Cyclopedia of logarithms

This page is incomplete and will be incomplete forever.
Suggestions and contributions are welcome.
Please do not alter this page but send them to the authors
Klaus Kuehn or Stephan Weiss

Inhaltsverzeichnis 1 Introduction 2 Complete Tables 3 History 3.1 In General 3.2 Periods 3.2.1 preNapier 3.2.2 Napier and the first Decades 3.2.3 nn 3.3 People: Calculators 3.3.1 John Napier 3.3.2 Henry Briggs 3.3.3 Jost Buergi 3.3.4 Johannes Kepler 3.3.5 Georg Freiherr von Vega 3.3.6 Johann Theodor Peters 3.4 People: Editors 3.5 People: Inventors of Methods of Computation 3.6 In General 3.7 Napier 3.8 William Oughtred 3.9 Difference Engines 4 Peripheries, Types of Logarithms 4.1 Logistische oder proportionale Logarithmen 4.2 Discrete Logarithms 4.3 Complex Logarithms 5 Applications 5.1 Calculating Aids 5.2 Astronomy 5.3 Navigation 5.4 Surveying/geodesy 5.5 Financial/Insurance 5.6 Music 5.7 Other fields 6 Meetings 7 Other topics

1 Introduction

Über Logarithmen ist schon fast alles gesagt und geschrieben. So bleibt uns recht wenig nachzuholen. Was aber bisher nicht geschehen ist, ist das Zusammentragen von Materialien zum Thema Logarithmus bzw. Logarithmen an EINEM Ort. Und das ist die Idee dieser Seite. Wir wollen versuchen, möglichst viel Material in welcher Form auch immer zusammenzutragen, um zu zeigen, welche Bedeutung die Logarithmen für Berufe aller Art und Anwendungen der verschiedensten Bereiche für viele Jahrhunderte hatte. Dies sehen wir als Teil der Vorbereitung auf eine Veranstaltung im Jahre 2014, die anlässlich der ersten Publikation einer Logarithmentafel von John Napier im Jahre 1614 organisiert werden soll. Nicht zuletzt soll es auch darum gehen, welchen Beitrag deutschsprachige Tafelmacher in den Jahren nach 1614 geleistet haben.

A lot has been said or written about logarithms in the past. Only a few topics might need to be added. But so far, there is no place where all the material which is existing has been compiled in ONE place. That is the idea of this page. We will try to bring together as much material as possible in order to demonstrate the meaning of logarithms for all kinds of professionals as well as for all kinds of applications in four centuries. We consider this as our contribution the preparation of a meeting in 2014 which should commemorate the quadricentenary of the first publication of a logarithmic table by John Napier in 1614. On the other hand our idea is also to review the contributions of German speaking tablemakers after 1614.

2 Complete Tables

•  LOCOMAT The LORIA COLLECTION of MATHEMATICAL TABLES
  (Reconstructed tables with extensive explanations: Napier, Briggs, Buergi, Gunter, DeDecker-Vlacq, Briggs-Gellibrand, Vlacq, Chinese Table, de Prony, Babbage, Sang, Mendizábal-Tamborre, Andoyer, Thompson)
  
•  Links to digitized tables in general
• Catalogue of some published Tables of Logarithms: Logarithmentafeln
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3 History

3.1 In General

In diesen beiden Mathematical Tables gibt es gute und ausführliche Darstellungen der Geschichte der Logarithmen(tafeln)
In the following mathematical tables good and extensive explanations about the history of logarithms and their tables can be found

• Sherwin_1717
• Hutton_1811

some other references:

• Maseres, Francis: Scriptores logarithmici: or, a collection of several curious tracts on the nature and construction of logarithms, mentioned in Dr. Hutton's historical introduction to his new edition of Sherwin's mathematical tables: together with some tracts on the binomial theorem and other subjects connected with the doctrine of logarithms.
  Vol.1, 1791  Google; Vol.4 1801  Google
• Glaisher 1874 eine umfangreiche Sammlung von Tafelwerken.
• Glaisher, James Whitbread Lee. Logarithm - Logistic or Proportional Logarithms. Encyclopædia Britannica, 1911, Vol. 16, S. 868ff. (online veröffentlicht).
• Charles Naux: Histoire des Logarithmes de Neper a Euler. Tome I, II, Blanchard, Paris 1966, 1971.
• Faustmann_1995
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3.2 Periods

