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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 169r, page id 00068198:0337
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068198&page=337
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 168 lines, status machine
# Lines: 168 recognised, mean confidence 0.73
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

1E f, 140E. 3
Ghoc.h+
LEoED +s 1E. DEDIF
p
E
CrcoEb
Gnsep 9 + FH. oE gth E
SC+)
hhor. Et hiLoE. E4 k, E
H SE+)
f1E E2. 21 + 1E. fr. 11 +, 1E. E) + LEr, 81 =9G
3)
3
3 5 22. 81 + 12 o Eb21) 11 + stE 0E. (9) E1 + 2E2. 22E) 81 = 53
16. 22.
1E0EE2 (V) EH DE E+ +E. oE(51, Et + Ex. 22(1) 01 = bS
OE. G2 (h). 16. 2E 22 s2.
D. . CE)9). 21 + oEE2 22 (2. 11 +, 22, 81 = E5
10E. Ex 21 + 1E. 0E. 22 (_ 21 + DE: 22. 11 + 1E. 0E (5d E = 25
OE. 22. 21 + 15. PE, 9, E) = 15 10  OEGFO5 pdis hunre 1
ns 8 =gosso ob t 12 n)
h∞I =X E1  = E1, 515
95+ A55 + + ht5 + h65 + Rus + A15 + RoS
EA+ dEoE E2t
+1E. 22+
1E. E2 + h15Er 222+
a
15.0E. (29+ 1E. DE. E2 bF E EF
51E.0E. 22. 4 + 1E. DE. 22. 9+ 128C22 + + 0h 22+
., 1E. 1E +. CtE. BG F 1E Ot 1V9+ 15, DE. 12 b r A, DE.12 = (312
1E. P22 +
1E. Er 12. 2 + 21E22. 122 + 1E. 12+
1Eot: Er. 2+ 11.0. (2. . B + 160E.22. 122 +
L 1E0FE2. 12. B + 1or N. N b + 150E; 12. 2 f
Si s oE. E2t LoL 52 2Z + oc 2222 +
si DEEm Er Ko5. 22 142+ si DE. 12 =
DE. S1+ sDE, ED + A, 1E. DE. G(+ sitE. DE 9 + fioE
EE +h E2. 22. E + A52. 22 E + f 122 +
A E2. 12 E + AE2. 22. 12. 9 +, A 132. 12. E +
Bcht h1 C. oC.9 +. Riti DE: L + h. BE 
REr: 12. E + R22. 12. E + fi. 12 
Etheect h2222+
hE2. 1. 2 +, h2E. 1C. 2 + h, 12
)aF1FOO1L) 1E.VC + h15. 0E 2 +hhoEC: cE2 + h2r +hh 12 g = X ret guipat. ho Et L X 21 + X11 + X 01
A b. Cht B+ Ca+ ut = Y ns 3Bd  B Gurmab ab d. + X3 + X 4 + X
Xd +Xut ca
1E0E()D. VE. EEZZ(2)C
e
1E. PE. E2 (9). 150E52. (2 IB
95. aEp2
h.11+
E5=
5
03) 2
V5
95b. 55 +95p 05p X: 15.C
25
15v: 15 + 95pX : 65 B5p. Z
95p2: f8 2 y 9ss = Et
25p2: 15 = 117. 95p = n H
+ h55. o
Et sbut. EE. An sib obr K1
1F+
11142: 2b.. lio
(EDHC+; EtiI. EF
ch Et. ob2
(RIV. 1V +
R2ti C. 2+ fitb ob. 2+  
Exthtth
ut
1-=
t
Eth15.0b 9t R1E
y  hon
Eb
yy = 12
2
2Z= 22
y+Z=v
Ex 3 fit
7
Cyy +ZZ + 2yZ = vv. Ex 4 per 1.2. fit t _ 22 - bv. 
