The Book As Instrument: Craft and Technique in Early Modern Practical Mathematics
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The Knowledge Bank at the Ohio State University Ohio State Engineer
The Knowledge Bank at The Ohio State University Ohio State Engineer Title: A History of the Slide Rule Creators: Derrenberger, Robert Graf Issue Date: Apr-1939 Publisher: Ohio State University, College of Engineering Citation: Ohio State Engineer, vol. 22, no. 5 (April, 1939), 8-9. URI: http://hdl.handle.net/1811/35603 Appears in Collections: Ohio State Engineer: Volume 22, no. 5 (April, 1939) A HISTORY OF THE SLIDE RULE By ROBERT GRAF DERRENBERGER HE slide rule, contrary to popular belief, is not in 1815 made a rule with scales specially adapted for a modern invention but in its earliest form is the calculations involved in chemistry. T several hundred years old. As a matter of fact A very important improvement was made by Sir the slide rule is not an invention, but an outgrowth of Isaac Newton when he devised a method of solving certain ideas in mathematics. cubic equations by laying three movable slide rule scales Leading up to the invention of the slide rule was the side by side 'and bringing them together or in line by- invention of logarithms, in 1614, by John Napier. laying a separate straight edge across them. This is Probably the first device having any relation to the now known as a runner. It was first definitely attached slide rule was a logarithmic scale made by Edmund to the slide rule by John Robertson in 1775. Gunter, Professor of Astronomy at Gresham College, About 1780 William Nicholson, publisher and editor in London, in 1620. This scale was used for multi- of "Nicholson's Journal", a kind of technical journal, plication and division by measuring the sum or differ- began to devote most of his time to the study and im- ence of certain scale lengths. -
Francis Bacon and the Transformation of Early-Modern Philosophy
Francis Bacon and the Transformation of Early-Modern Philosophy STEPHEN GAUKROGER University of Sydney PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building, Trumpington Street, Cambridge, United Kingdom CAMBRIDGE UNIVERSITY PRESS The Edinburgh Building, Cambridge cb2 2ru, UK 40 West 20th Street, New York, ny 10011-4211, USA 10 Stamford Road, Oakleigh, vic 3166, Australia Ruiz de Alarcón 13, 28014 Madrid, Spain Dock House, The Waterfront, Cape Town 8001, South Africa http://www.cup.org © Cambridge University Press 2001 This book 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. First published 2001 Printed in the United States of America Typeface New Baskerville 10.25/13 pt. System QuarkXPress® [mg] A catalog record for this book is available from the British Library Library of Congress Cataloging in Publication Data Gaukroger, Stephen. Francis Bacon and the transformation of early-modern philosophy / Stephen Gaukroger. p. cm. Includes bibliographical references and index. isbn 0 521 80154 0 – isbn 0 521 80536 8 (pbk.) 1. Bacon, Francis, 1561–1626. 2. Philosophy, Modern – History. I. Title. b1198 .g38 2001 192 – dc21 00–063097 isbn 0 521 80154 0 hardback isbn 0 521 80536 8 paperback Contents Acknowledgments page ix References to Bacon’s works xi Prologue 1 1 The nature of Bacon’s project 6 From arcane learning to public knowledge 6 A via media -
England's Search for the Northern Passages in the Sixteenth And
- ARCTIC VOL. 37, NO. 4 (DECEMBER 1984) P. 453472 England’s Search for the Northern Passages in the Sixteenth and. Early Seventeenth Centuries HELEN WALLIS* For persistence of effort in the. face of adversity no enterprise this waie .is of so grete.avantage over the other navigations in in thehistory of exploration wasmore remarkable than shorting of half the waie, for the other must.saileby grete cir- England’s search for the northern passages to the Far East. .cuites and compasses and .thes shal saile by streit wais and The inspiration for the search was the hope of sharing in the lines” (Taylor, 1932:182). The dangerous part of the.naviga- riches of oriental commerce. In the tropical.regions of the Far tion was reckoned.to .be the last 300 leagues .before reaching East were situated, Roger Barlow wrote in 1541, “the most the Pole and 300 leagues beyond it (Taylor, 1932:181). Once richest londes and ilondes in the the worlde, for all the golde, over the Polethe expedition would choose whetherto sail east- spices, aromatikes and pretiose stones” (Barlow, 1541: ward to the Orient by way of Tartary or westward “on the f”107-8; Taylor, 1932:182). England’s choice of route was backside ofall the new faund land” [NorthAmerica]. limited, however, by the prior discoveries of .Spain and Por- Thorne’s confident .opinion that“there is no lande inhabitable tugal, who by the Treatyof Tordesillas in 1494 had divided the [i.e. uninhabitable€, nor Sea innavigable” (in Hakluyt, 1582: world between them. With the “waie ofthe orient” and ‘The sig.DP) was a maxim (as Professor.Walter Raleigh (19O5:22) waie of the occydent” barred, it seemed that Providence had commented) “fit to be inscribed as a head-line on the charter especially reserved for England. -
Biographical Notes on Henry Briggs (1561 - 1630)
