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Vlacq (Vlack, Vlaccus), Adriaan


(b. Gouda, Netherlands, 1600; d. The Hague, Netherlands, late 1666 or early 1667), mathematics, publishing.

A member of a well-to-do family, Vlacq received a good education. Interested in mathematics, he became acquainted with a local surveyor and teacher, Ezechiel De Decker (ca. 1595— ca. 1657), for whom he translated into Dutch several recent books written in Latin by British authors on the new art of reckoning, notably some by Napier and that by Briggs on logarithms. They decided to publish these and related works in Dutch. Het eerste deel van de Nieuwe telkonst appeared in 1626 under the name of De Decker, who in the preface praised Vlacq for his help. It contained Napier’s Rabdologia in Dutch translation, a paper on business arithmetic by De Decker, and Stevin’s Thiende. Also that year De Decker published the Nieuwe telkonst, a small table of logarithms to base 10 for the numbers from 1 to 10,000, based on Briggs’s Arithmetica logarithmica (1624). The work promised a full table of logarithms, an accomplishment realized in Het tweede deel van de Nieuwe telkonst (1627), again under the name of De Decker with credit to Vlacq. It contained not only the Briggsian logarithms from 1 to 10,000 and from 90,000 to 100,000, already published by Briggs, but also those of all numbers from 1 to 100,000 (to ten decimal places). The latter, the result of Vlacq’s computations, did what Briggs had planned to do.

Vlacq took out the privileges on these books and had them published by the Gouda firm of Pieter Rammaseyn, in which he seems to have had a financial interest. Having paid for the publication of tables he himself had computed, Vlacq saw no objection to republishing them under his own name in the Arithmetica logarithmica (1628). Although De Decker was not mentioned, there is no indication that he later resented this. Vlacq’s fame rests on these tables, which were well received and contain relatively few errors. The Tweede deel of 1627, actually the first complete table of decimal logarithms, was long forgotten until a copy was rediscovered in 1920.

To the Arithmetica logarithmica, Vlacq added Canon triangulorum sive tabula artificialium sinuum, with the decimal logarithms of the trigonometric lines computed from Pitiscus’ Thesaurus mathematicus (1613). In a letter to John Pell of 25 October 1628, Briggs states that the 1,000 printed copies of this book, with Latin, Dutch, and French prefaces, were almost all sold. The probable reason is that they were used by George Miller for his Logarithmicall Arithmeticke (London, 1631), identical with Vlacq’s book except for the English preface.

From about 1632 to 1642, Vlacq had a book business in London, which he moved to Paris. After 1648 he was in The Hague, publishing many books and repeatedly involved in business or political quarrels. The books he published include Briggs and Gellibrand’s Trigonometria britannica, containing the logarithms of the trigonometric lines with angles divided into tenths (Stevin’s idea), and his own Trigonometria artificialis, using the traditional sexagesimal division of angles. They have log sine, log cosine, log tangent, and log secant for angles increasing by ten seconds. Both books were published by the firm of Rammaseyn (Gouda, 1633).

Since all these tables were large, Vlacq, with his keen business instincts, published the small Tabulae sinuum, tangentium et secantium et logarithmi sin. tang, et numerorum ab unitate ad 10000 (Gouda, 1636). These tables, carried to seven decimal places, were a great success and were often reprinted and reedited, and were translated into French and German (there is a Leipzig edition of 1821).

From 1652 to 1655 Vlacq waged a pamphlet war, in which he took the English royalist side, thereby provoking an attack by John Milton. In 1654 he is mentioned as successor to Johannes Rammaseyn. Between 1651 and 1662 he was regularly listed as a visitor to the Frankfurt book fair.


On Vlacq’s life and work, see D. Bierens de Haan. “Adriaan Vlack en Ezechiel De Decker,” in Verslagen en mededeelingen der Koninklyke Akademie van wetenschappen, Afd. Natuurkunde, 2nd ser., 8 (1874), 57–99; and “Adriaan Vlack en zyne logarithmentafels,” ibid., 163–199; C. de Waard, “Vlacq (Adriaan),” in Nieuw nederlandsch biographisch woordenboek, II (1912), 1503-1506; J. W. L. Glaisher, “Notice Respecting Some New Facts in the Early History of Logarithms,” in Philosophical Magazine, 4th ser., 44 (1872), 291–303, and 45 (1873), 376–382; and D. Bierens de Haan, “On Certain Early Logarithmic Tables,” ibid., 371–376. The rediscovery of the Tweede deel by M. van Haaften is reported in his “Ce n’est pas Vlacq, en 1628, mais De Decker, en 1627, qui a publié une table de log arithmes étendue et complète,” in Nieuw archief voor wiskunde,15 (1928), 49–54; he first reported it in Verzekeringsbode, 39 (4 Sept. 1920), 383–386. In “Quelques nouvelles données concernant l’histoire des anciennes tables néerlandaises de logarithmes,” in Nieuw archief voor wiskunde21 (1942), 59-64, and in Nieuw tydschrift voor wiskunde, 31 (1943-1944), 137–144, van Haaften supplements his account by reference to three documents on the business relationship between De Decker and Vlacq found by P. J. T. Endenburg in the Gouda archives, reported in “De oudste nederlandsche logarithmentafels en hum makers,” in Het Boek,25 (1938-1939), 311–320.

D. J. Struik

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