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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
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Analysis Fractio
Omnis summatio qualis
nferio
dividendos
6S
ex aquae est summabilis
re-t
1 reducit ad propime
hanc
e-1
saltem)
F dx tandem reducitur ad
X+b
dx
S.x +b
x +b
idanest sed et eodem modo sX, Odx reducitur ad proxime inferiorem
X+
o et ponendo dein b= c = d ex sed speciali tamen ratione idem consequi Bnam si addat si  summanda sit X multiplicata per C quamcunque
se
ax reducitur ad proxime inferiorem, nam si addas X
21b
ponatur x+b = XrC seu b = c, ita enim in valore ipsius (ax  haud dubie evanesqe  itaque omnis ut
reducetur res eodem modo
e
eodem modo reducetur ad
curentibus
cum
turam
IX Dax
4d
Hinc
X+b
si quaeratur
xtt
dx seu
db
Odx, res
Sed suppositis tamen ipsis fractione
3dx et et reliquis, usque ad s0dx
X+b
Hinc et si O sit ipsa 
X
. XX
+b
reduci posse ad s
X+b, Xtb
patet hanc quadra
dx
Xe +b, Xt b
et praeterea
a dx. quanquam potuissems
ad nominatoris simplicioris summationes, ut (X
etiam uti methodo articuli
C+b
Et cum hae rursus reduci possunt per artic.2. He hunc patet posse
ta b
x (Xe ax
dx
xtb, x +b
sXe dx
X +b
habeatur absolute hinc sequitur
saltem.
posse demum reducilad
X + b, X + b
Et  eodem modo pro cedetur in
ebt seu p = (d- b) n 3: c-d7 quib substitute inde fieri
dx
O
C, posito C esse
per artic. 3 reducitur ad (ax
Xtb
ax
X+b
re dx
X+
.Nam potest
XtbXb nam per quia redu
, seu ad ax quae datur absolute
X+
intervenientibus X Oax et similibus, seu intervenientibus
C-1
quas artic 5 jam reduximus ad sax
x+ b
Ergo
CXdx
e- 1
(X. dx
x+b, xtb
X+F3 reducitur ad (dx
Xtb
tunc methodo opus. Et puto supra dictam sucvessuram.  artic. 15. quanquam et res aliunde (7) Et pari jure ac methodo unusquisque nominatoris gradus per inferio ree
 sit) Xax reducetur tandem ope cognitarum
X+b
reducetur  adeoque
saltem ad  quadraturam hyper bolae seu
(dx
X+b
saltem inquam, nam interdum fieri potest, ut haec evanescat, et quaesitum
habeatur absolute, ut cum e = 0.
fiet