===== (80) ===== 



cuius ergo feriet fumrr.am indsgari oporfet, id quod fequenti 



modo fumus expedituri. 



j 



§. 20. Primo fcilicet , vt fadtores poflremi tollantur, 

 per integrationem formetur ifta feries : 



fs d x ~ 3 x — 7 -i± x" -+- LlLl x * — ? ' 9 '"- 9 x 7 -+ 7 ' 9 - TT - 13 Ir x 9 etc. 



J 2 2. 4 2. 4. 6 2. 4. 6. 8 



Vt nunc hinc denuo vltimos fa&ores tollamus , multiplicemus 

 per x d x et integrando reperiemus 



. fxdxfsdx — x 3 -~lx 5 -h~x 7 --~-^±-x 9 -\- T -^^~x u etc. 



J J 2.4 £.4.6 2. 4. 6. 8 



Cum igitur fit 



( x _l. **£"'? — 1 ^J^-4-__y — ^^ilx^-f- 7 -^-— x % etc. 



v ' 2. 4- 2. 4. o £. ,. 6. g 



manifeftum eft fore 



/jf d xfs d x — .v 3 ( 1 -f- .v x) 5 

 cuius differentiale per x d x diuifum dabit 



"5 



fsdxz=zsx(i-\-xx) 5 — 7 jc 3 (1 ~h.vx) 5 

 haecque formula denuo difFerentiata praebet 



jzz:3 ( i+.vx) 2 — 4.2.vi(i+ijt) 2 -+-63 jc 4 (i -f-.vjr) 



quae expreffio porro reducitur ad hanc: 



3 — 36 jt x -+- 24 x 4 

 j — — — ^ 



( r -f- .v x ) 2 



Scribendo igitnr — loco x x erit 



<2 7 (3 tf 4 36 tf tf f <? -f- ?4 T 4 ) 



( a a -\~ c cy 

 qnac formuia, ducla in factorem communem ■* 3 : 5 - ■ --^-, prafc- 



1 ' e*. 4*. o- a> - * 



bet 



