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Logarithms – a Journey of Their Tables to All Over the World 1
Logarithms – a Journey of their Tables to all over the World 1 Klaus Kühn, Nienstädt (Germany) 2 1 Introduction These days, nobody expects anything really new on the subject of logarithms. Surprisingly, however, there is still something to be written, something to be reviewed or something to be looked at again with fresh eyes. The history of logarithms has been described and dealt with on many occasions and is very clear. Nevertheless there are unnecessary discussions from time to time about who invented logarithms. Undeniably, a 7-place logarithmic table called "Mirifici Logarithmorum Canonis Descriptio" was published in 1614 for the very first time by John Napier (1550 – 1617). 6 years later "Aritmetische und Geometrische Progreß Tabulen / sambt gründlichem Unterricht / wie solche nützlich in allerley Rechnungen zugebrauchen / und verstanden werden soll " (translation see 3) was published by Jost Bürgi (1552 - 1632) – also known as Joost or Jobst Byrgius or Byrg. He published logarithms to 8 places; however this table failed to catch on because there were no instructions for its use included as mentioned. In the eyes of some of today’s contemporaries Bürgi is regarded as the inventor of logarithms, because he had been calculating his logarithms years before Napier, but he only published them on the insistence of Johannes Kepler (1571 – 1630). There is no information on the time it took John Napier to finish calculating his logarithms but in those times it would have been a matter of many years. The theories of the Babylonians (about 1600 B.C.), Euclid (365 – 300 B.C.), and Archimedes (287 – 212 B.C.) had already begun to move in the logarithmic direction. -
Post-Office Annual Directory
frt). i pee Digitized by the Internet Archive in 2010 with funding from National Library of Scotland http://www.archive.org/details/postofficeannual182829edin n s^ 'v-y ^ ^ 9\ V i •.*>.' '^^ ii nun " ly Till [ lililiiilllliUli imnw r" J ifSixCtitx i\ii llatronase o( SIR DAVID WEDDERBURN, Bart. POSTMASTER-GENERAL FOR SCOTLAND. THE POST OFFICE ANNUAL DIRECTORY FOR 18^8-29; CONTAINING AN ALPHABETICAL LIST OF THE NOBILITY, GENTRY, MERCHANTS, AND OTHERS, WITH AN APPENDIX, AND A STREET DIRECTORY. TWENTY -THIRD PUBLICATION. EDINBURGH : ^.7- PRINTED FOR THE LETTER-CARRIERS OF THE GENERAL POST OFFICE. 1828. BALLAN'fVNK & CO. PRINTKBS. ALPHABETICAL LIST Mvtt% 0quaxt&> Pates, kt. IN EDINBURGH, WITH UEFERENCES TO THEIR SITUATION. Abbey-Hill, north of Holy- Baker's close, 58 Cowgate rood Palace BaUantine's close, 7 Grassmrt. Abercromby place, foot of Bangholm, Queensferry road Duke street Bangholm-bower, nearTrinity Adam square. South Bridge Bank street, Lawnmarket Adam street, Pleasance Bank street, north, Mound pi. Adam st. west, Roxburgh pi. to Bank street Advocate's close, 357 High st. Baron Grant's close, 13 Ne- Aird's close, 139 Grassmarket ther bow Ainslie place, Great Stuart st. Barringer's close, 91 High st. Aitcheson's close, 52 West port Bathgate's close, 94 Cowgate Albany street, foot of Duke st. Bathfield, Newhaven road Albynplace, w.end of Queen st Baxter's close, 469 Lawnmar- Alison's close, 34 Cowgate ket Alison's square. Potter row Baxter's pi. head of Leith walk Allan street, Stockbridge Beaumont place, head of Plea- Allan's close, 269 High street sance and Market street Bedford street, top of Dean st. -
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]. -
The Cockburn Association Edinburgh and East Lothian
THE COCKBURN ASSOCIATION EDINBURGH AND EAST LOTHIAN DOORSDAYS OPEN SAT 29 & SUN 30 SEPTEMBER 2018 Cover image: Barnton Quarry ROTOR Bunker. EDINBURGH DOORS OPEN DAY 2018 SAT 29 & SUN 30 SEPTEMBER SUPPORT THE COCKBURN ASSOCIATION AND EDINBURGH DOORS OPEN DAY Your support enables us to organise city WHO ARE WE? wide free events such as Doors Open Day, The Cockburn Association (The Edinburgh bringing together Edinburgh’s communities Civic Trust) is an independent charity which in a celebration of our unique heritage. relies on the support of its members to protect All members of the Association receive and enhance the amenity of Edinburgh. We an advance copy of the Doors Open Day have been working since 1875 to improve programme and invitations throughout