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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 1
# Folio 12r, page id 00067996:0023
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 11v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067996&page=23
# Source image: https://digitale-sammlungen.gwlb.de/content/00067996/jpgs/default/00000023.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 82 lines, status machine
# Lines: 82 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.

y 1 r +2ra + a + 5 + 2sa 7 a
sic (y) ( ( + 294 +4 + 2ya + 29a + a +5 + 25a t a
Ergo VF 4 + 29 a + a + s + 2sa + a
 4 - 29- 2a
Ergo YY = ~ (+ 29 a) (a) +5 + 2sa ( a = (29a) (24)
- 24 - 2a.
Ergo 2a + b Y r 4 Era + a +s + isa + a
L
v
fier b F r + 2a + s + 25a  8947
sive b
q + 245 + 4 qsa + 5 +45 a + 45 a Y - 4) a 9a 5 9 194
+4q + B ag + +a
8gas,  - +a4 - 445 - 8 as, + 44578095 + 405 7 8 a5, asidsa
 a  X +Z
za
X +
u
a
N
 X ut ab. Ergo X B)
+ 74
Ergo X  ab -Z
1b
 I mulliplicemus ab 2Z, per ab +ZY
ponamus fier a V =74 quod ponatur aequari quadrato,
s
id vero sic efficiemus (aba
Ergo - Z ) 2ab y + 7.
X) +
2
+   +2
X
iu
1
Y + 5
fiet X ⊓
Eux fui:
fiet:
lx+ s(d
cequi
Ergo 
ia
1
S
ab
At idem XN rto
at
245
pone l + Z1
et fiei
qu  r + 2s 15
reS, 4 rs, 19
V
ab
pu qu 1I ++S
a
siveab. Ergo
res  rts
Ergo 4r
13
ab
4 215 +5, 4
ab
ab
s
id est, nere est
e
e
 ab
quadratum  un tate auctum
Jam l +Z A r +2rs +5 
quaeritur modus inveniendi duos qua summant duorum quadratorum, quadrati 
 cujusdam in ratione data muttiplam
ut - q2 p 2ab 12 
fiet
ab give qps
ab
ab Ergo
r+s.
ab
Vele: