LOCOMAT
The LORIA
COLLECTION of
MATHEMATICAL
TABLES
DTL (Digital Tables Library)
--- Reconstructed tables ---
Content:
Introduction
- Aim of the project: making available a number of interesting
and/or important historical tables, and facilitating the study of the
original tables by historians of mathematics; in some cases,
the entire original works have been reproduced; many of the original tables
have already been digitized, and can now be easily checked.
- Scope: currently, most of the tables in the collection
are tables of trigonometric functions,
tables of logarithms, or tables of factors.
- Recomputations:
most of the logarithmic and trigonometric
tables were recomputed using the GNU MPFR
floating point library.
- Digital versions: links to digital versions of the original works have been added, when they are known; the following tables have been reconstructed before any of them was available online (at least to our knowledge): Pitiscus 1613, Napier 1616, Briggs 1617, Bürgi 1620, Gunter 1620, Briggs 1624, Vlacq 1628, Briggs 1633, Vlacq 1633, Brancker 1668, Mouton 1670, Chinese tables 1720, Shuli Jingyun 1723, the third part of Felkel 1776, Schenmark 1780, Prony's tables, Crelle 1836, Kulik 1851, Kulik 1863, Sang 1872, Glaisher 1879, Tissot 1880, SGA 1891, Mendizábal-Tamborrel 1891, Lehmer 1909, Andoyer 1911, Lehmer 1914, Andoyer 1922, Gifford 1931, Peters 1935, Kaván 1937, Merritt 1947, Neville 1950, Beeger 1951, Thompson 1952, and Gingerich 1965.
- Errors: please notify us (roegel@loria.fr) of any error you might find in the reconstructions.
- Contributions: a lot more work is needed and contributions
are welcome.
- 1490 Regiomontanus
- 1490 Engel
- 1516 Peuerbach
- 1530 Fine
- 1533 Apian
- 1541 Regiomontanus
- 1542 Rheticus
- 1550 Fine
- 1551 Rheticus
- 1554 Reinhold
- 1558 Maurolico
- 1579 Viète
- 1583 Fincke
- 1591 Lansberge
- 1596 Rheticus
- 1613 Pitiscus
- 1614 Napier
- 1616 Napier
- 1617 Briggs
- 1620 Bürgi
- Jost Bürgi: Arithmetische und Geometrische Progress Tabulen,
sambt gründlichem Unterricht, wie solche nützlich
in allerley Rechnungen zugebrauchen, und verstanden
werden sol, 1620
- Denis Roegel: Bürgi's ``Progress Tabulen'' (1620): logarithmic tables without logarithms, 2010
(HAL record)
- Denis Roegel: Jost Bürgi’s skillful computation of sines, 2015
- Denis Roegel: A note on the complexity of Bürgi’s algorithm
for the computation of sines, 2016
- Denis Roegel: A preliminary note on Bürgi's computation of
the sine of the first minute, 2016
- Denis Roegel: Some remarks on Bürgi's interpolations, 2016
- Bürgi's Fundamentum Astronomiæ (1592)
- Fritz Staudacher: Jost Bürgi, Kepler und der Kaiser, 2013
- Kathleen Clark: Jost Bürgi's Aritmetische und Geometrische Progreß Tabulen (1620), 2015
- Dieter Launert: Nova Kepleriana : Bürgis Kunstweg im
Fundamentum Astronomiae -
Entschlüsselung seines Rätsels, 2015
- Denis Roegel: A reconstruction of Bürgi's sine table at 1' intervals (ca. 1587), 2016
- Denis Roegel: A tentative reconstruction of Bürgi's sine table at 2'' intervals (ca. 1600), 2016
- Denis Roegel: 9-digit interpolations for Bürgi’s hypothetical
2'' sine table, 2016
- Denis Roegel: 10-digit interpolations for Bürgi’s hypothetical
2'' sine table, 2016
- Jörg Waldvogel: ``Jost Bürgi’s Artificium of 1586 in modern view, an ingenious algorithm for calculating tables of the sine function'', Elemente der Mathematik, 71(3), 2016, 89-99
- Peter Ullrich: ``The mathematics behind Jost Bürgi's method for calculating sine tables'', Proceedings in Applied Mathematics and Mechanics, 16(1), October 2016, 891-892
- Grégoire Nicollier: ``How Bürgi computed the sines of all integer angles
simultaneously in 1586'', Mathematische Semesterberichte, 2017
- 1620 Gunter
- 1624 Briggs
- 1627 De Decker
- These tables were reprinted by Vlacq in 1628, without mentioning De Decker.