Biographical Notes 1 Biographical Notes on Henry Briggs (1561 - 1630). 1. Introduction. This introduction is related mainly to the professional life of Henry Briggs, and in particular to his work in table production. Briggs was the inaugural Professor of Geometry for many years at Gresham College, London. These notes are based partially on the chapter devoted to Briggs in J. Ward's : Lives of the Professors of Gresham College, (1740). In addition, the earlier work by T. Smith (1707), A Memoir of the Life and Work ..... Mr. Henry Briggs1 has been consulted and quoted from, and other sources, including letters. There is a fair amount of overlap of the material presented in these two sources, and we will mainly use the first reference, though it appeared later, as Ward's narrative holds the interest. Ward himself was professor of Rhetoric at the college at a later time, and he had available more contemporary material than we can readily muster to-day, so we must trust to his good judgement as to his selection - although according to Dr. Smith, most of Briggs' material had disappeared by the time he wrote his book. However, Ward was not a mathematician, and there were certain things to which he was oblivious, and there we must augment his presentation; and occasionally he got his dates wrong, and these we correct without further ado. This chapter has little to say about the actual mechanisms Briggs used to create his tables, instead it sets the stage historically on which this development was played out. Inevitably, the works of John Napier (1550 - 1617) are examined in addition to those of Briggs, in the remarkable unfolding of the story of the development of logarithms in the British Isles over the ten year period from the first appearance of Napier's tables in 1614 to those of Briggs in 1624. -
Napier's Ideal Construction of the Logarithms
Napier’s ideal construction of the logarithms Denis Roegel To cite this version: Denis Roegel. Napier’s ideal construction of the logarithms. [Research Report] 2010. inria-00543934 HAL Id: inria-00543934 https://hal.inria.fr/inria-00543934 Submitted on 6 Dec 2010 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. Napier’s ideal construction of the logarithms∗ Denis Roegel 6 December 2010 1 Introduction Today John Napier (1550–1617) is most renowned as the inventor of loga- rithms.1 He had conceived the general principles of logarithms in 1594 or be- fore and he spent the next twenty years in developing their theory [108, p. 63], [33, pp. 103–104]. His description of logarithms, Mirifici Logarithmorum Ca- nonis Descriptio, was published in Latin in Edinburgh in 1614 [131, 161] and was considered “one of the very greatest scientific discoveries that the world has seen” [83]. Several mathematicians had anticipated properties of the correspondence between an arithmetic and a geometric progression, but only Napier and Jost Bürgi (1552–1632) constructed tables for the purpose of simplifying the calculations. Bürgi’s work was however only published in incomplete form in 1620, six years after Napier published the Descriptio [26].2 Napier’s work was quickly translated in English by the mathematician and cartographer Edward Wright3 (1561–1615) [145, 179] and published posthu- mously in 1616 [132, 162]. -
Schuler Dissertation Final Document
COUNSEL, POLITICAL RHETORIC, AND THE CHRONICLE HISTORY PLAY: REPRESENTING COUNCILIAR RULE, 1588-1603 DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the Graduate School of The Ohio State University By Anne-Marie E. Schuler, B.M., M.A. Graduate Program in English The Ohio State University 2011 Dissertation Committee: Professor Richard Dutton, Advisor Professor Luke Wilson Professor Alan B. Farmer Professor Jennifer Higginbotham Copyright by Anne-Marie E. Schuler 2011 ABSTRACT This dissertation advances an account of how the genre of the chronicle history play enacts conciliar rule, by reflecting Renaissance models of counsel that predominated in Tudor political theory. As the texts of Renaissance political theorists and pamphleteers demonstrate, writers did not believe that kings and queens ruled by themselves, but that counsel was required to ensure that the monarch ruled virtuously and kept ties to the actual conditions of the people. Yet, within these writings, counsel was not a singular concept, and the work of historians such as John Guy, Patrick Collinson, and Ann McLaren shows that “counsel” referred to numerous paradigms and traditions. These theories of counsel were influenced by a variety of intellectual movements including humanist-classical formulations of monarchy, constitutionalism, and constructions of a “mixed monarchy” or a corporate body politic. Because the rhetoric of counsel was embedded in the language that men and women used to discuss politics, I argue that the plays perform a kind of cultural work, usually reserved for literature, that reflects, heightens, and critiques political life and the issues surrounding conceptions of conciliar rule. -
The Eighteenth-Century Origins of the Concept of Scientific Revolution Author(S): I
