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# Piece: https://leibnizlegible.com/api/records/60544/text
# Catalogue record: 60544 — [Aufz. zur Integralrechnung]
# Incipit: (∫(xx+a²)dx.∫(xx-aa)dx) = ∫,xx+aa,dx.∫√(xx-aa)dx - [...]
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=60544&katnr=57442
# Work: https://leibnizlegible.com/work/00068196
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folios: Bl. 161 (from the shelfmark LH 35, 13, 1 Bl. 161): 2 pages, canvases 319–320, page ids 00068196:0319 to 00068196:0320
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=319
# Lines: 187 recognised on 2 of 2 pages, mean confidence 0.65
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 161r — 00068196:0319
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000319.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 101 lines, status machine
a
e
AX + ut
= +
e
x
XX + anuX. F(XX-aa) ax)-r Sxx taa, dx six - an dx-
NXdx s X + ab, x) = SXxxax sx 1ab si dx constans
a
sit XX = aZ fet Adx = L act Z et fiet 4(adZ d Z 5 (a 1 b)
4
et quia dx constans Ergu A dqe adz: 2 tize fiet  dz. saq constans. Ergo
c-1 L
405
fiet = (, ap aque d2 s7 + a b) M Niut itaque hunt novi etsi ax
e
4 dLa
constras pountur
X( (X +bx)dq  sax f 5, de Sax 1( bX) + s SXda Y(X X +b)
2
EF X X siXlX S + bXX + 9) Xsi de ((X bXX +C) = (dx  abxxtc) + (dx sax H.... )
c
paertm (de Sa + a) fint a b
 = y Xt =- logue y X = Y logy ex =  d logy X loyy
 3.4)
fit (. lo. (lugy + lg Jligys, olloy logy
rg.
2
1
P-x
Et 9 = 2 (dx logx. X. B  = 2 Sdx logX. bloy X
lovoy
sin exD = logz seu 
= L
log.
Ployx
od an ergo hoc E fdx logX b
g
 X
We =logZ
1n - Z
e
de = dx 2P dv = dZ et dz. = 2nb do
Ergo 7 = 2 de ps
0g
vo-
V = logX. quaetitur cujus leg. sit BV sit b
fie VV = logZ
V
ve
e
Ve loyze iitaque si V sit logX Ert YY
s
es 
fiet
e
lg X GlogX 1 s X= co
p
2.3 - (63).
seu Z- XE
vo
9X q
e
 bes - (6)5
e q. O = X. Pu L=S
sit ve log2
v.H
b sit b- Zad- b
quadilosque
en
en
3. 4
V = ligX seu X = b, quaeritur quis
itans sit sellogx
sit numerus Z, cujus logarithmus sit V. seu setlogx. Ique
pono esse
Erit g =  - flogr
Iu. v2 - g.
itaque  Numeus cujus logarithmus est potentia e. loganthmi ab X)
erit  itaque Numerus cujus loganthmus est quadratum
0g. X) e-
cogx. Itaque ut hactenus habuimus
Loganthim ab X., est X
qodessumens quod faciat Logarithmorum additio, subtracta, multiplicatio
a
divisiou habemus nunc etiam quos nunceros faciant loganthmorum
potentiae. Cm Numeroum ellevatione, divisione, multiplicatione divisione
habemus quid fial in Logaithm rest jam quari potest, quid Namerou additia
vel subhactione praestetm in Loganitimus
l.X=
1.4r
 aX
E
de
a
p
k
e
pe
Ec Ergo si
ata

## Folio 161v — 00068196:0320
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000320.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 86 lines, status machine
et
Cex (dx
X 1+X
vocetur c
d sex sex
14p
o
cd, quod 
Xeobcetur ( C. Enit dx sit XV = y fiet dy = dxF +dx XdV
Et y-
c
xv
 scodx + fudco set deo dx fdx et Xdv = dx cos 
Ergo y = sse assa, posito ex esse constantas
1+X
sad Ssco,  (X dx C0 = _X Co dx = XX V XXW
du Sscodx (Exeodx = exxdco E Coxdx
X
orxxd
S1x+
naturalium
i
a st
sax
dx
X
ii
c
 + = + 2 + 2 =
+ 2
e
e
es
+
2a
+ 27 +4
(a
AxiXFA Sde
1X, u
X
A
7e
sax - ex: C Cdex Cdu
= at qu (see)
-(85, = + L +  + 4
2 + 1. t =a ab L + = = 
Ergo 4 +Z + 3 4
+
L
L + 2 + 3 + tet
4 + 3 + 3 + 4
3
10
+
+2
+ - 14
+ - =
+ 9 - 4
5, L + = + L +d
 + X +  X + 
deu (codx = 4 XCo = Sidco
d(sae (a
ix
dx Y dx. 1. Hoc ultimum ergo habetur
des dx 0.- u
=
nx ix
c
8,  + L + , +4
d (XC) = dxsax + L a codx. Ex XCd scodx +
2
(X X= xita
d
et
3
ex V cubicarum. Videndum cubica ad quadraticas aliqua
ex
m
L (X
sit
ex ed pendet summa fractionum imbicarum, quadratorum,
ratione reduci possint
f
5
du
16