- 1628 De Decker-Vlacq
- 1633 Briggs-Gellibrand
- 1633 Vlacq
- 1653 Smogulecki and Xue
- ca. 1670 Gabriel Mouton
- ca. 1720 Chinese tables (based on Vlacq's 1628 and 1633 tables)
- 1723 Shulin Jingyun (御製數理精蘊) tables (based on Vlacq's 1628 and 1633 tables)
- Original tables as copied in the Siku Quanshu (ca. 1782):
A,
B,
C,
D,
E,
F,
G,
H,
I,
J,
K,
L,
M,
N,
O,
P,
Q,
R,
S,
T
- Denis Roegel: A
reconstruction of the tables of the Shuli Jingyun
(1713–1723), 2011 (HAL record)
- Reconstructions of the eight original volumes of tables: (HAL record)
- Reconstructions of the Siku Quanshu version (28 volumes): (HAL record)
- 1793-1796 Prony (Tables du cadastre)
- The original tables have never been published.
- General information on the tables
- Denis Roegel: Tables du cadastre: Complete project 2, ca. 1794, 2010
- Denis Roegel: The great logarithmic and trigonometric tables of the French Cadastre: a preliminary investigation, 2010 (the version on
HAL is older and typos
have not yet been corrected, please get the newer version)
- Auxiliary volumes:
- Logarithms of numbers (each volume is 500 pages, except volume 1a which is a bit less, and volumes 1b and 1c which are 300 pages):
- with exact calculations: volumes 1a, 2a, 3a, 4a, 5a, 6a, 7a, and 8a
- with rounded interpolation: volumes 1b, 2b, 3b, 4b, 5b, 6b, 7b, and 8b
- with hidden interpolation: volumes 1c, 2c, 3c, 4c, 5c, 6c, 7c, and 8c
- Sines (each volume 400 pages):
- with exact computation (volume 9a)
- with rounded interpolation (volume 9b)
- Logarithms of sines:
- with exact computation: volumes 10a (550 p.), 11a (500 p.), 12a (500 p.), 13a (500 p.)
- with rounded computation: volumes 10b (550 p.), 11b (500 p.), 12b (500 p.), 13b (500 p.)
- Logarithms of tangents:
- with exact computation: volumes 14a (500 p.), 15a (500 p.), 16a (500 p.), 17a (500 p.)
- with rounded computation: volumes 14b (500 p.), 15b (500 p.), 16b (500 p.), 17b (500 p.)
- Multiples of sines and cosines (each volume 500 pages):
- with exact computation (volume 18a)
- with rounded computation (volume 18b)
- Volume 19 (introductory volume) will be redone in the future.
- Abridged tables (each volume 200 pages):
- with exact computation (volume 20a)
- with rounded computation (volume 20b)
1827 Babbage
1864 Shortrede
Tables by Edward Sang
- Table of logarithms, 1871
- Million table, 1872
- Denis Roegel: A guide to Edward Sang's tables and to their reconstructions, 2021
(HAL record)
- Denis Roegel: Edward Sang's computation of the logarithms of integers, 2021
(HAL record)
- Denis Roegel: Edward Sang's computation of sines, 2021
(HAL record)
- Denis Roegel: Edward Sang's steps for the construction of the logarithms of the primes (K1-K3), 2021
(HAL record)
- Denis Roegel: A reconstruction of Edward Sang's table of logarithms of the first 10000 primes (K4), 2021
(HAL record)
- Denis Roegel: A reconstruction of Edward Sang's table of logarithms of the first myriad of integers (K5), 2021
(HAL record)
- Denis Roegel: A reconstruction of Edward Sang's table of logarithms of the second myriad of integers (K6), 2021
(HAL record)
- Table of logarithms to 15 places (volumes K7-K38) (HAL record)
- Denis Roegel: Introduction to Edward Sang's table of logarithms to 15 places, 2021
- Denis Roegel: A reconstruction of Edward Sang's table of logarithms to 15 places (volumes 10-99), 2021
(36000 pages)(HAL direct access)
- 90 volumes:
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40,
41,
42,
43,
44,
45,
46,
47,
48,
49,
50,
51,
52,
53,
54,
55,
56,
57,
58,
59,
60,
61,
62,
63,
64,
65,
66,
67,
68,
69,
70,
71,
72,
73,
74,
75,
76,
77,
78,
79,
80,
81,
82,
83,
84,
85,
86,
87,
88,
89,
90,
91,
92,
93,
94,
95,
96,
97,
98,
99
(zip of the 90 volumes on HAL)
- Denis Roegel: A reconstruction of Edward Sang's auxiliary table for logarithms of almost unitary values (K39,1884), 2021
(HAL record)
- Denis Roegel: A reconstruction of Edward Sang's canon of sines (K40/1,1876), 2021
(HAL record)
- Denis Roegel: A reconstruction of Edward Sang's canon of sines (K40/2,1877), 2021
(HAL record)
- Denis Roegel: A reconstruction of Edward Sang's canon of sines (K41-K42,1881), 2021
(HAL record)
- Denis Roegel: A reconstruction of Edward Sang's table of logarithmic sines and tangents (K43,1888), 2021
(HAL record)
- Denis Roegel: A reconstruction of Edward Sang's table of sines in degrees (K44,1879),, 2021
(HAL record)
- Denis Roegel: A reconstruction of Edward Sang's table of circular segments (K45,1879), 2021
(HAL record)
- Denis Roegel: A reconstruction of Edward Sang's table of mean anomalies, volume A (K46,1880), 2021
(HAL record)
- Denis Roegel: A reconstruction of Edward Sang's table of mean anomalies, volume B (K47,1880), 2021
(HAL record)
ca. 1880 S.-L. Tissot
1891 Service géographique de l'armée
1891 Mendizábal-Tamborrel
1910-1911 Bauschinger and Peters
1911 Peters
1911 Andoyer
1912 Peters
1913 Peters
1915-1918 Andoyer
1918 Peters
1919 Peters
1921 Peters
1922 Peters
1922 Andoyer
1929 Peters
1930 Peters
1937 Peters
1938 Peters
1939 Peters
1939 Mathematical Tables Project
1940 Peters
1941 Peters
1941 Mathematical Tables Project
- Arnold Lowan (ed): Table of natural logarithms,
New York: Federal Works Agency, Work Projects Administration, 1941.
