PROBLEMATIS ANALYTICI. 157 



(Jl:a E, F vbicunque in fnperficie Sphaerica afluman- 

 tur, quae tam inter fe, quam cum pundis A, B, D 

 iungantur arcubus circulorum maximorum 



EF, AE, BE, DE, AF, BF, DF, erit 



cofEF-cofAEcofAF-f-cofBEcofBF+cofDEcor.DF. 



Demonftratio. 



Producantur arcus B E, B F vsque dum cir- 

 culo inaximo A D occurrant in M et N , eritque 

 ex elementis Trigonometriae Sphaericae : 



cof EF — cof-AEcof.AFH-fm.AEfin.AFcofEAF, 

 quum autem fit 



cofEAFzi:cof.EADcofFAD+fin.EADfin.FAD 



habcbitur 



cofEFzzcofAEGof.AF+fin.AEfin.AFcofEADcof.FAD 



4-fin.AEfin.AFfin.EADfin.FAD. 



Atqui eft fin. AElin.E A Dzrfin.EMzrcor.BE 

 fin.AFfin.FAD — fin.FN — cofBF, 



tum vero fin. AEcof. E AD — cof ED 

 fin.AEcof.FAD-cofFD, 



his igitur valoribus in: expreflione pro cof E F fub- . 

 flitutis , fiet: 



Gof £ F^cof A Ecof A F+ cof BE cof BF+cof DE cof DF, 



Coroll. I. 



Hinc fecile deducitur efle : 



2CofFEzifin.AE{in.AFfin.EAF+fin.BEfin.BFfin.EBF 



+ fin.DE(in.DFfin,EDF. 

 V 3.. Coroli 