the built and natural environment of the city the year to lectures, talks and events. – for residents, visitors and workers alike. If you enjoy Doors Open Days please We campaign to prevent inappropriate consider making a donation to support our development in the City and to preserve project www.cockburnassociation.org.uk/ the Green Belt, to promote sustainable donate development, restoration and high quality modern architecture. We are always happy If you are interested in joining the Association, visit us online at www.cockburnassociation. to advise our members on issues relating org.uk or feel free to call or drop in to our to planning. offices at Trunk’s Close. THE COCKBURN ASSOCIATION The Cockburn Association (The Edinburgh Civic Trust) For Everyone Who Loves Edinburgh is a registered Scottish charity, No: SC011544 TALKS & TOURS 2018 P3 ADMISSION BALERNO P10 TO BUILDINGS BLACKFORD P10 Admission to all buildings is FREE. -
Napier's Ideal Construction of the Logarithms
Napier’s ideal construction of the logarithms∗ Denis Roegel 12 September 2012 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]. A second edition appeared in 1618. Wright was a friend of Henry Briggs (1561–1630) and this in turn may have led Briggs to visit Napier in 1615 and 1616 and further develop the decimal logarithms. ∗This document is part of the LOCOMAT project, the LORIA Collection of Mathe- matical Tables: http://locomat.loria.fr. 1Among his many activities and interests, Napier also devoted a lot of time to a com- mentary of Saint John’s Revelation, which was published in 1593. One author went so far as writing that Napier “invented logarithms in order to speed up his calculations of the Number of the Beast.” [40] 2It is possible that Napier knew of some of Bürgi’s work on the computation of sines, through Ursus’ Fundamentum astronomicum (1588) [149]. -
The Origins of the Edinburgh Law School: the Union of 1707 and the Regius Chair', Edinburgh Law Review, Vol
Edinburgh Research Explorer The Origins of the Edinburgh Law School Citation for published version: Cairns, JW 2007, 'The Origins of the Edinburgh Law School: The Union of 1707 and the Regius Chair', Edinburgh Law Review, vol. 11, no. 3, pp. 300-48. https://doi.org/10.3366/elr.2007.11.3.300 Digital Object Identifier (DOI): 10.3366/elr.2007.11.3.300 Link: Link to publication record in Edinburgh Research Explorer Document Version: Publisher's PDF, also known as Version of record Published In: Edinburgh Law Review Publisher Rights Statement: ©Cairns, J. (2007). The Origins of the Edinburgh Law School: The Union of 1707 and the Regius Chair. Edinburgh Law Review, 11, 300-48doi: 10.3366/elr.2007.11.3.300 General rights Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 28. Sep. 2021 EdinLR Vol 11 pp 300-348 The Origins of the Edinburgh Law School: the Union of 1707 and the Regius Chair John W Cairns* A. INTRODUCTION B. EARLIER VIEWS ON THE FOUNDING OF THE CHAIR C. -
A Concise History of Mathematics the Beginnings 3
A CONCISE HISTORY OF A CONCISE HISTORY MATHEMATICS STRUIK OF MATHEMATICS DIRK J. STRUIK Professor Mathematics, BELL of Massachussetts Institute of Technology i Professor Struik has achieved the seemingly impossible task of compress- ing the history of mathematics into less than three hundred pages. By stressing the unfolding of a few main ideas and by minimizing references to other develop- ments, the author has been able to fol- low Egyptian, Babylonian, Chinese, Indian, Greek, Arabian, and Western mathematics from the earliest records to the beginning of the present century. He has based his account of nineteenth cen- tury advances on persons and schools rather than on subjects as the treatment by subjects has already been used in existing books. Important mathema- ticians whose work is analysed in detail are Euclid, Archimedes, Diophantos, Hammurabi, Bernoulli, Fermat, Euler, Newton, Leibniz, Laplace, Lagrange, Gauss, Jacobi, Riemann, Cremona, Betti, and others. Among the 47 illustra- tions arc portraits of many of these great figures. Each chapter is followed by a select bibliography. CHARLES WILSON A CONCISE HISTORY OF MATHEMATICS by DIRK. J. STRUIK Professor of Mathematics at the Massachusetts Institute of Technology LONDON G. BELL AND SONS LTD '954 Copyright by Dover Publications, Inc., U.S.A. FOR RUTH Printed in Great Britain by Butler & Tanner Ltd., Frame and London CONTENTS Introduction xi The Beginnings 1 The Ancient Orient 13 Greece 39 The Orient after the Decline of Greek Society 83 The Beginnings in Western Europe 98 The -
