I 



i\0 



.mVv^jt'»^^^. 00- L. EULERl OPERA POSTHUMA. jiro-^ \^om -^iA Astronomia 



1»''^; t^ng -\ {(^f^fp)-^ ^tang^-^{v -^gpy^ V 



uir tp^ddV f^d^V 



dv 



2dw2 



-I- 



Uv^ 



4-etc. = /V(ft-t- x). 



Cum igitur sit V—lSk, erit 



fdV qxpddV tp^d^V 



AQd iiiLiiliili.[ "u; 



.^>£iijCo^ 



ii-i*» ^ui.vSiiv^ii-j 





*, . dF i ' 'tang2 -5-1' 



At est — ' = "Trr--t?- T~ ^ ~'~TT~ 



df 2 cos^ -5- 1* 2 cos* -o f 'S cos* -o- «^ 



■.>: 4:.i 



\oi -.,.r.. 



ddV 



d^V 

 df3 



1 

 sin "2" i' 



COS* -2" f 

 1 



1 



2 co»* -9-v 2 co»6 -5- w 2 co»6 -5- V» 



lJ! = ^ i_j mclli Tjq aof. 



1 ^^ 1 1 



Ex his ergo flet 



etc. 



iV;^ = 



qy^ sin-j-t' 



5?»' "^: ^r^zvim'. <P^ 



2 cos* -»- i» 2 cos^ -s- 1' 12 cos' -r- " 3 cos* -|- 



etc. 



Ponamus jam esse g) z=: aNft-^ /3 N^x^ -t- yN^;i:^ -t- elc, atque facta substitutione habebimus: 



N>C = 



i ^^ 1 1 ^^ 



2 co8* -jj- f 2 cos* -j V 2 cos* -^" ** 



«2 iV^ x* sin -^ V a^N^ x^ sin -^ v 



etc. 



2 cos^ 4" " 



etc. 



:v-^)<ii« 



i^iiL- 



^a^N^x^ 

 H j— 



. . 12 co«« -j ,i» 

 iiJqHOO ff :'iit.i(| 



a' iV3 X» 



3 co«* 4 f 



His ad aequalitalem reductis erit 

 a = 2 cos^ -o- c 



/? = 



V cos'^ 4" ^ sin -5- V 



r = 



etc. 



— 2 aj3 sin -j- 1» 



1 



cos -j- y 



^" j *~ ^ ' seu y = -f cos^" -^^0 — 8 cos* f v) 



6 cos* -o- f 



Ex his igitur reperitur 



(^ = 2Ni< cos* 4. f» — !i.iV' ;^* cos'' 4-c sin 4 c h- -f iV^;^^ cos*<*-|- c(7 — 8 cos* -|- v) 



quae expressio, nisi differentia temporis x sit admodum magna, per approximationem satis proj 

 praebet valorem ipsius 9?. Primum enim si cometa a perihelio vehementer distet, angulus -f v m 

 inultum ab angulo recto differret, ideoque ejus cosinus fractio erit perquam exigua. Hinc terminJ 

 secundus multo minor erit primo, ac tertius secundo; ita ut plerumque primus terminus sufGccJ 

 possit ad 90 exprimendum, quo invento erit angulus quaesitus =v-i-cp, Q. £. I. 



