# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068000:0086
# Permalink to this reading: https://leibnizlegible.com/page/00068000:0086?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 3
# Folio 43v, page id 00068000:0086
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 42r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068000&page=86
# Source image: https://digitale-sammlungen.gwlb.de/content/00068000/jpgs/default/00000086.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 67 lines, status machine
# Lines: 67 recognised, mean confidence 0.78
# 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.

e
de Xx - yy = 1
XX ZZ = tum
 yy -ZZ = nn,
fiat
Xty = fl.a unde n  A . ras y-f a. l. raf jum draad lnos = puraa, m. raque
xtque = gm: a unde X =
gm: 209, g = 4g ga, m: 2a9
9Z = hn: a unde  y = hintoam: rati Z- hh -aa, n: 2gh
1= gytea f m n = gg-aa h et fiat L = htr + aa. 
ftaa g
hh- aa a
ff-aa) h
Sf . a, 1: 2a f = hhtaa, n: 2ah
g9- aa, M. 2a9 = hh- aa, n: 2at
= 99 + aa, Bhh -aa (f) Amlicet facere hh = g9
fftaa, 99- aa,  (h)
nec ff-qu
siferet  s = hsi fiert htrua jau stua = Notua. sed hiff.cula eficietur ut gytua ge. pa sissum hut
1faa +oguaa
Itaque pdeundum ad aequs , suagu + a  = +gina bi fiete C g = D d 9d bb + 2bga a + a,
fiet aug  gabb aag = bbus +2aab, seu 9 = 2aab:, aa - bb a9+a = auqu (bg + aa)
c(9. + b = b9 + aa ap bciul (G9 + aa, :, gg -na = b rg b9 taa,: ((9- a) = qu (85taa, ff - aa) et pro ponendo valorem
2
3e l
fet C= _qb tgea;  Zb- ata - b E
Unde tandened
et agndo daosi valores ipsus 9 fiet perab: 1aa. bb = pa a i c G
Estaa, ffaaa
Z aabb +4:, a ab +B3
C= Ga(aa +bb) f55 -aa): (Sstaa) (2ab - aa - bb) = aa: 
unde Cnabe alt = aC aabe) - b
aabo
seu C= aa bb ta, aaBtb.
seu c2 au:
seu  b Caardet s5 - aa) = a (st taa) (2ab - a a - bb) (5 - na = B(cit a b -a) e (b- a))
b(ca tl6) ee = sf tna qu Cs5 +aa) Ergo suffecertit
Aliter ex pag. praecedenti, si XX =gy = l et XX - ZZ = nim et gy. ZZ = nn, fi
fiet 2XX = l+ nim -na et 2yy = Hma l - mm + un et 2ZZ= U+ mntnn
Ergo qualibet horum devet aqua summarum debet aequari dimidio quatrato
sit tm bin = (f: a) m et x = poria fiat 2ppmaa = Am) (f: a) on ((- n tnm seu Eppm: aa = ff: a) (l- n) + m
l+m (4: an et y = gn: a fiet 299n: aa = (g: a) ((_n) + N sed culiudo absolito evanesceret, 1, m, n
denique n = (k. a)m et Z = rm:a fiet 2Yrm: aa = (h1 a) (+ 1) + in
Ad piius videtur brevius
Artic hoc: l= ext G +C n = X +Z+f
Alibi 3X - (379 = D (Dmm-(2nn
(1
fint X + y = b in + bn xc
X- y = 4m 1 qn
Utpry = bm + ln
(DXX 7Z-Obm-dnn
X = l + p Z = n 4
Elp+pp Bng79= 0
2lp +pp = 2nq + 44
Utp y=4 me4 an i  q-
(4
y +n +9-
3yy- 
3 + Z
y-
cl(F am
y - n -9 = al + am
n = y + 2+9
= (3I1-3) mm
=. El A)on
= 2l(B2m
ope harum ua aequationum quinque invenientur rationaliter t, p l, M, n, 9,