ASTRONOMICI &c. 9^ 



PROBLEMA. 



Ditis RcUac fixiic iii tribiis locis ABC riicccfTiuc Fis- 

 oblcriidtac nlciriidinibus liuc earuni coniplc- 

 mcntisZA, ZB, ZC, tcmporibusquc iiuer obfcr- 

 lutioncs practcrbplis , vcl angulis ad polum P, APB, 

 BPC , inucnire elcuationem poli feu ejus complc- 

 mcntum PZ, et declinationcm (UUae fcu cjus com- 

 plementum AP vel BP vcl CP. 



Soluti). Dicantur rmus altitudinis primac 

 vel cof. AZ, a\ Cofmus BZ, A et cof. CZ , c, 

 Atquc /APB, V; cjusquc cofuuis, /;; /APC , Q, 

 cjusquc cofiuus, f]. Sit aurcm/2PA~Z cjusque 

 coruius —z. Tum compendii caula fit cofi 

 ZPBzzr et cof. ZPC=c Ponatur porro cofi 

 (PZ-V-AP)=.v, ct co(:(PZ-AP)=:r. Habebitur in 

 triangulo ("phacrico ZPA, cof; AZ vel ^~ ^"'"^"^~'^~'^ 

 —LLrifrtLLt-^. Dcinde in triangulo ZBP eft 



b—- -' - ^^ — 2 -. Et fimihter in trian- 



gulo ZPC crit r— ^i^:^-^^^. Ex quibiis tribus 

 aequ.\tionibus trcs incognitas ;l-, ^ ct •; determinari 

 oportet. Acquationcs I ct II dabunt.y— "' ' ~^^ ' ~''\ 

 Sccnnda vero ct tertia dant r— ^^~~^\ Vndc 

 colligitur hacc aequatio ai^i—r){v—s)—Ki—^)0'—-0 

 zzl>ii—sXz~i')—c{i—i-)(z—r). Qiiac abit in hanc, 

 a(i-rXr—s)-i-c[i—r){z—r)—b(i-r)(z—s), atque di- 

 ui(a per i— ?• dat a(r—s)-{-c(z—7'y:^l>(z—s). Sed ex 

 conjuncflionc finuum fi^quitur cfiTe 7'—pz—?Z et 

 j=:^::-QZ. Vadc habcbitur az(p-^)-aZ(?-Q) 



N 2 -{-cz 



