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.
- Napier 2014: preparations for an international conference in 2014.
- 1551 Rheticus
- 1579 François Viète
- 1596 Rheticus
- 1613 Pitiscus
- 1614 Napier
- 1616 Napier
- 1617 Briggs
- 1620 Bürgi
- 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
1871 Sang
1872 Sang
ca. 1880 S.-L. Tissot
1891 Service géographique de l'armée
1891 Mendizábal-Tamborrel
- Joaquín de Mendizábal-Tamborrel: Tables des Logarithmes à huit décimales des nombres de
1 à 125000, et des fonctions goniométriques sinus,
tangente, cosinus et cotangente de centimiligone
en centimiligone et de microgone en microgone
pour les 25000 premiers microgones, et avec sept décimales
pour tous les autres microgones, 1891
- Denis Roegel: A sketch of Mendizábal y Tamborrel's table
of logarithms (1891), 2010
(HAL record)
1911 Andoyer
1915-1918 Andoyer
1922 Andoyer
1952 Thompson
- 1668 Brancker
- 1770 Lambert
- 1776 Felkel
- ca. 1780 Schenmark
- 1782 Vega
- 1797 Vega
- 1798 Lambert and Felkel
- 1804 Krause
- 1811 Chernac
- 1814 Burckhardt
- 1816 Burckhardt
- 1817 Burckhardt
- 1821 Vega
- 1825 Kulik
- 1841 Inghirami
- 1842 Crelle
- 1853 Hinkley
- 1862 Dase
- 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
Last update: D. Roegel, April 12, 2013
History of changes
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