# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068000:0043
# Permalink to this reading: https://leibnizlegible.com/page/00068000:0043?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 3
# Folio 22r, page id 00068000:0043
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068000&page=43
# Source image: https://digitale-sammlungen.gwlb.de/content/00068000/jpgs/default/00000043.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 96 lines, status machine
# Lines: 96 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.

invenire tres quadratos progressionis Arithmeticae
aa
bb ce. Egit aa - bb = bb -cc.
F(f: h) (b -c, a +b) = b+C, b =c
Et ex iper2
sit  a -b= f b = c) ifiet
seu fya +b, ih= b +C. fiet ex2, a ) F: h) (b - C) + b et
exa fint a = th: f) (b +C) -b quos duos valores aequando
(4)
4b = ffc + fh b = hhb + hhc - ftib. adeoque fiet
+
 +hk
quo valore ipsius C substituto in aequatione qualis E, quae
do
18
a
et ltb. (H - tit + 2fh) b : st
Aliter substituenda valoreum
C in aeg. 4
X
ficta= 
modo
seu utroque seu a-
fc + hb = h
F b, 2fh - ff +hh,:
2h ff thh
b
t Cth.h
F +hh
FF+hh
b = 213
ffthh.
C=
b, f- hh. + 2fh
f+nh
Ergo in interris, omisso communi denominatore, habemus tria
Habermus Ergo a =
ff +hh
quaesitorum quadratorum OO,
3
E
= b, fh - ff + hh.
D)
latera
b, ff-hh + 2Th
D = b, ff+hh
vel b, ff+hh = 2fh
ubi f, h, b, sumi possunt pro arbitrio, etb potestomiti
si h esset = f, fieret C) = bff 9 = 2bs, et
D = 2bff
poto esse errorem in calculo. sed statim, quod non licet,
∞
ita
enim fieret a = c. sed alia se Hert ratio brevior
ffieret sint a-b = b +c foret fiet a +b = b-c 49
l
si foret a +b = b -c firut a - b = b+ c
e
+h
+ fhiilit P shlib 2hbCBab
r to
 sliit sitib+ Fbst  Ctiha.
sen in a = lb hc = bG,: , firt a = hb +tbA hss  + ys
O
LC
24
su
1
=2fh - f + hh fs+hh. D s lin +2st
ffhh) +f +h 2 fh + 2fh D Hlt S + Essne +(4) stih afih t afh
ei
X + K
f
a
(a (45
+4fftih
+h _ fth + 4 Bh - 4fh _- 2 ffhh)
q
sa
)0-9 = 2fh rfh- 3ffhh  4fh - 4l 5 itaque res sulcedit
N
f.
 erectuna calculo
d
d0 - dD = 4fh 4F 4fk 2st 4h B 
 solutio ergo haec est: invenire trt in integris
tres quadratos progressionis Arithmeticae e erunt eorum latera
2fh + f- htival C- 2th D- f5 + hk
ff +hh
s h= 2 et f= 1 firit 3 = 4 3 =1 8 = 1+4 4 + 1- 4 male
2th -fF + hh
sit h3, et 5= 1 fint 6 - 1+9 =C =14 8=9+1 = 10 D = 6+1 = 9 = - 2, sed licet D sumtre
49
Crut 9, 8, D,
est 6- 1 +9 2
19 10, 2 hues trs quilus niel hombe 21 3. 1 aam l 1125.