............................................................................................. 27 4.3. Thābit ibn Qurra ............................................................................................................... 35 4.4. Al-Nayrīzī ........................................................................................................................
    [Show full text]
  • Sciences Recent Acquisitions
    BLACKWELL’S RARE BOOKS SCIENCES RECENT ACQUISITIONS 1 Blackwell’s Rare Books 48-51 Broad Street, Oxford, OX1 3BQ Direct Telephone: +44 (0) 1865 333555 Switchboard: +44 (0) 1865 792792 Email: [email protected] Fax: +44 (0) 1865 794143 www.blackwell.co.uk/rarebooks Our premises are in the main Blackwell bookstore at 48-51 Broad Street, one of the largest and best known in the world, housing over 200,000 new book titles, covering every subject, discipline and interest, as well as a large secondhand books department. There is lift access to each floor. The bookstore is in the centre of the city, opposite the Bodleian Library and Sheldonian Theatre, and close to several of the colleges and other university buildings, with on street parking close by. Oxford is at the centre of an excellent road and rail network, close to the London - Birmingham (M40) motorway and is served by a frequent train service from London (Paddington). Hours: Monday–Saturday 9am to 6pm. (Tuesday 9:30am to 6pm.) Purchases: We are always keen to purchase books, whether single works or in quantity, and will be pleased to make arrangements to view them. Auction commissions: We attend a number of auction sales and will be happy to execute commissions on your behalf. Blackwell’s online bookshop www.blackwell.co.uk Our extensive online catalogue of new books caters for every speciality, with the latest releases and editor’s recommendations. We have something for everyone. Select from our subject areas, reviews, highlights, promotions and more. Orders and correspondence should in every case be sent to our Broad Street address (all books subject to prior sale).
    [Show full text]
  • Treatise on Land Surveying Methods Using the Surveyor's Cross
    2019 IMEKO TC-4 International Conference on Metrology for Archaeology and Cultural Heritage Florence, Italy, December 4-6, 2019 The sixteenth-century find “Treatise On Land Surveying Methods Using the Surveyor’s Cross”, by Francesco Paciotti, military and civil architect to the Duchy of Urbino: the technical evolution of a surveying tool. Raffaella Marotti1 1 School of Conservation and Restoration of Cultural Heritage, Department of Pure and Applied Sciences (DiSPeA), Università degli Studi di Urbino "Carlo Bo", piazza della Repubblica, 13, 61029, Urbino, Italy, [email protected] Abstract - This paper focuses on the autograph Treatise Council Archive) at the Biblioteca Umanistica “On Land Surveying Methods Using the Surveyor’s dell’Università degli Studi di Urbino “Carlo Bo”, Cross” found at the Biblioteca Umanistica represents a primary source of information and data on the dell’Università degli Studi di Urbino “Carlo Bo” design and construction of this topographic tool, which (“Carlo Bo” Urbino University Humanistic Library). aimed to provide specific and precise measurements when The treatise was for many years erroneously included surveying land for the construction of fortifications. among the writings of the Urbino mathematician Furthermore, the treatise is of central importance as it Muzio Oddi (1569-1639), author of Dello Squadro (On bears witness to the wide and peculiar technical-scientific Land Surveying Methods Using the Surveyor’s Cross) of debate that characterised the Duchy of Urbino from the 1625, but through careful bibliographic research has second half of the 15th century to the first half of the 17th now been attributed to the civil and military architect century, making it culturally unique in Europe.
