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My Special Item - Mein Besonderes Stück

Vlacq Table of Logarithms, 1742

Acquired during april 2004 at the Dutch Circle stand in a collectors fair from a retired instrumentmaker at the Agricultural University of Wageningen.

Shown to the audience of IM2004 on 26 September 2004, according to the following

Principles of Collecting:

"with the acquisition of a special item, a collector acquires at the same time the responsibilities of its stewardship, to preserve the item well until a proper destination has been found for its future, to assemble and keep knowledge about the object, and to share this with the public"

Numerous Years of Publication for Vlacq’s Log Tables

(limited scan from Leiden Museums, Bierens de Haan and ZVAB/antiquarian bookhandlers)

1628 F-L (Arithm. Log. II)

1636 D (10 x 100,000)

1651 F-L (100,000)

1657 D (100,000)

1658 D (7 x 10,000, octavo)

1661 D-F-G-L (10,000)

1665 D-F-G-L (100,000)

1666 F (100,000)

1670 F (10,000 postuum)

1673 G (10,000)

1681 L (10,000)

1683 D (10,000)

1689 G (10,000)

1690 F (10,000)

1695 G (10,000)

1706 G (10,000)

1721 Chinese Arithm. Log. II

1721 G (10,000)

1725 G (10,000)

1732 G (10,000)

1738 G (10,000)

1742 L (10,000)

1748 G (10,000)

1757 G-L (10,000)

1760 F (10,000)

1763 G (10,000)

1768 G (10,000)

1775 G (10,000)

1778 G (10,000)

1784 L (10,000)

1790 L (10,000)

1808 G (10,000)

1821 G (10,000)

LEGEND

D=Dutch: "Nieuwe Konstige Tafelen … "

F=French: "Tables de Sinus … "

G=German: "Tabellen der Sinuum … "

L=Latin: "Tabulae Sinuum … "

Cooperation between Vlacq and de Decker

Adriaan Vlacq	Ezechiel de Decker

1600 born in Gouda
	1603 born in Leiden
	1621 moves to Gouda as surveyor & teacher
1624 reads Briggs’ "Arithm. Log." and starts planning a completer version
1625, 24/12: obtains copyright for plan
1625, 17/12: signs partnership contract with D.
	1626, 4/9 publishes "Nieuwe telkonst part I"
1626, 31/12: summons D. to calculate part II	and appitiser for part II with existing logtables
	1627 publishes "Nieuwe telkonst part II"
	"Het Groote Werk": 10 x 100,000
1628 publishes French and Latin versions of	(Rediscovered by Haaften in 1920)
"Arithm. Log. Part II extended"
(Copper plates for tables used from D.)
	1631 moves to Rotterdam, maritime work
1632 opens bookshop in London
1636 prints first "own" version of 1628 Tables
1642 opens bookshop in Paris
	1647 dies in Rotterdam
1648 opens bookshop in The Hague
1667 dies in The Hague

Some other thoughts and questions on log tables

Hundreds of errors have been reported in the Vlacq tables, presumably in the last digit(s), but largely corrected in newer editions

Ranges (1-100,000) are better expressed in digit precision (e.g. 4 digits in, by 7 out), which should be "balanced" to each other (Briggs was too precise with 14 digits out)

Were John Napier’s log-tables really practical?
With logarithms of sines, the calculation types are very limited:
only sin(a) : sin(b) = sin(c) : sin(x), as used in spherical trigonometry

Who calculated Vlacq’s Trig tables? Or was it copied from Edmund Gunter’s "Canon Triangularum"? Did Gunter compute these himself?

Gunter introduced a log-sine with values between 0 and 9.xxxxxxx, based on his assumption of an extremely large angle radius.
Why did log-sin tables keep this caracter convention deep into the 20^th century, long after the sine had been redefined to a radius of unity, resulting actually in a negative log-sine value?

Autor: Otto van Poelje