386 On the introduction of the 'words Tangent and Secant. 

 sec = tanfl + tan (i<5° — — J, 



and used it. Clavius gives the same demonstration of the 

 same formula. There is then no doubt that the celebrated 

 tables of Clavius, the first (I believe) introduced into this 

 country, are no other than the tables of Finck, deprotestant- 

 ized by the substitution of the name of Clavius for that of 

 Finck. If our Elizabethan mathematicians had known this, 

 they would not have let it pass unnoticed. 



The tables of Clavius were copied by Lansberg and Magini 

 (1591 and 1592), both of whom omit all mention of Finck, 

 though the second gives a list of the names which his several 

 predecessors gave to the trigonometrical lines. So completely 

 did the last name disappear from history, that it is not men- 

 tioned in its proper volume of Delambre (the Astron. Moyenne), 

 except in the index, in which it is stated, speaking of the tables 

 of secants, that " Rheticus l'a etendue d'abord a toutes les 

 minutes; et c'est ainsi que Finckius l'a reproduit en 1583 en 

 citant Rheticus mort en 1574." This is incorrect; Rheticus 

 published nothing closer than to ten minutes, and Finck, we 

 may suppose, could not have found out Valentine Otho and 

 the manuscripts at the age of twenty-two; he would have 

 made his final secants more correct if he could have done so. 

 When he cites Rheticus, it is for the name which the latter 

 adopted, not for any mode of calculating ; and as I have stated, 

 he made his own secants by his own method. 



This work of Finck is so clear and concise, and so much 

 above the usual writing of the sixteenth century, that its author 

 ought to rank very high among the secondary authors of that 

 period. 



Being engaged in an attempt to trace the earl}' progress of 

 trigonometrical tables in England, I annex the results which 

 I have obtained, in the hope that some of your readers may 

 be able to furnish additional information. I am not aware 

 that any one has ever investigated the point. 



Thomas Digges and John Dee, in their several works on 

 the new star in Cassiopea (both published in 1573, and in 

 Latin), mention and use sines, but refer to foreign tables; 

 Digges to the ten-minute canon of Rheticus, Dee to Regio- 

 montanus. William Burroughs, in his tract on the Variation 

 (written in 1581), mentions and uses tables of sines, but de- 

 scribes the doctrine of " signes and triangles " as new and 

 strange to English ears. He professes his intention of inter- 

 polating the ten-minute canon, and publishing it, if his pur- 