- Denis Roegel: A reconstruction of the Mathematical Tables Project’s table of natural logarithms (1941), 2017
(HAL record)
1952 Thompson
- 1668 Brancker
- 1770 Lambert
- 1776 Felkel
- ca. 1780 Schenmark
- 1782 Vega
- 1797 Vega
- 1798 Lambert and Felkel
- 1800 Ulbrich
- Florian Ulbrich: Factorentafeln, two volumes, 1791-1800, Österreichische Nationalbibliothek
- Denis Roegel: A reconstruction of Ulbrich's table of factors (1791-1800), volume 1, volume 2, volume 3, 2013
(HAL record)
- 1804 Krause
- 1811 Chernac
- 1814 Burckhardt
- 1816 Burckhardt
- 1817 Burckhardt
- 1821 Vega
- 1825 Kulik
- 1841 Inghirami
- 1842 Crelle
- 1853 Hinkley
- 1862 Dase
- 1862 Goldberg
- 1863 Kulik
- Jakob Philipp Kulik: Magnus Canon Divisorum, ca. 1825-1863 (only manuscript)
- Denis Roegel: A reconstruction of Kulik's ``Magnus Canon Divisorum'' (ca. 1825-1863): Introduction, 2011 (HAL record)
- Reconstructions of the eight volumes with interleaved pages: (HAL record)
volume 1,
volume 2,
volume 3,
volume 4,
volume 5,
volume 6,
volume 7,
volume 8
(each volume is about 40 MB)
- Reconstructions of the sixteen sequences of non interleaved pages: (HAL record)
volume X-1,
volume X-2,
volume X-3,
volume X-4,
volume X-5,
volume X-6,
volume X-7,
volume X-8,
volume X-9,
volume X-10,
volume X-11,
volume X-12,
volume X-13,
volume X-14,
volume X-15,
volume X-16
(each volume is about 20 MB)
- 1863 Dase
- 1865 Dase
- ca. 1878 Dase and Rosenberg
- 1879 Glaisher
- 1880 Glaisher
- 1883 Glaisher
- 1896 Jones
- 1909 Lehmer
- 1914 Lehmer
- 1931 Gifford
- 1935 Peters, Lodge, Ternouth, Gifford
- 1937 Kaván
- 1947 Merritt
- 1951 Beeger
- 1971 Lifchitz
- Henri Lifchitz: Table des nombres premiers de 0 à 20 millions,
Tome II : de 10 millions à 20 millions, 1971
- Denis Roegel: A reconstruction of Lifchitz's table of primes (1971), volume 1 (unpublished), volume 2, 2013
(HAL record)
- 1592 Magini
- 1610 Herwart von Hohenburg
- 1690 Ludolf
- 1762 Joncourt
- 1817 Voisin
- 1817 Bürger
- 1820 Crelle
- 1825 Centnerschwer
- 1827 Schiereck
- 1832 Merpaut
- 1836 Crelle
- 1847 Henry Knight
- 1848 Kulik
- 1851 Kulik
- 1856 Laundy
- 1887 Blater
- 1889 Zimmermann
- ca. 1896 Arnaudeau
- 1909 Bojko
- 1909 Peters
- 1930 Peters
- 1933 Plassmann
Last update: D. Roegel, 16 July 2023.
History of changes
Return to the main page.
This page is located at http://locomat.loria.fr/