    [Show full text]
  • The Development of Euclidean Axiomatics the Systems of Principles and the Foundations of Mathematics in Editions of the Elements in the Early Modern Age
    Arch. Hist. Exact Sci. (2016) 70:591–676 DOI 10.1007/s00407-015-0173-9 The development of Euclidean axiomatics The systems of principles and the foundations of mathematics in editions of the Elements in the Early Modern Age Vincenzo De Risi1 Received: 4 August 2015 / Published online: 24 February 2016 © The Author(s) 2016. This article is published with open access at Springerlink.com Abstract The paper lists several editions of Euclid’s Elements in the Early Modern Age, giving for each of them the axioms and postulates employed to ground elementary mathematics. Contents 1 Introduction ..................................593 1.1 The Euclidean tradition .........................593 1.2 Axioms and postulates .........................602 2 The principles .................................618 2.1 The principles of Euclid .........................618 2.2 Further principles in the Greek tradition ................619 2.3 Additional common notions and the foundations of the theory of magnitudes ...............................619 2.4 Principles on mereological composition and multiples of magnitudes . 620 2.5 The theory of ratios and proportions ..................622 2.6 The Axiom of Archimedes and the theory of indivisibles .......626 2.7 Principles of arithmetic and number theory ...............626 2.8 General principles of space, situation, and givenness ..........628 2.9 Principles of intersection, incidence and connection ..........629 2.10 Principles of continuity .........................631 2.11 Principles of congruence, motion, and transportation
    [Show full text]
  • Annals of Science
    This article was downloaded by:[Sidoli, Nathan] On: 11 October 2007 Access Details: [subscription number 782956906] Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Annals of Science Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713692742 What We Can Learn from a Diagram: The Case of Aristarchus's On The Sizes and Distances of the Sun and Moon Nathan Sidoli a a Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada Online Publication Date: 01 October 2007 To cite this Article: Sidoli, Nathan (2007) 'What We Can Learn from a Diagram: The Case of Aristarchus's On The Sizes and Distances of the Sun and Moon', Annals of Science, 64:4, 525 - 547 To link to this article: DOI: 10.1080/00033790701336841 URL: http://dx.doi.org/10.1080/00033790701336841 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
    [Show full text]
  • Euclid (In the Renaissance)
    EUCLID (IN THE RENAISSANCE) Jens Høyrup Section for Philosophy and Science Studeis Roskilde University, Denmark Article written for Marco Sgarbi (ed.), Encyclopedia of Renaissance Philosophy Preprint 20 March 2017 Abstract Although the Latin Middle Ages received a number of versions of Euclid’s Elements and several other Euclidean works, by the 14th century only the Campanus redaction from c. 1259 was in circulation. In the 14th and 15th century, this redaction was encountered by students of Arts or Medical university faculties, even though we have scant evidence that Euclid impressed their minds. In the fifteenth century, other circles discovered him: Alberti took over the idea of elements, Regiomontanus used Euclid alongside Archimedes as an argument for the superiority of mathematics over philosophy, and one Florentine abbacus school tradition was able to give correct references to the Elements. A turn arrived with book printing. In 1482, the Campanus Elements were printed, and in 1498 and 1501 Giorgio Valla inserted pseudo-Euclidean and Euclidean material in two bulky volumes. A new though somewhat problematic Latin translation from the Greek (including also some minor works) was published by Zamberti in 1505, and until 1540 a number of reprints or re-editions of Campanus’s and Zamberti’s texts were published – at times in combination. From the 1540s onward, revisions, selections and vernacular translations began to appear, all based on the same two texts. In 1572, however, Commandino made a new Latin translation from Zamberti’s text and a sounder manuscript, and in 1574 Clavius produced a didactically oriented redaction. These two set the scene for the next two centuries.
    [Show full text]
  • PAPPUS of ALEXANDRIA (About 320 AD) by HEINZ KLAUS STRICK, Germany
    PAPPUS OF ALEXANDRIA (about 320 AD) by HEINZ KLAUS STRICK, Germany PAPPUS OF ALEXANDRIA is considered the last of the great Greek geometers. Almost nothing is known about his life - not even exactly when he lived. The only historical link is a commentary he wrote on a solar eclipse that he himself observed in Alexandria, which can be dated to October 320 by a modern calculation. It is known that he lived in Alexandria and led a "school" (or Academy) there. His main work was entitled Synagoge (Collection) and consisted of eight books. It represented a successful attempt to revive the classical geometry of the Greeks. PAPPUS was obviously not interested in replacing the books of the "ancients", but in bringing the meaning of these books (which probably all still existed at the time) back to consciousness and supplementing them with insights that had been added subsequently by other scholars. The collection also contained some references to writings by authors whose existence we might otherwise not have known about. The first translation of the Synagoge into Latin was by FEDERICO COMMANDINO in 1589, but it was then another few decades before RENÉ DESCARTES, PIERRE DE FERMAT and ISAAC NEWTON recognised the importance of the work and made it the basis of their own research. Book I on arithmetic has been completely lost, of Book II only a part exists (the fragment was discovered in 1688 by JOHN WALLIS in the Savillian Library in Oxford). It dealt with a problem of recreational mathematics: In ancient Greece, numerals were represented by letters, among others in the Milesian notation.
