— 4-56 — 



tf = (x - xf 4- {y — yf — x' x' + y / -+- ^ >*~'f— 2?' 

 zz: i4 2 -f- v 1 — iuv cos (| — | 7 ) : 



unde posito angulo f — | 7 ==: (J) fit 



4i — (w 2 -j- v 2 — 2U z* cos (p) ~*. 



Quum v ratione distantiae u admodum exigua sit > quantitas — 



irrationahs ln senem juxta potestates quoti - ~ r progredientera 

 resoluta valde converget. Fit nempe 



■±zz±[L + 3rcos(p — lr 2 -h 3 -^ r 2 cos 2 (p-~ 5 r 3 cos(p-h 5 -^ 7 r 3 cos 3 (p 



r 4 cos 4 (J) -j- cet.]. 



3 . 5 



3.5.7 



4- i-i-V — — — r* cos 2 $> -+- 



5.7.9 



Quare quum terrnini periodici in aequationem saecularem non 



V 2 * 



ingrediantur, pro quantitate ^s termini duntaxat constantes hujus 



z 2 



seriei sunt asservandi, pro quantitate vero -5 nonnisi termini in 

 cos (f) ducti , ob z 2 zz u v cos (£>. Habemus itaque 



§. 43. Hinc obtinemus 



j! t. (t __L ^ 3 K2 I 3 ' 3 



w s u 3 V. ■ L 2.2- ~T~ 



5 . 5 



2*4-4 



r*), 



3-u 2 

 2u* 



3 . 5 



(1 -+■ 3 —V), et ^ - o : unde fit ($. 42.) 



R-=^(i + fr 2 ), 



neglectis nempe potestatibus quantitatis r secunda altioribusc 

 Positis jam anomalia media lunae ~ /«, solis rz*: //, per naturam 

 ellipsis est 



v z= a (i -f- |/l 2 -f-A cos -x -f- cet.), ejt 



M 



1 ~|- I* 2 -f- k cos p/-{- cet. 



