no OposcuLA 



§. V. 

 Evolutio in seriem functionis log. ( i 4.6^ ^ 

 Cum sit 



x' x' x' x' X* 

 log. (1-{-x) = r — 2-+3-— Y + J — ^+etc. 



posilo x = ey erit 



c'y e^y e'y e'y e^y 

 /og.(H-cT) = ey_ — + — - — 4.-^- --4-etc. 



Loco e', e^y, e^i etc. ponanlur series quibus hae funclioncs 

 aequivalcnt, ct erit 



1 2y 4y2 8y3 16 y« 32 yS 



2 2 2.2 2.2.3 2.2.3.4 2.2.3.4.5 

 1 3y 9j2 27 y3 81 y« 243 y* 



•4:- a + I "+" •) J •+* '1 J J "+* 



3^ 3 ^2.3 ^ 2.3.3^2.3.3.4^2.3.3.4.5 

 1 4y 16 r'^ 64 y3 256 y< 1024^^^ 

 ""1"" T~" 27r~ 23.1"" 2.3.4.4 "2.3.4.4.5 

 i 5/ 25j3 125yS 625j« 3125_r* 

 ■^■5 '^'5 '^ %S"^ 2.3T'^ 2.3.4.5"*" 2.3.4.5.5 



etc. etc. etc. 



Atque ordinando secundum poleslates quantitatis J 

 11111 



4-(1_l4,l_l4-1— 1-t- etc. ) y 

 4,(1_2-|-3 — 44-5 — 6+. etc. ) — 



-t-(1 _4 4-9 — 16-t-25 — 36-f»«tc. )~ 



y* 



4. ( 1 _ 8 +27 — 64 -t- 125 — 216 4- etc.)2y:j 



y' 



y* 



4,(1_16+i81 —256 4-. 625 — 1296 4* etc.) 2^^^ 