The Eighteenth-Century Origins of the Concept of Scientific Revolution Author(s): I. Bernard Cohen Source: Journal of the History of Ideas, Vol. 37, No. 2 (Apr. - Jun., 1976), pp. 257-288 Published by: University of Pennsylvania Press Stable URL: http://www.jstor.org/stable/2708824 . Accessed: 03/06/2013 11:30 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]. University of Pennsylvania Press is collaborating with JSTOR to digitize, preserve and extend access to Journal of the History of Ideas. http://www.jstor.org This content downloaded from 148.206.40.98 on Mon, 3 Jun 2013 11:30:35 AM All use subject to JSTOR Terms and Conditions THE EIGHTEENTH-CENTURY ORIGINS OF THE CONCEPT OF SCIENTIFIC REVOLUTION1 BY I. BERNARDCOHEN Many historians of science, like their fellow general historians, believe that the concept of revolution in science is of fairly recent origin, and that it has been superimposed anachronously-and even harshly-on events of the past.2 In fact, however, for some three centuries there has been a more or less unbroken tradition of viewing scientific change as a sequence of revolutions. In the eighteenth century, when this tradition appears to have taken its first rise, there was still some confusion and ambiguity about the sense of the word "revolution": in relation not only to science but to political events. -
Isaac Newton's TONOMETER and COLORIMETER1
Volume 22, Number 1, Spring, 2013 41 “In Experiments, where Sense is Judge” Isaac Newton’s TONOMETER and COLORIMETER1 Charles R. Adams In 1631, William Oughtred (1573-1660) published a small tones and colors, hearing and seeing. Newton was, of course, book on algebra, Clavis Mathematicæ (The Key of Mathe- no stranger to most fields of applied mathematics (such as matics), that was to become, through numerous editions and astronomy, mechanics, and navigation). But that he would commentaries, one the most popular and influential intro- also create significant uses for circular rules in the realm of ductory texts of the 17th century. He wrote the book, he said: sensory perception and the neurophysiological workings of audition and vision might seem unusual. However, he did “… to extend to students of mathematics, as it succeed in making technical advances in just those areas in were, Ariadne’s thread, by the help of which they part by incorporating a matho-musical model into his new may be led to the innermost secrets of this knowl- theory of light and colors, in effect tuning the rainbow. edge [such as Euclid’s mathematical demonstra- tions], and directed towards an easier and deeper Not only were discourses “on the consent and dissent of understanding of the most ancient and favoured visibles and audibles” (Francis Bacon) ubiquitous through- authors”. out all the sciences of the 17th century, but attention to the senses was a significant aspect of Newton’s own philosophy “Oughtred’s purpose was to use the method of analysis to of nature. He considered “the motion of light and sound … understand and recreate the work of ancient writers; Ari- [to be] topics that are most general and most fundamental for adne’s thread was to be a guide not to the future but to the natural philosophy”. -
Elias Ashmole's Collections and Views About John
Studies in History and Philosophy of Science 43 (2012) 530–538 Contents lists available at SciVerse ScienceDirect Studies in History and Philosophy of Science journal homepage: www.elsevier.com/locate/shpsa Elias Ashmole’s collections and views about John Dee Vittoria Feola Department and Collections, Medical University of Vienna, Waehringerstrasse 25, 1090 Vienna, Austria article info abstract Article history: In this paper I discuss Elias Ashmole’s collections and views about John Dee. I consider Dee as an object of Available online 20 January 2012 collection against the broader background of Ashmole’s collecting practices. I also look at the uses to which Ashmole put some of his collections relating to Dee, as well as those which he envisaged for pos- Keywords: terity. I argue that Ashmole’s interest in Dee stemmed from his ideas about the uses of antiquity in the Elias Ashmole reconstruction and transmission of knowledge. They partly reflected Ashmole’s interpretation of Francis Collections Bacon’s Advancement of learning as well as the influence of William Backhouse and William Oughtred’s Antiquarianism ideas about publishing natural philosophy in English. Natural history Ó 2011 Elsevier Ltd. All rights reserved. Ashmolean Museum Baconianism When citing this paper, please use the full journal title Studies in History and Philosophy of Science 1. Introduction to which Ashmole put his Dee-related collections reflected his be- lief that English should replace Latin as a scholarly language. Ash- In 1692, the Ashmolean Museum in the University of Oxford ac- mole viewed his collections of Dee material as useful sources for quired an oil portrait and forty-two volumes of material by and the pursuit of three projects to be carried out, either by himself about John Dee, which Elias Ashmole (1617–1692) had spent his or by posterity, in the vernacular. -
A Norfolk Gentleman - Thomas Blundeville Len Adam
