384; Prof. De Morgan on thejirst introduction 



student there (and where two years before he had published 

 an ephemeris) at the age of twenty-two. It is " Thoma Finkii 

 Flenspurgensis Geometries Rotundi libri xiiii. Ad Fridericum 

 Secundum, Serenissimum Dania et Norvegice Regem, fyc. Cum 

 Gratia et Privilcg. C&s. Majest. Basilece, per Sebastianum 

 Henricpetri :" quarto. The colophon is " Basiled, per Sebas- 

 tianum Henricpetri) anno salutis humanae M.D.LXXXIII. 

 Mense Augusto." The work itself is well-worthy of descrip- 

 tion for its contents, independently of its being the production 

 of so new a student. But I am here only concerned with the 

 table of sines, tangents, and secants, and with the audacity of 

 the young gentleman who presumed to alter the established 

 names of the latter two. In page 73, after drawing the circle, 

 &c, he thus proceeds : — " Erit AI tangens datae peripheries. 

 Sic vocare placuit quia sit perpendicularis extremae diametro. 



Geometria ipsa commodum suppeditavit nomen ; nee 



aliunde adferri commodius poterit. Nam quod quidem nu- 

 merum fcecundum rectam AI vocant, id ii videant quomodo 

 defendant: mihi non probabunt. Damus aliquid peritissimo 

 illi artifici Regiomontano homini Germano: qui primus hujus 

 vocabuli author dicitur: damus etiam aliquid receptae con- 

 suetudini. Verum id non facile damus ut verba ea in usu re- 

 tineamus quibus elegantiora, breviora, significantiora, veriora 

 habeamus." 



At page 76 the secant thus makes its appearance : — " Sic 

 peripheric AE secans est OEI, nempe radius OE continuatus 

 in terminum tangentis E cum continuatione EI. Et hoc 

 nomen huic recte accommodatum putamus. Joachimus Rhe- 

 ticus hypotenusam trianguli recti vocat respectu anguli recti 

 ad A cui subtenditur. Verum cum referatur non ad angu- 

 lum rectum, sed angulum in centro ad O, hoc est arcum AE : 

 an non potius arcus secans dicatur quam recti anguli hypo- 

 tenusa judicent alii. Maurolycus canonem Rhetici paulo mu- 

 tatum in Messanensi Menelai editione, nomine etiam mutato 

 edidit: et beneficum vocavit: tanquam recta OI seu numerus 

 hanc definiens beneficus diceretur. At recta OI non magis 

 est benefica, quam recta AI fcecunda." And again (p. 130), 

 " Sequitur canonis hujus triangulorum pars altera quae vulgo 

 canon fcecundus, nobis canon tangentium dicitur: et canon hy- 

 potenusarum Rhetico, nobis canon secantium vocatur." 



From these passages it is obvious that Finck gives the words 

 for the first time, and defends them as suggestions of his own. 

 How then does it happen that his right to them is entirely 

 unknown? Did his learned contemporaries dislike to owe 

 their terms to a youth of twenty- two years? or did the south- 

 erns wish to avoid acknowledging the young Dane ? 



