the early History of Logarithmic Tables, 295 



examined four copies of Miller^s edition ; and in a paper read 

 before the Royal Astronomical Society on May 10^ 1872, and 

 printed in the ' Monthly Notices ' for that date, which was 

 written before I was aware of the existence of Decker^s work, I 

 made the following remark: — ^' Three out of the four copies 

 mentioned contain, after the English introduction and before the 

 Tables, a title-page on w4iich is printed, " Tafel der Logarithmi 

 voor de Ghetallen van 1 af tot 100,000, while the corresponding 

 page in Vlacq^s Table is inscribed, Chiliades centum Logarith- 

 morum pro Numerus (sic) ab Unitate ad 100,000. This show^s 

 the Dutch origin of Miller^s Table; and it is besides curious, as 

 it seems to imply that Vlacq meditated a Dutch translation of 

 his work, but the Tables intended for the purpose were bought 

 and published by George Miller/^ This surmise is confirmed 

 by Decker's statement. It is possible, but not very probable, that 

 an edition of the Arithmetica wath a Dutch introduction absolutely 

 was issued. The fact that no such copy seems to have been 

 met with by Hutton, De Morgan, Murhard, &c. is not conclu- 

 sive as to the non-existence of any — as it is most likely, if there 

 was a Dutch edition, that nearly all the copies would remain in 

 Holland ; for although now the Table is the only thing that is of 

 interest, the authors at that time seemed to regard their own tri- 

 gonometry, explanations, &c., which were prefixed to the Table, 

 as the most important part of the work. 



Decker's book is of octavo size, the pages being 7*6 in. by 

 4'5 in. It contains two Tables — the first giving ten- figure loga- 

 rithms of the numbers from unity to 10,000, with characteristics 

 and difi*erences, and the second (to w-hich is prefixed the title 

 Edmundi Gunten Tafel van Hoeck-maten ende Raeck-lijnen, den 

 Wort el zijnde van 10000,0000 deelen) giving Gunter's logarith- 

 mic sines and tangents for every minute of the quadrant (semi- 

 quadrantally arranged) to 7 decimal places. There is a long 

 introduction, containing explanations of the Tables, trigonometry, 

 &c. It is incomplete in the Royal-Observatory copy, ending 

 abruptly at p. 50, where several pages, including the title-page 

 to the first Table, have been torn out. The four pieces of Latin 

 verse by Andreas Junius and Patricius Sandseus are printed after 

 the preface in this work, as in Napier^s Canon Mirificus, except 

 that the order is difi^erent. 



I have compared the Telkonst with the copy of the Sciographia 

 in the Royal Society's library, alluded to by De Morgan. The 

 first Table has the title quoted at the beginning of the extract 

 from De Morgan, ' Tables dcs Logarithmes ' &c., and is identical 



copies of the Table in Vlacq's Arithmetica (1628) and Briggs's (1624), 

 This has created much confusion; and, besides, the title-page does not 

 correctly describe the contents of the latter work. 



