Scliulerfs investigation of Kej^ler^s Problem, 



15 



e* 



Se* 



I e 



+ 2^3t'+I- + ^+^) 



'' i^+r+%-) 



2 



2 



2 



+ 



e 



3 



a'..=Ta(' + 2^ 



€ 



11 



2'«.3a' 



9L 



from ^ A^ sin 55.+ V ( I + -^^^^ }- — f- -^-^— ^ 



3 



4 "^"a*" 



7e 



e 



+171 



9 



J^i^a 



(1 + 



3e« 



4 



) 



e 



2 

 11 



2 



(1 + 



4 



-1- a* ; 



i^^i^o' 



from?-A* sm4.,-.^^ (l+ e^ + ._) +_^_^i+,a^ 



7r* 



e 



e 



11 



4 



^^3 



2 



from -A* sin 5*. + -^!— a+ — 1 



2»o.5 



11 



212 - " - 



.o'.a 



3i*.32 



3 



anj from — a« sin 6f, 



11 



6 



^^\o.o ' 



The following sines would give only products of sin ^a multi- 

 plied into powers of e higher than the 12th. Wherefore^ these 

 seven partial coefficients being collected, we shall find the whole 

 coefficient of sin ^ 





+e'C 



1 



8 



5 



1 



8 



1 



i 



0+e'G 



1 



+ 



1 1 



+ 



1 



1 



£6.3 '82*' 2«.3 8 ^23.3^2 



+ o 



\ 



1 



+ 57) 



1 



+ --L+ 1 



^+ • 



26 



4 « 29 1^ 07 



2*.3 



2 



+ eS 





+ 



1 



29.32,5 



+ 1 



2"^ 29.3 



11 ' oi 



1 



+ 



1 



313,33 ' 214.32,5 



27^ 97 



27.3 



1_ 



29 



1 



210 



3; .3 ^ 



2 



+e 



11 



1 



21 *7 



' ^> ? o 1 ' 



2i>.5 

 5 



27.3^ 2»°.o ^ 



1 



311.3 



1 



+ 



1 



1 



2T 



r 



5 



2»7.33.j3 • 20 210 > 2ia,3 2» 3.33~^ 3»«.3«.5~ 2» ^33.5» "fi'"^ 28 3 "2il~+ 



I 



2".38.5 



1 



7 



9 



2i6.33'^29 213 



+ 



s 



I 



r 



214.5 2i*.3*.5 2««».3 



+ 



1 



1 



10 ^ 012 c 2 



iio.0 2 



O'.J 



r + 



5 



1 



1 



2U. 



3 2i\3» 213.3.5 



The reduction of all the fractions, belonging to the same power of 

 g, to the least common 



n ■ 



denomination, will give the coefficient of 



8in«=±=Se 



e 

 4 



5 



+ ^ 



.3 



C 



107 



6217 



r 09 q» -I 01 3 o» 



2»3.3».5 



e 



565879 



+ ^ 



2i«.33.5« 



e 



" . 



which is the second term of 1? (A) (§ 3), the first bein 



<« 



