-^i ) 34 ( r«^<« 



coi. D a z — yin~5^» 

 codem modo ex triangulo a z c erit 



Cof. ftf S— ^T^, 



"vnde quia angulus bac efl: redus, fi quadrata addantur 

 prodit 



,, _ cof. /? a 2 -1- col. c a z — I — -^ — juf^ > 



ideoque 



fin. az^ =: cof. ^ z' 4- cof. f 2' ^ i — cof. <2 a*, 



vnde manifcflo fit 



cof. a z' -i- coC. b z^ -i- coC, c z^ — j . Q. E. D. 



Theorerna II. 



•j-glj jj^ §. 23. Propofuo triangulo fphaerko abc, cuius 



Fig. a. ow«/a /^z/fr^? fmt quadiantes, fi intra lel extra id capiotur 

 punCium quodcunque z , ex eoque in finguJa Jaiera ducantur 

 arcus perpen.iiculares z p , z q , z r , Jemper erit 

 fin. zp' + fin. 2; ^' -i- fin. 2 r' :=: I, 



Demonflratio. 



Euidens efl haec perpcndicula oriri, fi praecedentes 

 arcus flz, ^z, cz continuentur, vnde quia arcus ap., bqj 

 c r funt quadrantes erlf 



fin. z p' — cof. s fl' , 

 fin. z q" ~ cor. z b^ ct 

 fin. zr'' — cof. 2 6-*; 

 quare cum modo inuenerimus 



cof. z fl' H- cof. zb' ->r cof. « f ' == I , erit vtiquc 

 fin. 2 p' -i- fin. z q^ -\- fin. z r* rr i. Q- E. D. 



Theo- 