(6
Ex 1012 fit 49927 = 12. 22 Ergo ex 5 et 6 fit vt - 2. 1 vv + 127 =0. seu etiam
22
- 2. 12.22
Hinc ex 5 et 6 fit vv - 12 = 2 V12. 22 seu V = (12 + 2S12. 22
Et ex aq. 3 per 1 et 2. fit: V = s12 + 122
10 + 11 = 2 1
16
V_ _C XX L act bV XXLa, IIXX + AX + 13, : 20XX + 21 + 22 = y 7bY
+ 1IXX + 12 X + 13 =0
=201.
- 21. - 22y
X = Yu - 4. 10. 12 - 11, :, 2. 10
4. 101C 4. 10. 10
C=  er Sio gy - 2. 1221 + 1_ + 31y - 12: - 20y+ 11- sit y = 4 vV
datur rx y
=4. II. 22.
e
( Cak 10 X + WX + 42 = 0 X + 1 X + 11. 11 = 11. 11 = 4. 10. 12
(792022. - 4. 1320- +I1 13
El eb
A
Criydyterdes
fiet XB. Cxray = 2 vav f.. ∞ r. p +. V: e 20vv+ 11
X9 dy et t a se invicem sendent.
Hujus ergo datur quactatura.
et xydy
(r- 207
xy. (X du, hi reducitur ad 12XY 12X dy. Ergo si 20 = 0 reduatur
11 - 209
jam X dy = rgy +.. 9+ y   221y f... - 12,: 11
ergo xdu reducitur ad yS.. (et sed nit hinc lucramur
Eydu
X dus oducitur ad 12X dy Ergo ad
11-204
ad pay
S.. 2yt.
209y - H1. 20Y + 112
hoc mutat, ideo solum
aliter quae amus X dg. Nempe fit gy et +2i qy + 2. 21y f.  posito 12 = 0
EEg fit ut
209+u
monum =20GF1
x du alias pendet ab Xy dx sed xy dx datur ex quadraturis
rationalibus hinc videtur sequi desidentum
datur ex rationalibus quadraturis S. jus +9+. j.  y sit y
f. 9 +. .: Ly
y = v i dy = 3 vrde. fiat Y 3 updv Y. v +.. = 3ddo rutp
sit. y = v Eag B dy ay+b = 3vvdv (avtb = 3dx Sav + bP
rC
su G-v Ergo du Tagtb, :g = 5 v+ do sav + b, : v5 = 5udv Yav +bV
= b Ergo du fagibysi = e v do fav 1b, : v y = vet Erg dy rageb, ig -tet. V do Sa vE +b : et
E = 2et1 V aura
+E
20-1
e y = ve Ergo dus Pay +b, : y = 2e V. Sa r. +b, : B = 2C. v (a r +b
quin summari conice pt Tav + bY hinc fro V ponamus Z + m fiei S, a Z + +aM Z + bam Z + 4 a MZ
+ bab yl + bm
(it Rc ac+fCd +g. fiat co dh et pectibit aZ + 4ah Z + 6c hhi ZZr4 Ct Z + cht
+ f ddZZ +2fdhZ + fhh
sit
Ergo fii f = 0 seu non procedit comparatio
V)+bV = vtQZZ r ab LvEZ (V+ 2vrZ + E v - b ∞ + bb = bb-
1622
1637
g
4
set 6 th = 6chb +
ergusit facc
Z redil ad Nbb. 2E
et 1y+ byy +ila  sit yt + byy (+ et Vcoco +2yycoe (+ eD sit y + b = yycoco + 2coe
a
sit ycon
vel sic: y’+bytee yycoco +ryco dF ee) et yy +by = geo troe
. 2lcoro
= bb - 2b coco + Co  2bv + 2co V + H
sed ita seco = 2by +rcocov+V
sitco= XV siv 9ex = 2b + 2YX vB + B
e W =dVX 2b,. 1+ 2xC
4C
t ego
1
961
Amo hoc non
licet
od crxdu