of the earliest Trigonometrical Canon. 519 



minute, in his hiber Tabularum Dircctiommi^ published in 

 1554, three years after the Prutenic tables, on which his fame 

 principally rests. Regiomontanus had called the table of tan- 

 gents canon fcecundus, which name Reinhold adopted. As to 

 secants, the table of which was afterwards called canon fcecun- 

 dissimusj a name which I think first occurs in Vieta, the first 

 table mentioned is that of Maurolycus in the spherical treatise 

 which accompanies his edition of Theodosius and Menelaus, 

 published in 1558; this table goes only to degrees, and is 

 called tabula benejica. The Canon Matkematicus ofY'ietay pub- 

 lished in 1579, is said to have been the first work in which sines, 

 tangents, and secants were joined together ; that is, the first 

 complete canon printed. But all admit that Rheticus, who 

 died in 1576, had very nearly completed the enormous table 

 which Valentine Otho published in 1596, under the name of 

 Opus Palatinum. Still, the rigid rule is, that first publication 

 gives a right which nothing but unquestionable proof of fraud 

 can impugn ; and accordingly Vieta has been justly considered, 

 up to this time, as the first author of a complete canon. I 

 intend to show, however, that under the same rule, Rheticus 

 is not only the first who published either tangents or secants*, 

 but the first who joined the three into a complete canon, and 

 also the first who adopted the now universal semi-quadrantal 

 form. Before, however, I come to the description of the table 

 which establishes these things, I shall show that it once had 

 a recognised existence. It is not enough, if better may be, to 

 produce a printed book as the sole evidence of the fact of 

 publication. There may have been a suppressed edition, or 

 one accidentally destroyed by fire, and of which only a few 

 copies escaped : the forgery of a work is neither impossible 

 nor unexampled, and more than one big catalogue consists 

 entirely of pseudonymous works. 



Lansberg attributes the first publication of tangents, and 

 Bossut the first publication of secants, to Rheticus : on what 

 authorities I do not know. Moestlinus, in a letter written to 

 Kepler in 1594, and published in the folio correspondence of 



* Montucla gives the secants to Rheticus, and Delambre (Astron. Mod. 

 ii. 34) seems to assent, because Maurolycus only published them to every 

 degree. This is hardly fair: a person who points out the uses of a given 

 function, and tabulates it to a certain extent, is the inventor, and must not 

 lose his right because another gives more and better tabulation. But we 

 now see that Rheticus has a claim absolutely prior to that of Maurolycus. 

 Again, Delambre says that a certain Finckius gave secants to minutes, in 

 1583, referring to Rheticus : he seems to imply that Finckius had access 

 to the materials of the Opus Palatinum, not then published. Perhaps it may 

 now be held that the ten-minute canon described in the present article 

 was the original, the intermediate minutes being supplied by interpolation. 