3.2.1 preNapier

• Peter Holland acquaints the reader with "Archimedes - and his ideas of "logarithms" "[ Archimedes] which are know from the sand reckoner. [ [1]]
• Before logarithms were in the hand of astronomers, they facilitated their calculations by taking advantage of the Prosthaphaeresis which was developed by Ioannis Verneri: De Triangulis Sphaericis, Libri Quatuor; De Meteoroscopiis,. Libri Sex; cum Prooemio Georgii Ioachimi Rhetici; Band II In Abhandlungen zur Geschichte der Mathematischen ....Leipzig: B.G. compiled by Axel A. Björnbo in 1907 Google
  or see: Kühn, Klaus: Die Prosthaphärese und Johannes Werner (1468 - 1522) Prosthaphärese Wikipedia
• Stifel, Michael probably was the mathematician who triggered the calculation of logarithms by setting up his famous table of a geometric and an arithmetic row (partially depicted at the top of this page)
  
• Dietrich, Urs; Girstmair, Kurt, John Napiers Trigonometrie - ein Blick zurück. Math. Semesterber. 56 (2009), 215-232. Napiers Trigonometrie
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3.2.2 Napier and the first Decades

• Weiss, Stephan: Anmerkungen zur Idee der Logarithmen. 2009
   Link
• About the error regarding the identity of natural logarithms (to base e, called Napierian l.) and those published by Napier see Cajori, Florian: Notes on the History of Logarithms. In: Abhandlungen zur Geschichte der Mathematik, 9, 1899, S. 31 - 39
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3.2.3 nn

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3.3 People: Calculators

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3.3.1 John Napier

• Napier, Mark: Memoirs of John Napier of Merchiston: his lineage, life, and times, with a history of the invention of logarithms 1834
   Google
• Napier, John; Napier Mark: De arte logistica Joannis Naperi Merchistonii baronis libri qui supersunt 1839
   Google
• John Napier: Mirifici Logarithmorum Canonis Descriptio... & Constructio... translated and annotated by Ian Bruce
   Link
• Hawkins, William F.:The Mathematical work of John Napier, Bull. Austral. Math. Soc. Vol 26 (1982) 455-468
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3.3.2 Henry Briggs

• Briggs' Arithmetica Logarithmica translated and annotated by Ian Bruce.
  Worth to be read, esp. chapter 1 to understand the origins of logarithms.
   Link
  
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3.3.3 Jost Buergi

• Jost Bürgi
  
• Buergi 1620 (table)
  

3.3.4 Johannes Kepler

• Johannes Kepler
  

3.3.5 Georg Freiherr von Vega

• Jurij Vega
  

3.3.6 Johann Theodor Peters

• Jean Peters
  

3.4 People: Editors

• Friedrich Gustav Gauss
  
• Wilhelm Jordan
  
• Oskar Schlömilch
• Karl Christian Bruhns
• Ludwig Schrön
  

3.5 People: Inventors of Methods of Computation

• Edmond Halley (1656? - 1743)
• John Long 1714
• Brook Taylor (1685 - 1731)
• Thomas Manning 1806
• M. Borda

3.6 In General

• Young, John Radford: An elementary essay on the computation of logarithms 1830
   Google
  
• Whittermore, James Kelsey:The Calculation of Logarithms; Annals of Mathematics Vol 9, No 1, 1907 (available as reprint)
• Faustmann_1995
• Kühn, Klaus: "De Logarithmorum Ratione" (2023) A Collection of Sources on the History of Methods for Calculating Logarithms. Die Geschichte zum Berechnen von Logarithmen ist in einer umfangreichen Quellensammlung.(Deutsch/English mix) auf 695 Seiten zusammengefasst.  http://www.collectanea.eu]
  
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3.7 Napier

• Fischer, Joachim: Wie konstruierte Napier Logarithmen? 1997
   Text With the author's kind permission.

