Tables y and their Calculators, 377 



was equally remarkable ; and I expressed an opinion " that Vlacq 

 must have quarrelled with Decker, or for some other cause have 

 had a set purpose to ignore his book entirely." The hypothesis 

 of the quarrel rested on no other evidence except such as the 

 foregoing facts afforded ; and I am very glad Prof, de Haan, by 

 showing that friendly relations existed between Vlacq and De 

 Decker in 1631, has proved it to be untenable. He considers 

 the smaller tables were printed by Vlacq, and merely collected 

 by De Decker, and attributes the silence of the former in the 

 Arithmetica to the fact that, in comparison with this work, he 

 was rather ashamed of his earlier performances; while De 

 Decker did not keep his word, because Vlacq occupied the 

 ground he had intended to cover. The explanation is not very 

 satisfactory (as, whatever the circumstances may have been, De 

 Decker and the promises should not have been ignored) ; but it 

 is perhaps the best that will ever be obtained. Prof, de Haan 

 apparently grounds his statement that Vlacq was a bookseller 

 under the firm of Pieter Rammaseyn on the fact that the pri- 

 vileges are made out to him*. At the time of writing my papers 

 I was surprised, though I find that I have not alluded to the 

 matter, at Vlacq' s name being mentioned in both the privileges 

 (while neither De Decker's nor Rammaseyn's appear at all in 

 that of the Nieuwe Telkonst, where De Decker's alone appears on 

 the titlepage) ; and I do not even now see the reason very 

 clearly. With regard to the date when Vlacq became a book- 

 seller, his own words are : — " Ignosce quseso, Benevole Lector, si 

 nimis prolixus sum in narranda historiuncula vitse mese quam 

 abhinc 26 annis institui : ex eo enim tempore, nescio quo 

 fato, in librorum commercium incidi. In Hollandia, quae mea 

 patria est, turn temporis vivens, ex Anglia acceperam insignis 

 Mathematici Henrici Briggii Arithmeticam Logarithmicam, Opus 

 sane aureum, et omnium inventionum in artibus Mathematicis 

 meo judicio excellentissimam ; in quo erant Logarithmi pro 

 numeris ab unitate ad 20000 et a 90000 ad 100000. Cum- 

 que viderem Logarithmos pro numeris a 20000 ad 90000 ibi 

 desiderari, animus mihi erat lacunam istam explere, quod et in- 

 credibili temporis brevitate solus peregi, ita ut D. Briggius 

 aliique Mathematici in Anglia admirati fuerint, quod non solum 

 laborem istum, sed et operis promulgationem tarn brevi tem- 

 pore absolverim Cum libros istos imprimi curabam, 



Typographiam nondum habebam, neq; Bibliopola eram, sed 



* Since writing the above I have received a letter from Prof, tie Haan, 

 in which, in answer to my inquiry, he says, " I conclude that Vlacq was a 

 bookseller in 1626 from the privilege having been given to him, although 

 he was not the author of the work named on the titlepage. In general 

 these privileges were granted with us to the booksellers themselves. 



