ifftmon 



Aslronomia mechanica. 209 



erit colliffendis his terminis: 



-H (1 -\-\nn-^ |-7i* H-etc.) 



(/i -♦- f/l^ -I- ff/i'' H- etc.) cos 6 



( ^/i/i-f- |-/i* -I- etc.) cos 2 (J 

 c?5 = (1 — nnjido 



(^ n^ -f- j^ /i^ -I- etc.) cos 3 a 



(^/i*-f-etc.) cos k0 



etc. 



Est vero 1 -+--^/i/i-i-^ /i''-i-etc. = (1 — /i/i)~2 



et /i-i- |-/i^H- J|/i^ -+-etc. =— ((1 — nn)~T — i\ 



ita ut pro primis duobus terminis habeatur 



ds = ao (i -h- -{{ — y(l — nn)) cosou ideoque s = 6 -t — (1 — yfl-— /i/i)) sin ff. 



Quo autem hanc seriem ulterius continuare queamus, ponamus 



ds = d0 (i -i-A cos 6 -Y-B cos 2 <? -i- C cos 3 <? -i- D cos k6 -\- E cos 5 ^ -+- etc.) 



et cum sit - — -^ cos (7 = y[\ — nn) , ob cos ^ cos ^^t? = -|- cos (^' — 1) 6 -^- ^ cos {v -^ i) 6 fiet 



1 -4- ^ cos <? -I- 5 cos 2 (? -»- C cos 3 <7 -f- D cos ko -i- E cos 5 <? -i- etc. ^ 



— \nA — n — \nA — \nB — ^nC — \nD )> = y(l nn) 



^inB —inC — i/iD —\nE -^inF \ 



unde coefficientes sequenti modo determinantur 



^ = i(,_y(,_^)) seu ^ = 2('-^<^""> 



B=i(^_„) seu i? = 2( '-^'„'-""' y: 



C = i(2B-«^) seu C=2( *-^<;^-""y , 



D = i(2C_nB) seu D = 2( '-'''^ -""> )'> 



E=i(2/)-nC) seu E=2( '-^<;-""y , 



f = l(2E-„D) seu F^^^l^^fclL»)',. 



etc. 



Enlerl Op. portbnma T. II. 27 



uu »-r^n.\ 



