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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. -
Former Fellows Biographical Index Part
Former Fellows of The Royal Society of Edinburgh 1783 – 2002 Biographical Index Part Two ISBN 0 902198 84 X Published July 2006 © The Royal Society of Edinburgh 22-26 George Street, Edinburgh, EH2 2PQ BIOGRAPHICAL INDEX OF FORMER FELLOWS OF THE ROYAL SOCIETY OF EDINBURGH 1783 – 2002 PART II K-Z C D Waterston and A Macmillan Shearer This is a print-out of the biographical index of over 4000 former Fellows of the Royal Society of Edinburgh as held on the Society’s computer system in October 2005. It lists former Fellows from the foundation of the Society in 1783 to October 2002. Most are deceased Fellows up to and including the list given in the RSE Directory 2003 (Session 2002-3) but some former Fellows who left the Society by resignation or were removed from the roll are still living. HISTORY OF THE PROJECT Information on the Fellowship has been kept by the Society in many ways – unpublished sources include Council and Committee Minutes, Card Indices, and correspondence; published sources such as Transactions, Proceedings, Year Books, Billets, Candidates Lists, etc. All have been examined by the compilers, who have found the Minutes, particularly Committee Minutes, to be of variable quality, and it is to be regretted that the Society’s holdings of published billets and candidates lists are incomplete. The late Professor Neil Campbell prepared from these sources a loose-leaf list of some 1500 Ordinary Fellows elected during the Society’s first hundred years. He listed name and forenames, title where applicable and national honours, profession or discipline, position held, some information on membership of the other societies, dates of birth, election to the Society and death or resignation from the Society and reference to a printed biography. -
The Logarithmic Tables of Edward Sang and His Daughters
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Historia Mathematica 30 (2003) 47–84 www.elsevier.com/locate/hm The logarithmic tables of Edward Sang and his daughters Alex D.D. Craik School of Mathematics & Statistics, University of St Andrews, St Andrews, Fife KY16 9SS, Scotland, United Kingdom Abstract Edward Sang (1805–1890), aided only by his daughters Flora and Jane, compiled vast logarithmic and other mathematical tables. These exceed in accuracy and extent the tables of the French Bureau du Cadastre, produced by Gaspard de Prony and a multitude of assistants during 1794–1801. Like Prony’s, only a small part of Sang’s tables was published: his 7-place logarithmic tables of 1871. The contents and fate of Sang’s manuscript volumes, the abortive attempts to publish them, and some of Sang’s methods are described. A brief biography of Sang outlines his many other contributions to science and technology in both Scotland and Turkey. Remarkably, the tables were mostly compiled in his spare time. 2003 Elsevier Science (USA). All rights reserved. Résumé Edward Sang (1805–1890), aidé seulement par sa famille, c’est à dire ses filles Flora et Jane, compila des tables vastes des logarithmes et des autres fonctions mathématiques. Ces tables sont plus accurates, et plus extensives que celles du Bureau du Cadastre, compileés les années 1794–1801 par Gaspard de Prony et une foule de ses aides. On ne publia qu’une petite partie des tables de Sang (comme celles de Prony) : ses tables du 1871 des logarithmes à 7-places décimales. -
Former Fellows Biographical Index Part
Former Fellows of The Royal Society of Edinburgh 1783 – 2002 Biographical Index Part One ISBN 0 902 198 84 X Published July 2006 © The Royal Society of Edinburgh 22-26 George Street, Edinburgh, EH2 2PQ BIOGRAPHICAL INDEX OF FORMER FELLOWS OF THE ROYAL SOCIETY OF EDINBURGH 1783 – 2002 PART I A-J C D Waterston and A Macmillan Shearer This is a print-out of the biographical index of over 4000 former Fellows of the Royal Society of Edinburgh as held on the Society’s computer system in October 2005. It lists former Fellows from the foundation of the Society in 1783 to October 2002. Most are deceased Fellows up to and including the list given in the RSE Directory 2003 (Session 2002-3) but some former Fellows who left the Society by resignation or were removed from the roll are still living. HISTORY OF THE PROJECT Information on the Fellowship has been kept by the Society in many ways – unpublished sources include Council and Committee Minutes, Card Indices, and correspondence; published sources such as Transactions, Proceedings, Year Books, Billets, Candidates Lists, etc. All have been examined by the compilers, who have found the Minutes, particularly Committee Minutes, to be of variable quality, and it is to be regretted that the Society’s holdings of published billets and candidates lists are incomplete. The late Professor Neil Campbell prepared from these sources a loose-leaf list of some 1500 Ordinary Fellows elected during the Society’s first hundred years. He listed name and forenames, title where applicable and national honours, profession or discipline, position held, some information on membership of the other societies, dates of birth, election to the Society and death or resignation from the Society and reference to a printed biography. -
Biographical Index of Former RSE Fellows 1783-2002