th A 16 Century Norfolk Astronomy Writer and Educator – Thomas Blundeville Len Adam A Story of the Seven Planets, Copernicanism and The Gresham Circle. A Norfolk Gentleman - Thomas Blundeville Len Adam In March 2019, in an attempt to compensate for my somewhat isolated astronomical existence in the clear skies of Andalucia in Spain at Albox Observatory, I rented a converted barn in Norfolk for the month, adjacent to the village of Newton Flotman. This was so I could attend meetings of the Norwich Astronomical Society, based at nearby Seething Observatory, and also pursue my daytime interest of photography with all the opportunities that Norfolk offers. What I had not realised, when I chose the location, was that 497 years earlier a man named Thomas Blundeville (1522 – 1606) was born at Blundeville Manor in the village, less than a mile from my temporary residence in Norfolk. Blundeville, an expert horseman, was a man of many talents including mathematics, astronomy and logic and was a prolific author. He is credited by some with having invented the protractor – well known to all of us as an essential requirement at school. Looking closely at his published scientific works gives the reader an insight into a man attempting to educate others in mathematics, geography and astronomy to be used for practical purposes such as navigation. He explained the movement of the Sun, Moon and planets, identifying appropriate supporting resources such as the astrolabe, maps, and tables, using the work of others and translating books or articles as he deemed necessary to support understanding for his readers. -
Slide Rule and Logarithmic Tables
History of Slide Rules and Logarithmic Tables Applications of Slide Rules and Logarithmic Tables References Slide Rule and Logarithmic Tables James Quintana and Margarita Ryan University of Texas at El Paso March 2, 2015 James Quintana and Margarita Ryan History of Technology History of Slide Rules and Logarithmic Tables Applications of Slide Rules and Logarithmic Tables References Overview 1 History of Slide Rules and Logarithmic Tables 2 Applications of Slide Rules and Logarithmic Tables 3 References James Quintana and Margarita Ryan History of Technology History of Slide Rules and Logarithmic Tables Applications of Slide Rules and Logarithmic Tables References Slide Rule and Logarithm Tables History James Quintana and Margarita Ryan History of Technology History of Slide Rules and Logarithmic Tables Applications of Slide Rules and Logarithmic Tables References Scientific Development The late sixteenth century saw unprecedented development in many scientific fields; astronomy, long-distance navigation, and efforts to measure and represent the earth. These investigations required much from mathematics. James Quintana and Margarita Ryan History of Technology History of Slide Rules and Logarithmic Tables Applications of Slide Rules and Logarithmic Tables References Computation Demands of the Late Sixteen Century Reducing the calculation load that resulted from dealing with such large numbers, and with it, the errors that unsurprisingly came into the results, became a prime objective for mathematicians. As a result, much energy and scholarly effort were directed towards the art of computation James Quintana and Margarita Ryan History of Technology History of Slide Rules and Logarithmic Tables Applications of Slide Rules and Logarithmic Tables References John Napier The Scottish mathematician John Napier was famous for his devices to assist with computation. -
Chopping Logs: a Look at the History and Uses of Logarithms
The Mathematics Enthusiast Volume 5 Number 2 Numbers 2 & 3 Article 15 7-2008 Chopping Logs: A Look at the History and Uses of Logarithms Rafael Villarreal-Calderon Follow this and additional works at: https://scholarworks.umt.edu/tme Part of the Mathematics Commons Let us know how access to this document benefits ou.y Recommended Citation Villarreal-Calderon, Rafael (2008) "Chopping Logs: A Look at the History and Uses of Logarithms," The Mathematics Enthusiast: Vol. 5 : No. 2 , Article 15. Available at: https://scholarworks.umt.edu/tme/vol5/iss2/15 This Article is brought to you for free and open access by ScholarWorks at University of Montana. It has been accepted for inclusion in The Mathematics Enthusiast by an authorized editor of ScholarWorks at University of Montana. For more information, please contact [email protected]. TMME, vol5, nos.2&3, p.337 Chopping Logs: A Look at the History and Uses of Logarithms Rafael Villarreal-Calderon1 The University of Montana Abstract: Logarithms are an integral part of many forms of technology, and their history and development help to see their importance and relevance. This paper surveys the origins of logarithms and their usefulness both in ancient and modern times. Keywords: Computation; Logarithms; History of Logarithms; History of Mathematics; The number “e”; Napier logarithms 1. Background Logarithms have been a part of mathematics for several centuries, but the concept of a logarithm has changed notably over the years. The origins of logarithms date back to the year 1614, with John Napier2. Born near Edinburgh, Scotland, Napier was an avid mathematician who was known for his contributions to spherical geometry, and for designing a mechanical calculator (Smith, 2000).