298 Mr. J. W. L. Glaisher on some new Facts in 



it is remarkable tliat so little information has been given about 

 one who played so prominent a part in their first calculation. 

 All the work done by Briggs and Tlacq was, as it were, work 

 done for all time j and we save labour and time by the use of 

 logarithms simply because we are enabled to utilize so much of 

 the work performed by them, instead of having to do it our- 

 selves over and over again as often as it is required*. The debt, 

 therefore, that their successors owe, not only to the inventor, but 

 also to the calculators of logarithms, is very large : and eveiy 

 fact connected with the original calculation is of great interest, 

 having regard to the enormous number of subsequent calcula- 

 tions, of which it has, so to speak, formed part. The first men- 

 tion of Ylacq^s name is very hkely that quoted from Decker in 

 this notice; and the facts of his life that are beyond question are 

 as follow. In 1626, as he tells us himself, he became acquainted 

 with Briggs^s Arithmetica. He spent the next two years in cal- 

 culating the logarithms of the numbers from 20,000 to 90,000_, 

 and also the logarithmic sines, tangents, and secants (from the 

 natural sines &c. of Rheticus) for every minute to ten decimal 

 places, and in passing through the press his Arithmetica (which 

 appeared in 1628). Vlacq then undertook at his own cost and 

 under his own care the printing of Briggs^s Trigonometria Bri- 

 tannica-f : most of it was com^pleted by 1631 ; but the book did 

 not appear till 1633. In the same year also was published 

 his Trigonometria Artificialis, the calculation of which, he tells 

 us, he had completed three years before. Thus for seven years 

 Ylacq was continually occupied with the calculation of loga- 

 rithms ; and how earnestly he worked is evident, not only from 

 the enthusiastic tone of his prefaces, but from the amount he 

 performed in the time. 



The above facts are all that can be obtained relative to 

 Ylacq^s life from his mathematical works ; and I had in vain ex- 

 amined all the biographical and mathematical dictionaries I 

 could obtain access to, with the ^iew of learning some particulars 

 of his life after 1633, and had finally come to the conclusion 

 that none "were known, w^hen I came upon a small 12mo book 

 (5*1 in. by 3 in.) in the Cambridge University Library, printed 

 by Ylacq, in which he, in 1654, gives an account of his own life. 



The book consists of t^ro v.orks bound together, the first title- 



* " Universahs finis tabulamm est, ut semel pro semper computetur, 

 quod scEpius de novo computandum foret j et ut pro omni casu computetur, 

 quod in futururn pro quovis casu compuiatura desiderabitur." Lambert, In- 

 trod. ad Supplementa &rc. (179Sj. 



t "Rogatus deinde a clarissimo Tiro D. Briggio P.M. an Canonem .... 

 quern ante multos annos construxerat, Meis impensis et cura typis maadare 

 vellem, hbentissime voto ejus annui." Preface to the Trigonometria Arti- 

 ficiaUs, 



