7
Fact 6
One of the safeguards of the project was the extensive guide for computing the
missing numbers, which Briggs gave in chapter XII and XIII of his Arithmetica
Logarithmica. However, the calculations following Briggs' guidelines proved to take
too much time. Vlacq knew that Briggs was working on his own version of a
"Great Table", and in panic he summons De Decker by notary to finish the agreed
calculations before May 1, 1627, see [21], He even offers his own assistence to
provide half of the remaining effort of calculations, if necessary. Now we follow
Bruins' hypothesis [25], that De Decker discovers a shortcut to the lengthy
calculations. Briggs' directions required first to determine all primes in the gap
from 20,000 to 90,000, calculate their logarithms, and from there work to the
remaining numbers. De Decker decides to use a different strategy of extrapolation
and interpolation: he first determines - in the missing region - the logarithms of
all multiples of Briggs' numbers by adding log(2), log(3) etcetera to their known
logarithms, and then he determines the remaining logarithms by interpolation,
greatly assisted by the decrease in precision from 14 down to 10 decimals. This
hypothesis seems to be supported by Vlacq's introduction to his Arithmetica
Logarithmica, Part II, refering to Briggs' high estimate of the work effort needed
and claiming the credit for himself: "so I adjusted the method to find easily every
logarithm with not more than 10 decimals".
Fact 7
De Decker is so pleased having finished the calculations by his own method,
that he feels himself freed of his contract with Vlacq and immediately asks
Rammaseyn to prepare the printing plates for the "Great Table". He had already
written the text for part II of his Nieuwe Te/-Konst in Dutch, which consisted of a
very practical guide to use the logarithmic tables for commercial purposes
(including compound interest calculations). His preface is written in "we" form,
implying Vlacq's assent, and the distinction between this publication and Vlacq's
later one, is logically explained, see [5]. Again the future publication by Vlacq is
announced in the introduction. Did Vlacq know? If not, he was bound to hear soon.
Fact 5
Part of the marketing plan was to include a preannouncement of the "Great
Table", and some preliminary (already existing) logarithmic tables in De Decker's
Nieuwe Tel-Konst Part I. This book contained Napier's texts on "Rabdologia"
(Napier bones), as translated by Vlacq, and De Decker's own text on commercial
arithmetic; also a copy of Simon Stevin's De Thiende on decimal numbers was
attached. This "non-logarithmic" book was combined with a separate booklet
Nieuwe Tetkonst, inhoudende de logarithm! \_A\d\, containing the logarithms of 1 to
10,000 copied from Briggs [3], and the trigonometric logarithms copied from
Gunter [2]. In each of both books, the introduction announces the future
publication by Vlacq of the "Great Table" ("Het Groote Werck") in 3 three
languages: Latin, French and Dutch.