# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068200:0262
# Permalink to this reading: https://leibnizlegible.com/page/00068200:0262?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 130v, page id 00068200:0262
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 131r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068200&page=262
# Source image: https://digitale-sammlungen.gwlb.de/content/00068200/jpgs/default/00000262.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 84 lines, status machine
# Lines: 84 recognised, mean confidence 0.72
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

ut ergo. sit
ponendo Z
gp
200
c 7d  co-
2C0
Z X, e) quadratas facile effici potest
2c0
12
1 Co -X + sh Male, nam dudum inclu X includit 2.
et duendur praeteren co - Z _ = X e quadrato nempe co - Z ) + cor Z 0
rh
Cc 2cd 1co
et siet -X et Co Zm +m  sive -XC B c m -Z m  ma, et explicundo Z per co  nconta
fier -x co, et ponendo X e, mp fiet -m , com Z m + m,, sive m,c +2.
ponamus Z in se continere co, seu esse e _ cop fiet -X cd r7 Co: m = co 2p  + mco, sive
Va
pam - in t 12. Hec forte imulilio massumendum  cd  -mito
coqo
et 1
C et m + X (
et eut X0 s e 17= s
fac mco 1, B S fet + mco Y BS S si
hinc duo valores ipsus seo pror scon B - 35 Csm  es
ec X
restat aquatoe: inter 18 + Z F + (050
vi
zast
sive   d2 + BS, m dX
NIm
Y Unde valor ipsis X
gag1 pro A ponatur eius valer inventus d-d)
veo
noZ H G  + 3ustr. ut ego hinc duamus vnlorem
fiet - Ho Z  e on - dx, sive 3V54 pyV
agr
iph3. Z) faconus Bapo  qu + 129 + qu, entue Z sive (d 1 Z + 4, siuve Z B Bd - 9.
xvr 2
_t eadem Z H 348 - qu - ( s2
2+nv
12 AZ 2 hRectius ipsam Z explicabinus,
pounozue ZB B5 =4 9, fui 2 e ∞72
34 pg
A2 n2 = + 29 (31 + q r
β0pu
12
+29βd + q et habebimus
habetur ergo Y pure, et Z. est posita Y.
X etiam et posita V, seo, exposita em quae habatur at in potest sumi
pro aubitiio Z. Jam X, etiam habetur ex Z. conferendi ergo duo valoes ipsius
X, alter per Z, supra notus, alter hic inventus
imo ita potius. Sad invenitur suppo sita sm et B. d. d. Reliu
quatur ii pro arbitro, o
2B gr
42a ) +q+ ponamus ps h+ + 1 +t pont
fet Jugy,  + 2a β)ht
fiet e ri . eer +nf
pugo 4 2a Y + a7
ax
ap7 +   (37 +1
Jam Bas
ay 1. seu aHfi5.
 N
alite Vtr
v)
habebimus: 24) x + r 4 La β7 quadrato
et a7 +raen 
ao 2aY + Y
5) ponendoruisus 247r +r
7. Ergo  β
a25 +  a () eA n. uno 1152 a )() () 2A  + a D 2da de e
X 1 8 + 2aβ), 2+ + (ht + h
a confercurh t +1. pone A 1a, a Y   5. fiet aY
et Ca BY) (+  10 fiet a ( y + 2 et BA L
pont)
restant () 2A (F)) )Ne + N  conterenda cmn ht. quod ut fiat pore Ap a
et fiet )  h t. aliqua ergo nempe a habetur pure
sed quia id nocet ideo num t, intrabit in nominatorem ver resumto:
 (+ Aa B) YNe A d p p ht pone A M p Lit. et habelas valorem iptius ht
sed t et hoc cocet cod modu et rndis erit 427  +1 (t 4) . et pontudo
n a fiet radio a(B  f 1. (+) n 1 S h at sioc e t, F
phite
(2a (aβ5 (2 A e  F arp X) Ja) +ar n llt.) Aa + N 
alass pre