of the earliest Trigonometrical Canon. 523 



The degrees and the sines, &c. are in black ink, the minutes 

 and the differences are in red ink. The tables extend across 

 the open book, the ^^, ^^, and ^™*,, being on the left; 

 the eSent' Tcanf' ^"^ -'-^^S on the right. Thus at 30° 0', 

 we read along the double page, as follows, all in one line, 

 differences coming before the semicolon which is here substi- 

 tuted for the double line in the work. 



30 5000000 25171; 8660254 14-581; 



11547005 194-74; 5773503 38851; 



20000000 100180; 17320508 115774; 60. 



The words sine, tangent, &c., are not used. The running 

 title is, " Canon doctrinae triangulorum in quo triquetri cum 

 angulo recto in planitie partium 10000000 ponitur." This 

 running title is not a complete sentence, the nominative of the 

 last verb being wanted : it is completed in three different ways 

 in the three great compartments of the table; the three nomi- 

 natives are " Subtendens angulum rectum," — " Majus latus 

 includentium angulum rectum," — " Minus latus includentium 

 angulum rectum." Under the first heading come four co- 

 lumns, the perpe7idiculum and its differentia^ and the basis and 

 its differentia. Under the second come the hypotenusa and 

 perpendiculum ', under the third the hypotenusa and basis: all 

 with differences. The words -peypendiculum and basis are of 

 course interchanged in the running titles at the bottom of the 

 page, where also no other part of the running title is repeated. 

 This system of headings is faithfully preserved in the Opus 

 Palatinum. 



Modern teachers of trigonometry have pretty generally 

 abandoned the system of independent lines, which used to be 

 called sines, tangents, &c. ; and have substituted, for the mean- 

 ing of these words, the ratios of the sides of right-angled 

 triangles. It appears that they have antiquity in their favour; 

 indeed so completely has the idea of representing the ratios of 

 the sides of triangles taken possession of the mind of Rheticus, 

 that he abandons the use of the word sine. He dwells on the 

 importance of the right-angled triangle, without any reference 

 to the circle: his maxim, expressed in the dialogue, is Tri- 

 qiietriim in planicie cum angido recto, est magister Matheseos, 

 It would also seem as if his choice of the semi-quadrantal ar- 

 rangement with double descriptions was dictated merely by 

 the convenience of heading one division with majiis latus, and 

 the other with minus latus. This is worth noting: most per- 

 sons suppose that this disposition must have arisen from the 

 circumstance of the sines and cosines of the latter half of the 

 quadrant being only repetitions of the cosines and sines of the 



