25 2 DE TRANSLATIONE 



Ell vcro 



Tab. III. cof. A Z B =r - cot. A Z. cot. B Z , 



■^'o- ^" ex priiicipiis Sphaericoruin , hinc 



fin. A Z. fiii. B Z cof. A Z B n - cof. A Z cof. B Z. 

 Porro habetur quoque ^in. A Z B " ^^_-'^°^'.J— ^ , id 

 quod fcquenrem in modum demonftratur. Produca- 

 tur arcus B Z, vsque dum circulo maximo AC in 

 R occurrat , eritque 

 fm.AZ.fia.AZB=fin.AR = cor.CRzi:^?^--^^=z;f-" 



Hinc itaque colligitur 



fin. A Z. fin. B Z. fin. A Z B = cof. C Z. 

 SubQitutis vero his valoribus, prodit : 

 cof. A ^-cof. A ZcofBZd - col.B Z^)-l cof.CZ fin BZ6. 

 Simiii modo, ob 



cof.Ba = cor.BZcof.«Z-f fin.BZnn.flZcof.BZ^, 

 quum fit <2Z— AZ ct BZ(7 :z:BZ A-[-AZ(2, col- 

 ligitur 



cofBfl:! cof.cz cof.AZ-ffin.EZrin.AZ(cofAZBcofAZ« 



-fin.AZB.fin.AZrt), 



quae ob 



fin.BZfin.AZcof.AZB — -cof AZcofBZ ct 

 fin. B Z fin. A Z fin. A Z B = cof C Z, 

 reducitur ad hanc 



cof B a-zoi. A Z cof. B Z( I - cof. A Za) - cof.CZ fin. A iLa, 

 Simili modo has confcqucmur expreffiones : 

 cof.Af~cof AZcof:CZ(i-cof;CZO-col.BZ.fin.CZc 

 cof. Ca — cof. A Z. cof C Zf i - cof. CZt) f cof BZ. fi n . C Tj: 

 cof.Bt- = cofBZcof.CZ(i-cofBZ^)-Hcof AZ fm.BZ^ 

 coi:C^z::cof.BZcofCZ^i-cof.BZ^)-cofAZfin.BZ^, 



vbi 