Brio 56.2-PROOF 2
BRIO Vol. 56, No. 2 SPECIAL ISSUE: ‘Claimed from Stationers’ Hall’: papers from an AHRC-funded network project Edited by Martin Holmes & Karen E. McAulay IAML (UK & Irl) gratefully acknowledges financial support for this issue of Brio from the Royal Conservatoire of Scotland BRIO Vol. 56 No. 2 Autumn/Winter 2019 EDITORS: Martin Holmes and Karen E. McAulay CONTENTS Editorial 1 Obituary: Clifford Bartlett 3 Malcolm Jones ‘Neither exhaustive nor selective’: Legal deposit, Sir Thomas Bodley, 6 and the growth of the music collections at his Library in Oxford Martin Holmes Early music legal deposit (1710-1836) in the National Library of 16 Scotland and its predecessor library, the Library of the Faculty of Advocates Almut Boehme Legal deposit music at University of Glasgow Library, 1710-1836 31 Robert MacLean Discovering Copyright Music in the University of St Andrews Library 38 Briony Harding, Elizabeth Henderson & Karen E. McAulay Stationers’ Hall music at Aberdeen 50 Jane Pirie (Dis)Claimed from Stationers’ Hall: the case of Trinity College Dublin 54 Roy Stanley The ones that got away: Sion College and King’s Inns 60 Karen E. McAulay & Sile O’Shea Skulduggery in St Martin’s Lane: a nasty case of piracy? 62 Margaret Jones Performance potential of Stationers’ Hall collections 77 Brianna E. Robertson-Kirkland Non-Print Legal Deposit and Music in the UK: a progress report 87 Richard Chesser & Rupert Ridgewell Exhibition review 96 Book reviews 99 IAML (UK & Ireland) Executive Committee 110 Notes for contributors 111 Advertising and subscription rates 113 Brio is abstracted and indexed in Library, Information Science & Technology Abstracts (EBSCO), RILM Abstracts (EBSCO), The Music Index (EBSCO) and the Music Periodicals Database (ProQuest). -
Scotland Research Outline
Scotland Research Outline Table of Contents Introduction Obtaining Copies Of Publications Using This Outline Scottish Search Strategies Records At The Family History Library The Family History Library Catalog Records Selection Table: Scotland Archives And Libraries Biography Cemeteries Census Church Directories Church History Church Records Nonconformist Church Records Civil Registration General Historical Background Information Recorded In Civil Registers Finding Civil Registration Records Indexes To Civil Registration Records Court Records Types Of Courts Finding Court Records For More Information Directories Emigration And Immigration General Background Emigration From Scotland Records Of Scottish Emigrants In Their Destination Countries Immigration Into Scotland Gazetteers Genealogy Heraldry Historical Geography History Land And Property Language And Languages Maps Merchant Marine Military Records Army Navy Militia Other Branches Of The Military Handbooks On Military History And Military Records Names, Personal Newspapers Nobility Occupations Periodicals Probate Records Determining The Court Finding Probate Records Indexes To Probate Records Difficulties In Finding A Probate Record Poorhouses, Poor Law, Etc. Schools Societies Taxation Other Records For Scotland For Further Reading Comments And Suggestions INTRODUCTION This outline introduces you to records and strategies that can help you discover your Scottish ancestors. It describes the content, use, and availability of major genealogical records. Generally, you must know the specific parish or town in Scotland where your ancestor was born before beginning research in Scotland. You will need to understand some basic genealogical research procedures. You may want to use the booklet, Guide to Research (30971), available at the Family History Library and at Family History Centers. Obtaining Copies of Publications This research outline refers to publications written by staff at the Family History Library. -
FACULTAD De FILOSOFÍA Y LETRAS DEPARTAMENTO De FILOLOGÍA INGLESA Grado En Estudios Ingleses
