**Adriaan Vlacq** was born into a well off family. It is unclear how much mathematical training Vlacq had but he became friendly with a surveyor Ezechiel de Decker who was particularly interested in the new ideas of calculating using tables of logarithms. Vlacq worked with de Decker and translated Latin books written by Napier and Briggs into Dutch for him. Together they decided to publish Dutch editions of these important aids to calculation. In 1626 *Het eerste deel van de Nieuwe telkonst* Ⓣ was published under de Decker's name with acknowledgement to Vlacq for considerable help. This contained three items: a Dutch translation of Napier's *Rabdologiae* Ⓣ which described a method of multiplication using "numbering rods"; a paper by de Decker written to help businessmen undertake arithmetical calculations; and Stevin's *La Theinde* Ⓣ which gave an account of decimal fractions.

Briggs had published *Arithmetica logarithma sive logarithmorum chiliades triginta, pro numeris naturali serie crescentibus ab unitate 20,000 et a 90,000 ad 100,000 *... Ⓣ in 1624 and de Decker published a small part of this in 1626 under the name *Nieuwe telkonst*. This contained Briggs' logarithms from 1 to 10,000 but promised to publish, with Vlacq's assistance, a further work giving the logarithms from 1 to 100,000. Briggs' own tables were, as the above title indicates, of logarithms of 1 to 20,000 and 90,000 to 100,000 so 70,000 values needed to be calculated to complete the table. The full table of logarithms of 1 to 100,000 appeared in 1627 as *Het tweede deel van de Nieuwe telkonst* Ⓣ under de Decker's name with again acknowledgement to Vlacq. Struik writes:-

The 'Tweede deel' of1627, actually the first complete table of decimal logarithms, was long forgotten until a copy was rediscovered in1920.

In 1628 Vlacq republished the 10 decimal place logarithm tables as *Arithmetica logarithma sive logarithmorum chiliades tentum, pro numeris naturali serie crescentibus ab unitate ad 100000 *... Ⓣ. He appears to have had a connection with the Gouda firm of Petrus Rammaseyn and it is this firm that published the work, this time under Vlacq's name. A French translation, *Arithmetique logarithmetique, ou, La construction et usage d'une table contenant les logarithms de tous les nombres depuis l'unité jusque 100000* Ⓣ by Vlacq was also published Petrus Rammaseyn at almost the same time. It had long been believed that the new calculation of the 70,000 missing logarithms from Briggs' work were made by Vlacq so, as Struik writes in [1]:-

Having paid for the publication of tables he himself had computed, Vlacq saw no objection to republishing them under his own name ... Although de Decker was not mentioned, there is no indication he later resented this. Vlacq's fame rests on these tables, which were well received and contain relatively few errors.

In [2], however, Bruins concludes that Vlacq was not a mathematician, and that most of the work was done by de Decker.

Vlacq became a bookseller and publisher who, in 1632, settled in London and opened a bookshop. Tension between King Charles I and the House of Commons steadily increased during 1641 and after his unsuccessful attempt to arrest five members of Parliament on 4 January 1642 Charles left London on 10 January and King and Parliament prepared for war. Vlacq decided that London was not a good place to sell books with the approaching unrest so he left for Paris in 1642. A dedication in a book he published 10 years later suggests that he sympathised with the Royalist side in the Civil War.

In Paris Vlacq again set up a book business. He remained there for six years before returning to The Hague where he again sold and published books.

Vlacq also constructed logarithm trigonometric tables which he published as *Trigonometria artificialis* Ⓣ in 1633 during his time in London. These were again published by Petrus Rammaseyn in Gouda and gave values for angles at 10 second increments. Since these tables were bulky, he decided to publish a smaller version. This appeared in 1636 as *Tabulae sinuum, tangentium et secantium et logarithmi sinuum, tangentium et numerorum ab initate ad 10000* Ⓣ. A French version *Tables de sinus, tangentes, secantes, et de logarithmes* Ⓣ was published by Rammaseyn in the same year, as was a German version [1]:-

These tables, carried to seven decimal places, were a great success and were often reprinted and reedited...

Vlacq also published many mathematical works by other authors including, perhaps surprisingly, Briggs himself and also by Gellibrand.

**Article by:** *J J O'Connor* and *E F Robertson*