FORMER RSE FELLOWS 1783- 2002 SIR CHARLES ADAM OF BARNS 06/10/1780- JOHN JACOB. ABEL 19/05/1857- 26/05/1938 16/09/1853 Place of Birth: Cleveland, Ohio, USA. Date of Election: 05/04/1824. Date of Election: 03/07/1933. Profession: Royal Navy. Profession: Pharmacologist, Endocrinologist. Notes: Date of election: 1820 also reported in RSE Fellow Type: HF lists JOHN ABERCROMBIE 12/10/1780- 14/11/1844 Fellow Type: OF Place of Birth: Aberdeen. ROBERT ADAM 03/07/1728- 03/03/1792 Date of Election: 07/02/1831. Place of Birth: Kirkcaldy, Fife.. Profession: Physician, Author. Date of Election: 28/01/1788. Fellow Type: OF Profession: Architect. ALEXANDER ABERCROMBY, LORD ABERCROMBY Fellow Type: OF 15/10/1745- 17/11/1795 WILLIAM ADAM OF BLAIR ADAM 02/08/1751- Place of Birth: Clackmannanshire. 17/02/1839 Date of Election: 17/11/1783. Place of Birth: Kinross-shire. Profession: Advocate. Date of Election: 22/01/1816. Fellow Type: OF Profession: Advocate, Barrister, Politician. JAMES ABERCROMBY, BARON DUNFERMLINE Fellow Type: OF 07/11/1776- 17/04/1858 JOHN GEORGE ADAMI 12/01/1862- 29/08/1926 Date of Election: 07/02/1831. Place of Birth: Ashton-on-Mersey, Lancashire. Profession: Physician,Statesman. Date of Election: 17/01/1898. Fellow Type: OF Profession: Pathologist. JOHN ABERCROMBY, BARON ABERCROMBY Fellow Type: OF 15/01/1841- 07/10/1924 ARCHIBALD CAMPBELL ADAMS Date of Election: 07/02/1898. Date of Election: 19/12/1910. Profession: Philologist, Antiquary, Folklorist. Profession: Consulting Engineer. Fellow Type: OF Notes: Died 1918-19 RALPH ABERCROMBY, BARON DUNFERMLINE Fellow Type: OF 06/04/1803- 02/07/1868 JOHN COUCH ADAMS 05/06/1819- 21/01/1892 Date of Election: 19/01/1863. -
Calculation and Tabulation in the Nineteenth Century: Airy Versus
1 Calculation and Tabulation in the Nineteenth Century: Airy versus Babbage Doron David Swade Thesis submitted for the degree of PhD University College London 2003 2 Abstract Charles Babbage (1791-1871) is widely recognised as the great ancestral figure in the history of computing. He designed the first automatic calculating engines and failed to realise a complete design in physical form. This thesis argues that historical accounts of Babbage’s work are based on a set of contemporary sources provided by Babbage himself and that the subsequent interpretation of the major movement to automate calculation and tabulation in the nineteenth century is dominated by Babbage’s own account of events. George Biddell Airy (1801-1891), Astronomer Royal for forty five years, consistently rejected arguments advocating the utility of the engines. Airy had a defining influence on the fate of the engines yet his views barely feature in the canon. Using new archival sources, Airy’s views are explored through a series of case studies: Babbage’s Difference Engine No. 1 and the Swedish calculating engine used at the General Register Office for the 1864 Life Table. In addition, his views on the use of calculating aids are explored using instances in which he was petitioned by inventors, specifically by Thomas Fowler and William Bell. The thesis situates Airy’s views in the context of manual methods used in the production of printed mathematical tables – techniques that automatic calculating engines were intended to replace – and in the context of contemporary expectations of the largely unbuilt engines. The treatment includes new work on the mathematical implications of the engines, specifically Babbage’s speculations on computation as a systematic method of solution, and presents a revisionist view of tabular errors as the primary motive for the development of the engines. -
Alphabetical List of Graduates of the University of Edinburgh From
18 5 9-88. $*— #2 LI BR AR Y UNIVERSITY OF CALIFORNIA. GIFT OK Received , _$?g^L.„„_ /^^ . ccessions ^ No. 4 Shelf No. _ _$_f__ % 3 <A? 30 Stni&jersitjj of (Strittbttrglj LIST OF GRADUATES 1859-88 f/ <yK' OF TH uitive: '4zirm$ ; ALPHABETICAL LIST OF (Srab»at£0 of the Eroteraitg of (Sbiuburgh From 1859 TO 1888 [both years included) WITH HISTORICAL APPENDIX (Including Present and Past Office-bearers) AND SEPARATE LISTS HONORARY GRADUATES AND GRADUATES WITH HONOURS INFORMATION AS TO UNIVERSITY LIBRARY, MUSEUMS, LABORATORIES, BENEFACTIONS TO THE UNIVERSITY, ETC. EDINBURGH JJubltshcb bij (Drbet of the $enatns JUftbemtme BY JAMES THIN, TUBLISIIER TO THE UNIVERSITY <? '/ > 7 7 f-3 1 CONTENTS. Introductory ..... 5 Table of Abbreviations .... 16 Alphabetical List of Graduates from 1859 to i< BOTH Years included .... 17 HISTORICAL APPENDIX. Constitution of the University 9.3 Names of Present Office-Bearers 93 Laboratories and Museums .... 99 Statement regarding Library and its Benefactors 101 Do. do. Benefactors of University 102 Do. do. Portraits and Busts >°3 Chronological Lists of the— Chancellors .... 103 Vice-Chancellors .... '03 Rectors ...... «°3 Representatives in Parliament 104 University Court .... 104 Curators of Patronage 105 Representatives in General Medical Council 106 Principals and Professors . 106 University Examiners 1 Librarians ..... 13 Graduation Ceremonials. Academic Costume 3 Honorary Graduates in Divinity 13 Do. Do. Law '7 Sponsio Academica, Signed by students on Matriculating 124 Sponsio Academica, Signed by Graduates in Arts [24 List of Graduates in Arts with Honours i»5 Do. Do. Law with Honours 27 Sponsio Academica, Signed by Graduates in Medicine ^7 Lists of Graduates in Medicine, Gold Medallists 28 Do.