(10) 



in qua a, b, c sunt latera et A angulus oppositus lateri 'a , ' relata ad 

 trigonum TRQ , abit in sequentem 



cos(x' } tf) = cosvj/ cos$ -j- sinvf/ sin<J> cosfl (14) 



observando 



a=TQ = (x',x), &=TR=cp, c = RQ = ^, A = TRQ = 0. 

 Eadem formula ad trigonum STR translata, dat 



cos ( x'j y ) = sinxj/ cos< cos\J/ sincp cos0 (i5) 



annotando 



K), 6=SR= 4/,c = TR = cJ>A = TRS = T ~ 0. 



In triangulo PRT rectangulo in P, ex proportionnalitate sinuum an- 

 gulorum ad sinus laterum oppositorum concludimus 

 sin TRP : sin TPR = sin TP : sin TR 



sed TRP = 0, TPR = - , TR = d>, TP = (x' } z} 



2 ' 2 V ' ' 



ergo 



cos (x'f .z) = sincp sin0 (16) 



pergamus ad investigationem valorum cos^', a:), cos^',^), cos(j-'jz): 

 sit AY' (Fig. 2.) normalis ad axem AX': in duobus trigonis spha3ricis 



URQ, URS, habemus UQ = (y 1 , x} , UR = UT + TR = - + <J> , 



= fl, US = (y',y}> RS =QS QR = - 4/, URS 



f 



2 

 If 

 2 



Porro referendo (M) ad trigonum URS , et ponendo a =. (y' , x ) , b = 

 -j-<|),c = 4 / 5A.= 0? hanc reperimus 



cos(jx'j^) = sincp cos\|/ + cos<p sin\{/ cosfl (17) 



et pro trigono URS, ponendo a = (?',$}, b = ^ c = ty -\- -- ? 



A = w 9 , habemus 



cos^', y) = siin|/ sincp cosv(/ coscp cosfl . . . . (18). 



In piano ZAY' ducatur arcus magni circuli ZUL = > qui producius 

 piano xy in L occurrit: e trigono spha3rico rectangulo URL eruitur : 



