A S T R N M I C A. 47 



C<^ii3tis omnilwis lateribus invenitur angulus SZL» , 

 Tum in triangulo S'ZL', e cognitis duobus late- 

 ribus et angulo Z inclusp, invenitur oppositum 

 latus S'L\ Porro in triangulis Z'ZS' , Z'ZL' , 

 cognitis ZZ' , Z'ZL', Z'ZS' , ZS' , ZL' , inveniun- 

 tur ZS' , Z'L'. Tum in triangulo L^S^L* , cognitis 

 ouinibus lateribus , invenitur angulus S'ZV , qui 

 in triangulo S"ZL" , aim utroque latere adjacente , 

 dabit oppositum S"L" , hoc est distantiam geocen- 

 tricam. In triangulis^^L ,yZL' , S^ZU , S'>Z'L'*, 

 habemns : ^ 



:os SL = cos ZS . cos ZL + sin ZS . sin ZL .cos SZL 

 :os S'V = cos ZS' . cos ZL' + sin ZS* . sin ^L' .cos S'ZL' 

 3os 5a' = cos Z'S'. cos ^'i' + sin Z'S' .sin ^'i.' .cos 5'Z'Z,' 

 Zos S"L"= cqs ^5".cos ^'i"+sin ^'^".sin Z'L".cos. S"Z'L" 

 E prima cos SZL in sccundam, e tertia autem 

 cos S'Z'L' in quartam substituitur ; erit: 



sin^5' .sin2'i.' 

 sm Zr i . sin /!> •'' 

 (cbs ^i — cos ZS . cos ^X) 

 sin Z'S" . sin ^'X" 

 Cos^^'i,"= cos^'^".cos ^I^'+ ^^s'.smZ'L' ' 



(cos S'Zr' — cos Z'S' . cos ^'Z,') 



unde, substituto valore cosinus S^L' , erit: 



r.r. smZ'S".smZ'L'* 

 CosS"L" = cos Z'S" . cos Z'Z/'+ . „,^ — . „/,-1 . 



sin Z'y . sm Z'L' 



„«. ^,. smZS'.smZL' , „.. ' ^ „_. 

 cos ^<. cos <2X' + -7-^ r— ^ 7 . (cos SL- cos Zi^.cos ZZ) 



--cos^'y.cosZ'Z']. 

 Cos 



