Opcscula 99 



Dillerenlialione aequationis (c) obtioebimus 



dx i,ix (\dx- Gdx 6dx l.i.dx I.IA. d x log.x 



"b" 



log-x log-x Ivg-x xlog.x 



i.1.5 d xlosi.x'^ i.S.Sd xlog.x^ 



' — ' etc. 



J X 



"^ l:iA.5.G.x ^ %i.'\.5 6.:.x 

 Ablato communi faclore clx, et ducta acr[nalionc per jt ha- 



Lcbimus. 



X Zx fi.r 6.r 6 2.3 2.3.4 /og.x 



/^~"/J^' ;—•*"/—»"■ /— -' 2.3.4 2.3. 4.j 



Z.A.S log.x A.5-6log-x 



2.3.4.5.6 J. 3.4.0.6./ ^ 



Posito x=e, et log.x= i , erit 



e — 3e^-6e — 6er= — 2e 

 2.3 2.3.4 3.4.5. 4.5.6. 



— ""^"^274 "^ 2.3.4.5 "^2.3.4.5.6 "^173117 "*" *""' 

 Dlffercnlialione aequationis (<■/) deducemns 



<f X \dx 12^/x 24 (Zx 24 J X 24</x 3.3.4tZx 

 "o "^ /tig.x" /og.x log.x log-x X logx'- 2.3.4.5 x 



2.i.i.5 d X log.x 3.4.5.6 ^x/o^* 4.5.GJdxl~x^ 

 ^ 2.i.4.5.6x ^ 2.3.4.5.6.7 x '^'T.3.4.5.6.7 x ' "^ *"'' 



Ablato communi faclore dx, et ducla aequatione in quantita- 

 tcm X, habebimus 

 X 4x 12 X 24 X 24 X 24 3.3.4 2.3.4.5/og.x 



'°S-^ /J^' '"fi-^' /og.x ~^—s— /og.x5^ 2.3.4.5"^ 2.3.4.5.6 



3.4.5.6/"^^^ 4.5.6.7/^* 

 ■^ 2.3.4.5.6.7. +2.3.4.5.6.7.8 -^^'•^- ^'^ 

 Posito x = e, el /og.x=i erit 



f_4e4-12e — 24e-f-24e=:9e 

 _ 2.3.4 ^3.4^ 3.4.5.6 4.5.6.7 



- "^ "*"2.3.4.5 "^23:47576 "*~ 2.3.4.5.6.7 "+ 2.3.4.5.O.; .6 "^ *'^- 

 Eodem calculo ex aequatione (/-) deducemus 

 _f___£_^ 20«: 60x 120x 120x 120 2.3.1.5 



o log.x log.x log.x log.x^ log.x^ log.x ^. >••».'' o. 



