the early History of Logarithmic Tables. 303 



are several references to him in the preface : but this communi- 

 cation is already so long that I refrain from making quotations ; 

 it is enough to mention that Decker states that he was unac- 

 quainted with Latin, and that Vlacq, who was then applying 

 himself with great zeal to geometry*, made the translations for 

 him. There does not appear to be any mention of the octavo 

 work in the preface ; but I have not examined the book with 

 sufficient care to be quite certain on this point. At first I 

 thought it possible that this was the publication to which 

 Decker referred as the Groote Werck in the octavo work^ and 

 not the (improved) reprint of Briggs' s Arithmetica ; and the pro- 

 bability of this seemed increased by the fact that, in a printed 

 extract from a bookseller^s catalogue gummed on to the title- 

 page, the book was described as Eerste {en Tweede) Deel ^c. 

 A careful reexamination of the preface to the octavo work, how- 

 ever, has convinced me that the words cannot possibly have any 

 other meaning than that here attributed to them j so that the 

 quarto work was the Eerste Deel, and Briggs^s Arithmetica, 

 translated into Dutch, was intended to have been the Tweede 

 Deelj the octavo work being merely a makeshift till the appear- 

 ance of the latter. The inaccuracy in the bookseller^s catalogue 

 is accounted for by the fact that Napier divided his Rahdologia 

 into two books, so that the Dutch headings run loannis Neperi 

 Eerste Boeck and loannis Neperi Tweede Boeck, and the com- 

 piler mistook the latter for the Tweede Deel. I did not succeed 

 in finding the Graves copy of the octavo work; but this is of very 

 little consequence, as its interest would be almost wholly biblio- 

 graphical. To show not only the great scarcity of Decker's 

 works, but also the total oblivion into which he and they have 

 fallen, I may mention that his name does not appear at all in 

 the catalogues of the libraries of the British Museum, the Royal 

 Society, the University of Cambridge, or several smaller libraries 

 that I have examined ; nor is any mention of him to be found 

 in the most complete works of mathematical bibliography, in- 

 cluding Lalande, Rogg, PoggendorfF, Ebert, Ersch, Murhard, 

 Heilbronner, and Kastner, the last three of which are especially 

 valuable for notices of arithmetical works about the period of 

 the invention of logarithms. Kastner speaks of having heard of 

 a translation of the Rahdologia by Ursiuus ; but he knew nothing 

 of Decker. In conclusion I will add that Poggendorff assigns 

 to Vlacq a book, " Ephemerides Motuum coelestium ab a. 1633 

 ad a. 1636, 4to, Goudee, 1632,^^ to which I have seen no other 

 reference. All authorities agree in stating that he published at 

 Gouda in 1636 a small table of logarithms, "Tabulse sinuum,&c.^' 

 September 23, 1872. 

 * " Die dem doenmael met grooten yver inde meetkonst oefFende.'* 