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Repositorio Documental de la Universidad de Valladolid FACULTAD de FILOSOFÍA Y LETRAS DEPARTAMENTO de FILOLOGÍA INGLESA Grado en Estudios Ingleses TRABAJO DE FIN DE GRADO Seventeenth-Century Titles Relating to Science in the Historical Library of Santa Cruz, Valladolid: Toward a Study of their Circulation in Spain Marina Sánchez Zubiaurre Tutora: Anunciación Carrera de la Red 2018-2019 Abstract The study of the reception of seventeenth-century British scientists in Spain has been carried out only partially. Key figures representing early modern English and Scottish scientific thought are well researched, like Newton or Napier, but in general, the presence of their books in Spanish libraries remains to be precised. This BA Dissertation will use such bibliographical study to provide fresh evidence on the circulation of the works of British scientists within our libraries in the 1600s. It looks at the copies of the works of John Napier, Hugh Semple, John Selden, and Francis Bacon kept in the Historical Library of Santa Cruz, Valladolid, and describes their copy- specific features and marks of provenance. The aim is to confirm whether these authors only began to be studied in Spain in the late 1700s, as is generally sustained, and contribute new pieces on evidence of how and why that may have been. Keywords: early modern science, early modern Spain, circulation, Historical Library of Santa Cruz, bibliography, provenance Resumen El estudio de recepción de la obra de los científicos británicos del siglo diecisiete en España se ha llevado a cabo solamente de forma parcial. -
A Reconstruction of Briggs' Logarithmorum Chilias
A reconstruction of Briggs’ Logarithmorum chilias prima (1617) Denis Roegel To cite this version: Denis Roegel. A reconstruction of Briggs’ Logarithmorum chilias prima (1617). [Research Report] 2010. inria-00543935 HAL Id: inria-00543935 https://hal.inria.fr/inria-00543935 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. A reconstruction of Briggs’ Logarithmorum chilias prima (1617) Denis Roegel 6 December 2010 This document is part of the LOCOMAT project: http://www.loria.fr/~roegel/locomat.html I ever rest a lover of all them that love the Mathematickes Henry Briggs, preface to [47] 1 Henry Briggs Henry Briggs (1561–1631)1 is the author of the first table of decimal loga- rithms, published in 1617, and of which this document gives a reconstruction. After having been educated in Cambridge, Briggs became the first profes- sor of geometry at Gresham College, London, in 1596 [74, p. 120], [65, p. 20], [80]. Gresham College was England’s scientific centre for navigation, geom- etry, astronomy and surveying.2 Briggs stayed there until 1620, at which time he went to Oxford, having been appointed the first Savilian Professor of Geometry in 1619 [65, p. -
War Medals, Orders and Decorations
War Medals, Orders and Decorations To be sold by auction at: Sotheby’s, in the Upper Grosvenor Gallery The Aeolian Hall, Bloomfield Place New Bond Street London W1A 2AA Day of Sale: Thursday 29 November 2018 at 12.00 noon Public viewing: Nash House, St George Street, London W1S 2FQ Monday 26 November 10.00 am to 4.30 pm Tuesday 27 November 10.00 am to 4.30 pm Wednesday 28 November by appointment Or by previous appointment. Catalogue no. 98 Price £15 Enquiries: David Kirk or James Morton Cover illustrations: Lot 894 (front); lot 724 (back); lot 725 (inside front); lot 893 (inside back) Nash House, St George Street, London W1S 2FQ Tel.: +44 (0)20 7493 5344 Email: [email protected] Website: www.mortonandeden.com This auction is conducted by Morton & Eden Ltd. in accordance with our Conditions of Business printed at the back of this catalogue. All questions and comments relating to the operation of this sale or to its content should be addressed to Morton & Eden Ltd. and not to Sotheby’s. Online Bidding This auction can be viewed online at www.the-saleroom.com or www.invaluable.com Morton & Eden Ltd offers live online bidding via www.the-saleroom.com and www.invaluable.com. Successful bidders using either of these platforms will be charged for this service. This facility is provided on the understanding that Morton & Eden Ltd shall not be responsible for errors or failures to execute internet bids for reasons including but not limited to: i) a loss of internet connection by either party ii) a breakdown or other problems with the online bidding software iii) a breakdown or other problems with your computer, system or internet connection.