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The German version was first published in Amsterdam by Johannes van
Ravensteijn and also by the family Boom, but after 1700 it was reprinted many
times in Frankfurt and Leipzig by J.F. Fleischer. Its title was Tabellen der Sinuum,
Tangentium und Secantium: wie auch der Logarithmorum vor die Sinus,
Tangentes, und die Zah/en von 1 bis 1OOOO.
This version was improved in the 1748 version by Johann Jacob Hentschen,
and in the 1789 version by Joh. Jac. Ebert. The very last version, published by
Fleischer in 1821, was restructured by Gottlob Nordmann. Those tables looked
very different from the ones which had been stable since the 1650's, now
containing explicit difference columns and additional square, cube and root tables.
The original introduction, unchanged for more than 150 years, was completely
replaced by a new introduction and a user manual.
The French version has been published in Amsterdam by Doncker, and until
1699 in France (Jean Thioly in Lyon and Jean Jombert in Paris). It had as title
Tables de sinus, tangentes et secantes et de iogarithmes des sinus, tangentes, et
des nombres depuis /'unite jusques a 10000.
Posthumous Editions of Viacq's "Small" Tables
After Vlacq died in 1667, many reprints have been published - under his brand - of
the small pocket-sized tables (the numbers from 1 to 10,000). This indicates the
stature of his name on the continent. The reprints have been published in four
different languages, not very important for the numerical tables but relevant for
the title pages and the 30 to 40 pages of introductory text, consisting of
instructions for use, four additional chapters on plane and spherical trigonometry
(largely derived from Gellibrand) and an annex on astronomical questions
(sometimes even on interest calculations).
It is not clear if after Viacq's death a Dutch book, containing only the small
tables, has ever been published under the name Vlacq, but his tables certainly
have been used as annexes in numerous Dutch handbooks on navigation at sea
(see also the following section), for example under the name De Taeffeien der
sinuum, tangentium en secantium, ofte der hoeckmaeten, raecklijnen en
snyiijnen, alsmede de logarithm! der hoeckmaeten, raecklijnen en snyHjnen, en
achter de se/ve de logarithm us numeri van 1 tot 10,000.
(Note that some of the Dutch publications had the logarithms of secants
("snyiijnen") added, in addition to Viacq's standard set of logarithms for sines and
tangents [see fig. 5, eds.J).
The Latin version, published first in Lyon (Jean Thioly), Amsterdam (family
Boom) and after 1700 mostly in Frankfurt (Johann Friedrich Fleischer), was often
called: Tabulae sinuum, tangentium, et secantium, et logarithm! sinuum,
tangentium, et numerorum ab unitate ad 10000
