# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068000:0013
# Permalink to this reading: https://leibnizlegible.com/page/00068000:0013?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 3
# Folio 7r, page id 00068000:0013
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068000&page=13
# Source image: https://digitale-sammlungen.gwlb.de/content/00068000/jpgs/default/00000013.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 90 lines, status machine
# Lines: 90 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.
# 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.

nx
XxIMX. aequari debet quadrato, et XX-  etiam aequani d debet quadrato
a XX +ax = XXyy fit aax ta Xyy et aa = Xyy- aax et x = aari, gy -aa
aa
aanx
Aursus  aaxX ga = XX vY sit aaX. ~ = xvo et a aa X - X WV et X = aapi, aa - vV
sit ha-Wv = yy ga seu yyrvo = 2aa sit ay  az -aa et av = tz- aa
et
fiet ergu ob pagy + a 1vv = 2a fiet auZZ  2a7+ ) + (t 2 2adtZ (F a) = (2a +) 
 aaZ= 2a +. HZ. = 2aat - 0 seu aaZ F HZ = 20 + 2aat fit Z = 2aa, att,: at H
1 5
ut y = a pEaat (a- aH;, a aq + H = a, rat + na - H,:, aa t H- y
etrm,
seumaC: et v lZ : a =a, seu v- Gat + (aH = a F att), :, eaa + H
epuunct ut
aa, gaa+ 4uet4a B a  2uat + V 1 aa - 4a rat ra (rai B 13
seu v = a, Eat= aa + H, : aa + H A a L+
gy+ 00 = m
a t eL  qu (aa + H)
6
s
are
fiet gy+ vo = 2aava + t + 2 auH,: qu (aa +H) = 2aa
c
n = a   B gma y A V
mvaq
Requla quaer antur duo numeri, quorum quadrata in unum addita faciant 2.
n nome
e in
x et 
nete
eitque x jam guaa Canin: quaeruntur duo Numeri, quorum summa 
in num addita faci quorum quadrati in unum additi faciant quadatum 2aa
nea
Fiat y = a, 2at + aa  -, et v - a, 2a t - aa +H
aa t
aatu
ata
Hinc jam _ aa m:, gg. ap ana ffina vu pa = 
H
+
Hinc ry-aa = (4aD 4at- 4at a2ataat a (2a aa,: qu (aa TH)
s
seu gy.aa = 2 Aat, a- eat,: qu (na +H). Et X (am, qu (aat ) at (aa - H - at)
Et X = aa m qu (aa +H): q aut  4at (aa = H)
et X+ m = m  n qu (aat H) + Aamt I4atm,: 4at (a a -H)
_ = Xgy = maa qu (2at taa - H), : 4at (ag - H)
4
a+ 2aat + t f qut )4 aB = qufeat taa (H)H, qu (Adt Faa L H)
Ergo x, X4m) qu (aat H). qu (+at faa + H), : 16aat (aa - H)
n
23
Itaque  Itaque quaeritur ut sit XX + mX = quadrato, et XX = mx = quadrato
(autB
sit X = in quadrat (aa +H)  m + 2a met +mt = M qu (aa + H) ingulam te)
v
4at - 4 at
4at (aa - H) tad (D. ad
SietxX + nx aequale quadrato a m aatH, in tat f pa- H vet a X 1 4
(7XX -MX aequale quatrato ac
qua +4)
seu X = m
+at Gutua - H)
4at= 4a t3
aatH, in, 2at  aa tH
4a+ = 4 a +3
 Catm. aF
Aaati qu (aa r H)
fiet X =
625 + 3 2
8 64 X
si aaaH + qu(aa -) 41 c. ∞.g (2a+. + (aa +t))
in qu 2ab - (aa -t
Ergu XX +IaX, in YX-mX =liquadinto 
p
Aequ. qu ( 4 a a (= qu lo ne lt) u qu (aa + H)
ab. (aa Lt), Caa + H),: 4 a t - 4a +3
1.
600
et a = 1
1D- aa = 3
Obraa = 5
4ab
sit sit m = 3, e1- 2
25+2. 25
54
625 +600
1225, 23
_ 7.25
5d