    [Show full text]
  • DEFENDING HYPATIA Archimedes NEW STUDIES in the HISTORY and PHILOSOPHY of SCIENCE and TECHNOLOGY
    DEFENDING HYPATIA Archimedes NEW STUDIES IN THE HISTORY AND PHILOSOPHY OF SCIENCE AND TECHNOLOGY VOLUME 25 EDITOR Jed Z. Buchwald, Dreyfuss Professor of History, California Institute of Technology, Pasadena, CA, USA. ASSOCIATE EDITORS Jeremy Gray, The Faculty of Mathematics and Computing, The Open University, Buckinghamshire, UK. Sharon Kingsland, Department of History of Science and Technology, Johns Hopkins University, Baltimore, MD, USA. ADVISORY BOARD Henk Bos, University of Utrecht Mordechai Feingold, California Institute of Technology Allan D. Franklin, University of Colorado at Boulder Kostas Gavroglu, National Technical University of Athens Anthony Grafton, Princeton University Paul Hoyningen-Huene, Leibniz UniversitätHannover Trevor Levere, University of Toronto Jesper Lützen, Copenhagen University William Newman, Indian University, Bloomington Lawrence Principe, The Johns Hopkins University Jürgen Renn, Max-Planck-Institut für Wissenschaftsgeschichte Alex Roland, Duke University Alan Shapir , oUniversity of Minnesota Nancy Siraisi, Hunter College of the City University of New York Michael R. DietrichDartmouth, College Michel Morange , IHPST, Paris Hans-Jörg RheinbergerMax-Planck-Institut, für Wissenschaftsgeschichte Noel Swerdlow, University of Chicago Archimedes has three fundamental goals; to furtherintegration the of the histories of science and technology with one another: to investigate the technical, social and practical histories of specific developments in science andnology; tech and finally, where possible and desirable, to bring the histories of science and technology intocontact closer with the philosophy of science. To these ends, each volume will have its own themetitle and and will be planned by one or more members of the Advisory Board in consultation with the editor. Although the volumes have specific themes, the series itself will not be limited to one or even to a few particular areas.
    [Show full text]
  • Max Planck Institute for the History of Science Archimedes
    MAX-PLANCK-INSTITUT FÜR WISSENSCHAFTSGESCHICHTE Max Planck Institute for the History of Science 2017 PREPRINT 487 Jens Hµyrup Archimedes: Knowledge and Lore from Latin Antiquity to the Outgoing European Renaissance Abstract With only Apuleius and Augustine as partial exceptions, Latin Antiquity did not know Archimedes as a mathematician but only as an ingenious engineer and astronomer, serving his city and killed by fatal distraction when in the end it was taken by ruse. The Latin Middle Ages forgot even much of that, and when Archimedean mathematics was translated in the 12th and 13th centuries, almost no integration with the traditional image of the person took place. With the exception of Petrarca, who knew the civically useful engineer and the astrologer (!), fourteenth-century Humanists show no interest in Archimedes. In the 15th century, however, “higher artisans” with Humanist connections or education took interest in Archimedes the technician and started identifying with him. In mid-century, a new translation of most works from the Greek was made by Jacopo Cremonensis, and Regiomontanus and a few other mathematicians began resurrecting the image of the geometer, yet without emulating him in their own work. Giorgio Valla’s posthumous De expetendis et fugiendis rebus from 1501 marks a watershed. Valla drew knowledge of the person as well as his works from Proclus and Pappus, thus integrating the two. Over the century, a number of editions also appeared, the editio princeps in 1544, and mathematical work following in the footsteps of Archimedes was made by Maurolico, Commandino and others. The Northern Renaissance only discovered Archimedes in the 1530s, and for long only superficially.
    [Show full text]
  • Galileo, the Telescope, and the Science of Optics in the Sixteenth Century
    Galileo, the Telescope, and the Science of Optics in the Sixteenth Century A Case Study of Instrumental Practice in Art and Science Sven Dupré Proefschrift voorgelegd ter behaling van de graad van doctor in de wijsbegeerte Promotor : Prof. dr. Marc De Mey | Co-Promotor : Prof. dr. Fernand Hallyn Universiteit Gent - 2002 Contents List of illustrations page IV Acknowledgements XI Chapter I. Galileo’s Telescope in the History of Science 1 Chapter II. The Appropriation of Optics in the Sixteenth Century: Sixteenth Century Mathematical Practitioners and Medieval Optics 17 Chapter III. Optics and Instrument Design in the Sixteenth Century: Breaking Rays and Shadows Running Backwards 84 Chapter IV. The Point of Inversion in Sixteenth Century Optics: The ‘Theory of the Concave Spherical Mirror’ of Ettore Ausonio 127 Chapter V. Galileo, Mathematical Practitioner: His Early Sources on Optics 175 Chapter VI. ‘As Distant Cities in Flemish Paintings’: The Point of Inversion and the Invention of the Telescope 234 Chapter VII. ‘As Little Moons’: Galileo’s Exploration of Light 285 Chapter VIII. Postscript: Big History, Small History 319 Appendix I. Ausonio, Fragments 323 Appendix II. Transcription and Translation: Ausonio’s ‘Theorica Speculi Concavi Sphaerici’ 326 Abstract 327 Bibliography 333 III List of Illustrations List of Illustrations Cover Illustration Hans Bol, Flood Lanscape with a View of a City, 1562, ADV (Graz). Chapter I. Galileo’s Telescope in the History of Science. 1. Galileo, Telescope I, Museo di Storia della Scienza (Florence). 2. Replica of Telescope I by the Author. 3. Galileo, Telescope II, Museo di Storia della Scienza (Florence). 4. Galileo, Single Broken Lens, Museo di Storia della Scienza (Florence).
    [Show full text]