sin UL : sin URL = sin UR : i 

 sed UL = I. ZU= i (.?',*), UR = + <p, URL = 0;his 



ergo substitutis , proportio praecedens fit : 



cos (y, z) = sinfl cos<J) (19). 



Quacramus tandem valores cos(z', a;), cos(z'jjy), cos(z',z) (Fig. 3.). 

 Si describantur arcus 'magnorum circidorum VNQ in piano Z'AX , TRK 

 in piano X'AY' et VSK in Z'AY ; duo trigona sphjerica NRQ et KSR 

 erunt rectangula. Nam i arcus TRK situs in piano ( x' t y' ) , normaliter 

 occurrit arcui VNQ descripto in piano (z f , x), ope radii AV piano 



(x',y r ) verticalis: itaque (z' f x) = +NQ, undeNQ = (*'.,*) , 



V 'J I \ i a 'a 



QR = \|/ , NRQ = , et prodit proporlio 



sin NQ : sin QR = sin NRQ : i 

 ergd 



cos(z', or) = sin\f/ sinfl (ao) 



a In trigono KRS , arcus TRK descriptus in piano ( x' /y' ) , occurrit nor- 

 maliter in K, infra planum xy, arcui SK descripto in piano (z'^) cum 



radio AV piano x'y' verticalij ergo (z',jp) = VK SK = SK, 



unde SK = - - (z',y} ; SR = ^- ^, KRS = NRQ = d: ita ut 



proportio 



sin KS : sin SR = KRS : i , 

 del 



cos(z', i y) = cosxf/ sinfl (21) 



tandem accedit relatio 



cos ( z'f z ) = cosfl (22) 



ubi angulus (z',z) inclinationem planorum x'y' et xy jam per 6 nota- 

 tam , metitur. 



Substitutis valoribus (i3), (i4) (ai)in formulis (i), (a), (3), 



prodeunt sequentes 



x =: x' ( cosfl sinv^/ sincp -|- cos\p costy ) 

 -\-y' (cosfl simp coscp cos^ sinCp) 

 z' sinfl sin\L 



