Astronomia mechamca. 247 



daobus casibus evenire debeat, quibus angulus quidem s fit vel vel 180°, denominator faclorem 

 habebit sin s. Statuamus ergo v =■ - — , et denominator erit 



° i-*-qcoss 



2 2m-»-3ncos2$) (C — 3n5) 



D 



2p^ PP 



^qcoss 3?oos«(2m-4- Sncos^f) 2? cos«(C — 3n5) v^ ^ *o» vJiiV ^ 

 P 2p3 pp .) ^ ,,v, 



S^^ycos^s^^mn-Sncos^^?) gg' cos^^^^C — 3n5) 

 2p^ pp 



g^ oos'4(2m-H3«cos2^) ■'><»n« nci 



2p3 



Fiat nunc j^ , ^ , 2m-i-3ncos2y (C-3nS) ^ 3gg(2m-4- 3ncos2y) gg(C-3n5) __^ 



P 2p3 pp 2p8 pp » 



. 3(2m-f-3ncos2y) 2(C — 3nS) g? (2m-f- 3ncos 2?)) ^ 



2pp p "ipp ' 



eritque formula irrationalis in denominatore 



q sin s -t) ( p q c 3 (2m-t- 3ncos29)) j cosi(2m-i-3ncos 295)\ 

 P \ 2p 2iJ / 



, df qd(p%ms-y^ (3-«- j coss) (2m-i- 3n cos 29))\ 



w ^ '^ \ 2p(C — 3nS) y 



Jam ex illis aequationibus quantitates p et g definiantur, quae si esset w = et /i = 0, prodrrent: 

 p = C et qq = i -i- CD^ atque hi erunt quasi valores medii ipsarum /) et q, qui statuantur /* et ft, 

 ut sit C = fet D = — — . Deinde cum m et n sint quantitates valde parvae, in terminis per m 

 et n affectis scribere licebit p=zf et q = k, sicque habebimus 



i^ 1_ (3 -t- kk) (2 m -t- 3 n C082 y) 3nS qq . kk (1 -t-3A:fc) (2m-i-3n cos 2?^) 3nS(l -«- /tft) 



P~r"*" 2/^» '^T fp~J'* W* *" f^ 



unde fit 



/. (3-H*A)(2m-H3ncos29)) o o * ?i (i -ft*) (2m-»- 3ncos 2?)) 3n(l-ftfc)5 

 />=-r j-^ ZnS et qq = kh-\-^ ^-^—^ tl^-±- 



Quoniam nunc habemus valores litterarum p et g, ob f = — erit 



* ' Ih-^^cos» 



o /'df (l-i-oco8«)sin2«) , d\> dp dqcoss qdssins qdpcoas 



S= — — et —=.— i i-i 1-— — , seu 



^ p ^^ JPP P p PP 



dv dp (pdq—qdp)coss qdssins 



vv pp ^^ p ' ^ 



At est superioribus formulis difierentiandis 



dp 3 n (3 -♦- kk) drp sin 2 y 3 n (1 -♦- j cos «) d r/j sin 2 9) 3n (1 — 2il:co8»-t-M) dysin^? 



pp— 275 ffi, ' *^" — 2?^ *-'' 



2?(p<l7 — gdp) — 3n(l-4-3*A)d9>8in29) 3n(l -f-**)^^? (1 -4-4 008 ») sln 2 ?> 



-^ = 1 -, , , 



