Cooperation between Viacq and De Decker: the Facts
4
The major achievements of these four players in the game of calculating and
publishing tables of 10-based (Briggian) logarithms, are summarized in Table
Number 1.
Note: if we consider a logarithmical table as a transformation from a
number to its logarithm, then we can describe the input precision of a table of
numbers 1 to 1,000 as "3 decimals". Hence the precision notation "3 x 14" in the
first entry of table 1, which means 3 decimals in, and 14 decimals out (in the
"mantissa", the part after the decimal point). This is a better notation because the
table is not literally restricted to the numbers 1 to 1,000: any position of the
decimal point is allowed, as indicated by the "characteristic" of the logarithm (the
part before the decimal point).
WT
This paper will expose how Adriaen Viacq and Ezechiel de Decker have extended
Briggs' Aritmetica Logarithmica [3] into a complete table of the numbers 1 to
100,000.
Much has been written about the strained relationship between these two
Dutchmen, because their early agreements for cooperation have surely not been
executed as intended.
The following documented events give the facts of the story:
1. 1625: Viacq happens to read Briggs' Aritmetica Logarithmica, and decides to
publish a completed version ("Great Table") of this book, see preface of [6]
2. 1625, Dec. 24: Viacq obtains copyright for his planned publication, see [21]
TRIG precision
1 min. 7 dec.
2
1620
Arithmetica Logarithmica
3
1624
1 min. 7 dec
4
1627
5
1627
6
1628
1633
Tri go none tria Bri tannic a
8
1633
Trigo nome tria .4 rtifie ialis
Ezechiel de Decker
(Holland)
Adriaen Viacq
(Holland)
Ezechiel de Decker
(Holland)
Table 1 Main publications of early tables of Briggian logarithms,
indicates contribution by actual computations.
Arithmetica Logarithmica
Part II
1 to 20.000:
4(+) x 10 dec.
1 min. x 10 dec.
Author
Henry Briggs
(England)
Edmund Gunter
(England)
Henry Briggs
(England)
Henry Briggs
(England)
Adriaen Viacq
(Holland)
Nieuwe Tel-Konst
Part I. plus attached
booklet with tables
derived from Ref. 2 V 3
Nieuwe Tel-Konst
Part II
i
Year
"wTT
Title
Logarithmorum
Chilias Prima
Canon Triangulorum
1 to 100.000:
5 x 10 dec.
(the “Great Table")
*1 to 100.000;
5 10 dec.
(the “Great Table")
NUM precision
numbers 1 to 1.000:
3 dec. in x 14 dec. out
1 to 1.000:
3x7 dec.
1 to 20.000 and
90.000 to 100.000:
4(+) - 14
1 to 10.000:
4 x 10 dec.
1/100 min.
14/10 deg.
10 sec. x 10 dec.
