372 .oV,in.msiii EULERl OPERA POSTHUMA. va Astronomic 



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%it' ex his observatlonibus solis locus nodi exacte dienniri nequeat. Hancobrem in subsidium vocai 

 debent aliae observatipnes, veluti si in eclipsi totali, praeter initium et finem ejus, quoque immersi 

 fit emersio observetur. Si enim tempus ab initio eclipsis ad firiem elapsum sit = A, horarum, • 

 setnidiameter apparens umbrae = ce , ac semidiameter lunae apparens == /5, erit /*=«-!-/?., J^ 

 immersione autem et emersidne erit' arcus SL ===sl=^ a — /?, qui ponatur == F; tepqpus autem a^ 

 iininersione ad emersionerii^ elapsum ' sit = /f horarum. Quodsi ergo ponatur -{ H{n-^k)=:Af 



^ /1 (»1 -♦-«) = ^, manente ^ ; ^ — - — — = c. repenetur simm modo * 



^JiiaJoq hc.bmtn^' 9hiu ^finuf fninpl.mi nfmfr.i 'y fjr^i cos^ ~ cog» -| - f cos {a ~ j? -^- <?> )» q.joI s^\fi^y-, 

 8j)dilnoifiqqfi ?ii»fi«i«il> / . f . ..imn: h i> U I, A^ <;imj; u^Pf alfi. .n.;»-ll,m anoii^^-no» mol.i .- 

 -qi^j§ i9. !Si jam aequatio prius inventa iu^ia 9opT)lw 1i« ,iofn'»b oj^tfyt ziIm 9k/uiI Jo on! 



^"' ^^ '' *'^~^rl/c{!2"' '»J"»'pl ^{' .•eo.ir-cos'i|><J6s(d-^6-*-c) ofiidrftn fn.r . ^' 



cos (aa? — a — o — c) =: j — ^-^-^ 



per istam dividatur, reperietur 



'■■■''■" ^' "■■■':■'■'— ■■' • '"'i t^''-*-' ■''^'■- ^i<i iJii; ) ,^cJii.-()3 



^j.iw:...' r . f ' ,co8 {2aj— rOj— 6 — c) cos ^ — cos^ "y p co» {a — ft -♦t e) 



^' coi(2;r-^-5-c)""cosF-cos*iVcosU^i^-^V^^^ ^"^**^ SlipiflUie ,r.>;n 



fn quam Talof sm*-f ^ noii amplius ingr^ditur. Etsi autem in ea etiaDDmunc terminns C(is^^() inctel^ 

 tamen levis incertitudo in angulo q, cum ipse angulus sit valde parv^s, valoreooi termini cos* -^ q 

 non sensibiliter afficit, atque qrrores hinc oriundi in numeratore et denominatore fere se mutuo 

 compensabunt. Aequatio autem inventa resolvetur in sequentem 



co8 (a-H 6-f-c)-i- sin (a-*-ft-4-c) lang 2« C08 Z' — cos^ -^- p cos(o — b-t-c) 



co8(J-i-B-»-c)-«-8in(.4-*-.B-i-c)tang2» cosF — cos * -|- f cos (.i — B-*-e) » |'i ;- 



ex qua valor tang 2a7, ac proinde ipse arcus Q^, quo nodus a loco centri umbrae mcdio eclipsis 

 momento distat, assignari poterit. Sit enim brevitatis gralia 



coi» f — cos ' -2" P cos (a — 6 -j- c) , 



-o-ga^ ,8iIidBlon mnbomhfi ii) «««^eosF- cos 2 i-fcos(^- i?-h«) ~., mcirioup .oooiJnupqr. moirffi oai 



o — dsin (4-1-^-1- c)-i-sin(o -4-6 -H«).if6iip9B Tliiuiimioq a 



§ 20. Invento loco nodi seu distantia Q<? = cc, existente <? loco centri umbrae momento medio 

 eclipsis, inde porro inclinatio orbitae lunae ad eclipticam^ seii angulus Q=q, accuratius definirl 

 poterit. Cum enim iste angulus q jam tam prope sit cogniJtus, nt terminus cos*-^ q minime a veri- 

 tate discrepet, erit :(•«»('*-*- #' 



. « 1 cos f — cos^ ■^ Q cos (a -'b-t-e) cos f— cos (x — a — c) cos (x — b) 

 Sm'-f(>=:i ■ ,- ^ ^ i^ r -, SeU C0SO = - ■' ■<. , ■ —7^-, rr 



* ^ ■: ._. cos (2x — o — 6 — c) /» 8in (» — o — c)siii(x — b) 



,,\lU\ii(r'.'ywifv.i wd<T tR r, ^ «uf;l,-;>.> m u ofnan. sin/^"*""~^"^'\sin/^~^^'^ 



.. .91 cos(a — &-i-c}-^cos^ dos(o— 6-f-c) — cosf \ 2 / \ 2 / 



sive etiam sm^^Qs=——^ -, ^ = — ^ ~— — — — :=^ —, r^— ; — n — * 



* ^ ,28in(fl! — d-=-c)sin(^— 6) co»(a — 6-f-c)— co»(2a?— o — b—e) »m{x — o — c) sin (X: — o) ,, , 



