Vlacq came from a well-off family. His father Cornelius Vlacq (1556-1656) was community leaders in Gouda. He received a good education, especially in Latin and other languages.
About an acquaintance with the surveyor Ezechiel de Decker Vlacq began to be interested in logarithms and translated for these Latin works of John Napier and Henry Briggs on logarithms into Dutch. Decker and Vlacq published in 1626 a book about then new Het eerste deel computational methods van de Nieuwe telkonst ( The first part of the new Zählkunst ) with a translation of Napier 's Rabdologiae ( Napiersche computing rods) and La Theinde by Simon Stevin ( with decimals ). In another part Decker published a part of the logarithm of Briggs (based on logarithms to the base 10 ) of 1624 ( Arithmetica logarithma ), but only a part of logarithms to 100,000 contained ( the logarithms 20000-90000 were missing). The rest followed in 1627 ( Tweede deel van de Nieuwe telkonst published under Decker's name). Moreover, they were reduced to ten digits. Of this edition only a few copies are known and the rest was obviously very limited. Published in 1628 in Gouda Vlacq a second edition under his own name ( Latin and French). Since Decker has raised no objection long generally believed (Dirk Struik ) that Vlacq had calculated the panels. The panels had relatively little error, found widely distributed and made Vlacq known. From the first edition of 1000 copies were in October 1628 a letter from Briggs most already sold, many went to the London bookseller Miller, who made a personal copy of it.
Was Vlacq publisher and printer, and moved to the success of its panels in 1632 to London. At the start of the English Civil War in 1642 he moved to Paris, where he remained until he moved to The Hague six years.
1633 and in a smaller version in 1636 he published in Gouda tables of trigonometric functions with their logarithms ( Trigonometria artificialis immersive magnus Canon triangulorum logarithmicus, in Latin, French, German ), with an accuracy of seven decimal places ( ten digits in the logarithms and angle at a distance of 10 arc seconds ). These were a great success. As a publisher, he published works by other mathematicians such as the Briggs.