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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 20r, page id 00068124:0039
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Hinc patit talia omnia seduli ad quadratunam Hyper
bilae et logarithinos, si absolute haberi nequeant nam
dx
ese logarithums ipsius bc Xfb, et sicotrte
X+b
Cdx
et similiter
est lugarithmus ipsius. X+c.
xtc
pergamus jam ad PX dx
Ccompendii causa
, quae fam utemurque
Apotius quam articuli 1.,  X+b, X+C, X1d
methodo articuli 4 (proque hac summa scribemus (X x ponendo
be x1b, xtC cum ergoS
= m
X +
V xta
reducatur ad (Odx
 et ad
rie dx reduci ad
S Xtb, XtC, Xtd
Xtb, XtC, Xtd
jam est reducta  Per artic. 10. prd ad. (ax
Ergo
Xdx
 reduximus ad ax
X+b, XAC, X+d
12) Sed cum pari jure possit
ad
dx
X +
O ex et similibus per artic. 3. hinc fiet
e-1
una cum d
patet
Oax
ax
et ad -
xtC
Xtb
xib, XtC, Xtd
edx
e
dx
x1b, XtC, Xtd
SXib, XtC
et ad
et ad (dx
X+b, XtC, X +d
quae
sax
XtC
, et
xtb
sax
XtC
reduci ads
et (ax vel aliter combinando
habebitur ipsiue
xtd C
hinc duos valores aequando inter se
(Xdo
Oxib, XICXId
aequando inter se ad secundum modum articuliusro habebitur
Cax
Cdx
 per
Xtb
dx, ex
X+d
fdx.
X+C
13 et quidem ita ut b c, d observent legem justitiae inter se.
X+b, XtC, Xtd
valar ipsius
13) Hinc tandem et (X dx
reducta erit (per artic. I1 junct
X+b, X+C, X+d
artic. 12 ad imitationem articuli 10). ad
(ax Cdx (dx
Xtb 1 C X+d
14) Unde tandem methodus habetur quamcunque formulem
hujusmodi, cujus numerator est potentia ipsius X, sed nominator est
productus ex simplicibus, ut X+b, XtC, X+d etc. In se invicem ductis
posse haberi saltem per Quad raturam Hyperborae seu Logarithmt
habem
et adedque
Vix med elle ex
ax
seu
re. dx
X+b, XtC, Xtd etC
ete adeque ad quadratur
adeoque posse haberi saltem per quadraturam Hyperbolae seu Loga
ib,xtC  Xtd
reduci ad
rithnos. e nam (ax est ua iperis it sen grohmu e
pax est logar. etC et ita porro
Logarithmus ipsius Xb Xtb et
aauentur inter sesut jam dicstur eo