of the words Tangent and Secant. 385 



The first after Finck who used the words tangent and se- 

 cant was the celebrated Jesuit Clavius, whose edition of Theo- 

 dosius *, with trigonometry and tables attached, was published, 

 according to Lalan.de, in 1586. Blundeville, who copied these 

 tables into his Exercises, and who is, as far as I can find, the 

 first Englishman who gave complete trigonometrical tables, 

 cites this date. These tables of Clavius are those of Finck, 

 with the use of the terms tangent and secant; but Finck's 

 name is entirely suppressed. Clavius does not mention the 

 name of the condemned Protestant Rheticus : it is not sur- 

 prising that he should have served the other Protestant, 

 Finck, in the same way. I do not suspect Clavius of wanting 

 to pass the work of another as his own ; he mentions Regio- 

 montanus and Purbach freely enough, and excludes none but 

 persons whom a reputable Jesuit could not name, as Pro- 

 testants and Copernicans. But I proceed to make good my 

 assertion. 



The tables of Clavius are to the same radius and interval 

 as those of Finck. The sines are avowedly from Regiomon- 

 tanus : the latter gave differences to every ten seconds ; Cla- 

 vius does the same. But Finck gave no differences : Clavius 

 gives no differences to his tangents and secants. In the tables 

 of this period, the tangents and secants in the last degree were 

 often very wrong, having hardly one of what we call the de- 

 cimal places right. Clavius agrees with Finck in every deci- 

 mal place, and differs from Vieta and what had then been 

 published by Rheticus. For instance, we take the tangent 

 and secant o"f 89° 50'. 



Tan 89° 50'. Sec. 89° 50'. Date. 



Correct value 343-77371... 34377516... 



Vieta 343-77371.. 34377516... 1579 



Rheticus 3437829002 3437843784 1551 



f Finck 3437829002 3437843546 \ 1583 



\ Clavius 343-7829002 3437843546 J 1586 



And it is the same throughout : whenever Finck differs in 

 two or three decimal places from Rheticus, so does Clavius in 

 the same manner. And whereas Vieta and Rheticus have the 

 semiquadrantal form, Clavius agrees with Finck in retaining 

 the quadrantal form. 



There is a particular reason why Finck should differ from 

 Rheticus in the secants. The former used the reciprocal of 

 the cosine carried to more figures than it would give truly; 

 the latter demonstrated the formula 



* I have before me the tables in the complete edition of Clavius' s works, 

 and have never seen the original edition. 



