APPENDIX I. 



REMARKS ON THE PRECEDING TREATISE, 

 BY BOLYAI FARKAS. 



[From Vol. II of Tentamen, pp. 380-383.] 



Finally it may be permitted to add something 

 appertaining- to the author of the Appendix in 

 the first volume, who, however, may pardon me 

 if something I have not touched with his acute- 

 ness. 



The thing consists briefly in this: the form 

 ulas of spherical trigonometry (demonstrated 

 in the said Appendix independently of Euclid s 

 Axiom XI) coincide with the formulas of plane 

 trigonometry, if (in a way provisionally speak 

 ing) the sides of a spherical triangle are ac 

 cepted as reals, but of a rectilineal triangle 

 as imaginaries; so that, as to trigonometric 

 formulas, the plane may be considered as an 

 imaginary sphere, if for real, that is accepted 

 in which sin rt. /- \. 



Doubtless, of the Euclidean axiom has been 

 said in volume first enough and to spare: for 



