De motu cometanm in orbttts parabolicts, solem tn foco habentibus, 413 



Post primam observationem ponamus cometam ad perihelium pertingere spatio k diemm, et sit 

 anomalia vera cometae tempore primae observationis =Vy tempore secundae =c — (p, tempore 

 tertiae =v — «//, erit, uti vidimus, 



cp=z2NH cos* ^v-^ kN^x^ cos' 4 ^ sin -J- p -*- etc. 

 yj = 2NX cos* fc H- li-iVU* cos"^ j: vsm^v-t- etc. 

 Jam erit per (19), posito r loco ^ 



1) sin^=sin(r — c)sin5 2) tang{f — 9) = tang(r — p)cos5 



sin ^r' = sin (r — p -i- 90) sin s tang (/*' — 9) = tang (r — f -h 9?) cos 5 



sin g' = sin (r — v-i- ip) sin s tang (/*" — q) = tang (r — f -h 1//) cos s 



itemque 



3) tang g = sin (/* — g) tang 5 k) cos (r — c) = cos g cos (/* — g) 



tang ^ ' = sin (/*' — g) tang 5 cos (r — c h- ^) = cos ^r' cos [f — g) 



tang5r"= sin (/"' — g)tang5 cos (r — v-\-yf)=cosg"cos{f" — g) 



Ex aequationibus N° 3 sequitur 



8in(/'' — 5) tangg' ixnf^coiq — cos^^sing 



sin (Z' — q) tanggf sin /"cos 9 — coifsiaq 



. I . ^ tang/sin/"— tangflfsin/^' iUJfldqs 



indeque tang g = —^-^t — - — -^ — ^,- ^ 



* " ' tang g cos /^ — tang g cos f 



Idem valor pro longitudine nodi q prodire debet ex binis quibusvis aliis aequationibus ejusdem ordi- 

 :ais, siquidem observationes omni cura sunt institutae; erit ergo pariter 



. __ tang /' sin f' — tang </' sin f'^ ^ 



^^ Ung g'^ cos f — tang g^cos f" 



(nventa autem longitudine nodi ascendentis g, simul innotescit inclinatio orbitae cometae ad eclipti- 

 cam s ex aequatione tang s = . ^°^ ♦ Quia porro cp et ifj sunt anguli perquam exigui, erit 

 sin (r — v-*~fp) = sin (r — p) -i- g) cos (r — f) et sin (r — c-f-^) = sin (r — 9) -f- V' ^os (r — v) 



unde ex ordine aequationum primo habebitur .fctoi<u«l'->#. 



j 



^=l-f-«)C0t(r— p) et '^=i-^yjcot{r-v) 



. tiag'^ — sing V» X-t-2N^^ co»^ ^ v»in-YV 



unde - — ; = — = — —, — ; — ^i— 



«injr — tiag q> x-»-2iVx» cos» -5-f »In -jf i» 



Praeterea vcro cum sit sin (r — v) = ^ » dabitur quoque cot (r — c), unde erit 

 '*°g'~"°^ = cp =2iV;^cos*f ('-i-4iV*x'cos'icsin4-P 



sin g col (r — *') 



et .""^^'-"'"^ =^ =2iVAcos*l p-4-^iV*A»cos^f csin-i-c. 



iin(jfcot(r — v\ 