3.8 William Oughtred

• The Radix Method: A publication by J.W.L. Glaisher (1848 - 1928) from 1914 The earliest use of the radix method for calculating logarithms, with historical notices relating to the contributions of Oughtred and others to mathematical notation covers a 16-page appendix, which appeared 1618 in the 2nd edition of "Mirifici - A description of the admirable table of logarithmes…" translated from Latin by Edward Wright. This appendix describes a method to calculate logarithms by the Radix Method. Initially this appendix was attributed to Henry Briggs. But Glaisher took some hints from A. de Morgan and after further investigations he concluded, that this appendix was written by William Oughtred (1574 - 1660).  William Oughtred and Logarithms

3.9 Difference Engines

• Rapport sur la machine à calculer présentée par M. Wiberg. In Comptes rendus 56 (1863): 330-39.
   Google
• Weiss, Stephan: Difference Engines in the 20th Century. 2010
   Link
• Die Differenzenmaschine von Hamann, Beschreibung und Anwendung (1910)
  (Original description of Hamann's Difference Engine, taken from the introduction of Bauschinger and Peters (ed.): Logarithmisch-Trigonometrische Tafeln mit acht Dezimalstellen, 1. Bd., Leipzig 1910)
   Link
• How to calculate logarithms with Hamann's Difference Engine.
  (Original description in English language, taken from Bauschinger and Peters: Logarithmic-Trigonometrical Tables with eight decimal places, Leipzig 1910
   Link
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4 Peripheries, Types of Logarithms

4.1 Logistische oder proportionale Logarithmen

• Weiss_2020.3

4.2 Discrete Logarithms

• Schumacher 1909
  
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4.3 Complex Logarithms

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5 Applications

•  History of Logarithms and Applications; Text and some Videos

5.1 Calculating Aids

• Werner Rudowski asked "What do we need logarithms for ?" and gives some examples of the replies he got from some committed people. [ [2]]
  
• The introduction of logarithms in German and Austrian schools as calculating aids is reviewed in this paper as well as their route out of the schools.  Logarithmen und Schule - Erstveröffentlichung (5 MB)
  

5.2 Astronomy

• (Grimme, Natalis u. Co., Braunschweig:) Astronomische Rechnungen a) mit Hilfe einer 5-stelligen Logarithmentafel, b) mit Trinks-Triplex Rechenmaschine (ohne Autor, ohne Ort u. Jahr)
  A comparison of astronomical calculations with logarithms and with a calculating machine, published by the manufacturer of calculating machines Grimme, Natalis & Co. in Brunswick (without author and year, probably 1st half of 20th century). The machine is winning, of course.
   Text
  
• At the IM 2009 this paper was intended to reflect the meaning of logarithms for astronomy, and finally somehow resulted in a history of logarithmic tables.  English Abstract PDF (.3 MB) Full paper in German:  K. Kühn: Logarithmen und Astronomie (25 MB)

5.3 Navigation

• Handbuch der Schiffahrts-Kunde, mit einer Sammlung von Seemanns-Tafeln, zwei See-Karten, zwei Stern-Karten und einer magnetischen Karte; C. Rümker, 1850  Google
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5.4 Surveying/geodesy

• Rainer Heer has compiled some examples where logarithms are being used for applications in geodesy. His article is published here for the first time, Feb. 26, 2011! It is written in German, but the examples should be understandable in other languages too. Anwendung der Logarithmen in der Geodaesie
  
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5.5 Financial/Insurance

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5.6 Music

• Kühn, Klaus; Shepherd, Rodger: Calculating With Tones - The Logarithmic Logic of Music 2. edition (2023)  [3]
  
• In addition to the list of references in the above mentioned book we recently came across another important source: HANS KAYSER - THE TEXTBOOK OF HARMONICS
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5.7 Other fields

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6 Meetings

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7 Other topics

• A collection of rarest, mainly original, items on the History of Calculation are compiled and documented in the Erwin Tomash Library with more than 3000 entries on a 1600 page catalogue [ [4]]

Seite eröffnet von: stewe 10:16, 17. Jan 2011 (CET)
Klaus Kühn 21:56, 26. Jan 2011 (CET)

last change: 00:02, 14. Sep. 2011 (CET)

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