of the words Tangent and Secant. 383 



of elegance over all which existed. On looking at the para- 

 graph of Vieta's Liber Inspect ionum, which Delambre was then 

 describing, we find not the smallest allusion to the word tan- 

 gent, nor to any name for the table, except the old one of 

 tabula fcecunda. So that Delambre must have proceeded 

 upon a general impression, that the word tangent was in use 

 in Vieta's time. But as he does not quote any authority for 

 this impression, though much given to incidental allusion to 

 one writer in his description of another, it is not necessary to 

 give it any weight in the face of the positive evidence which I 

 shall produce. I say this, because an impression on the mind 

 of Delambre as to a usage deserves more consideration than 

 the same thing in the case of any other mathematical histo- 

 rian. His memory might fail on an isolated fact, or his in- 

 formation might be incorrect on books which he had not seen ; 

 but he was occupied at each one time with masses of writers 

 of one period, and came to each author fresh from that au- 

 thor's own contemporaries, and frequently from very close 

 reading of them. 



After writing the above paragraph, I happened to find a 

 passage in a later writing (the Responsorum liber octavus, pub- 

 lished in 1.593) which might have left the above impression on 

 Delambre's mind. Here Vieta distinctly names and objects 

 to the words tangent and secant, and proposes to call the 

 former prosines or amsines, and the latter transsinuous lines. 

 Laugh if you will, he says, at the allegory of the Arabs (mean- 

 ing the use of the word which is correctly Latinized by sinus), 

 but either adopt it altogether, or reject it altogether. This 

 passage strengthens the presumption, that when Vieta wrote 

 the Canon, &c. he had never heard the words tangent or se- 

 cant. The same impression on the part of Delambre occurs 

 again in speaking of Pitiscus (Astr. Mod. ii. 33), when he 

 says, " II a eu le bon esprit de n'imiter ni Viete, ni Rheticus ; 

 il a conserve les noms de sinus, de tangentes et de secantes." 

 But where either Rheticus or Vieta (in 1579) was to have 

 found the last two names, we are never told. 



The Canon Mathematicus of Vieta, to which the Liber In- 

 spectionum above-mentioned is an appendix, was published in 

 1579. The work in which tangents and secants are first 

 mentioned under those names, was published four years after. 

 Its author was Thomas Finck, of Flensborg in Denmark, 

 who was successively professor of mathematics, rhetoric, and 

 medicine at Copenhagen, where he died in 1656, at the age 

 of ninety-five (Aikin, Gorton, and Biogr. Univ.): there are 

 references to his astronomical observations in Tycho Brahe. 

 The work we speak of was published at Basle, when he was a 



