LONGIT. LOC. EX OBS. ECLIP. SOLIS. 343 



s^* angulus i^ — cr -{- (a) ob angulum cr variabilem, 

 3^'*' -vero difl:ant'a 3 A — P ob corrcdionem quam 

 paralhxis n poftulat , atque hinc etiam variabilis 

 erit angulus Cj), cum diftantia O A = V quam ob 

 rem differentientur hae duae aequationes 



Vfm.Ct)— j-fin.(^~a-+w) et Vcor:$=:P-j'cof.(^-(7+w) 



atque adipifcemur duas fequentes aequationes diffe- 

 rentiales 



L ^ V fm. Cf) H- V ^ $. cof. $ = ds. fm.(^-cr + m ) 



— j- ^(J cof (^— cr 4- w) 



IL ^Vcof$-V^(I)fm. Cpzz^P-^j-cofC^-or-f-u) 



— j- d^cr. fm. (^ — cr -f w) 



multiplicetur prior in fm. (^y pofterior vero in cof $ 

 et fumma harum aequationum praebebit : 



i^V^iP.cofCp+^J-fin.Ct^.fin.^-^-cr+co^-^j-.cofCp.coff^^-cr+a)) 

 — j-^cr(fm.(f).cof ( <^-(r-i a))-f-cof.Cf).fin.(<^-a--i-oj) 



quae formula reducitur ad fequentem 



</V— <^P.cofCp»-^j-.cof.(Cp-f^-cr-|-w)-jt/a-.fm.(Cl)+<^-(r+a3) 



quem valorem inueftigare nobis erat praecipue pro- 

 pofitum. 



XVI. Subftituamus hcic loco ^j- et ^cr, eos 

 valores quos fupra §. VI. alTignauimus , fcilicet 

 <^j" — ATcof. o--hjfm.cr et Jrt^cr— jcof.cr— .^fin.o-, at- 

 que formula inuenta , induet fequentem formam : 



</V— ^P. cofCt)-A'.cof(Cl) + <+a))-/.fm.(Cp + ^+a)) 



