# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068200:0239
# Permalink to this reading: https://leibnizlegible.com/page/00068200:0239?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 119r, page id 00068200:0239
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 120v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068200&page=239
# Source image: https://digitale-sammlungen.gwlb.de/content/00068200/jpgs/default/00000239.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 98 lines, status machine
# Lines: 98 recognised, mean confidence 0.76
# 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.

ys se s
ita ut
tres Numeros qui venore quorum summae et differentiae duorum quorum libet sint
quadrati Ut differentiae sint quadrati ita efficitur, ponatur pimus al, secundus
al -X tertius al -x- 7 ~ quod si jam 7_ r C V X-c
trium numerorum dat erunt quadrali, at a. X
et numerus tertus erit: al - x - 47 - 2X+ CF C. pro carbitrio assumtis; et
4 e
Jum ut summae quoque sint quadiati, at + al - x, debent esse quadratus e d,
fietque a p d + X fientque tres termini tales: primus a d +X sundus d. L X -X  
tertius erit ut ante
do +X X4- 2X E cui si addatur primus d X productum
(x - x) xa- 2x , 
si
act
40
 aequabitur quadrato, ut d +2de +C
d - C = X4- 2∞ c + C, et vel dp, =eC- x 4 + 2X- et
4ce
et habebimus.
vel = C = 2 et d +e e 1
Jungatur jam terminus secundus Ct + 2Z +F - X, tertio e + 2C
summa: et + 2C) + 4
2
et fiet ex - eq0  er +Z0.  2f + fe, et explicando.
yd
2 = fiet
= X - Z 1 quadrato, cujs latus e +Z + f
e+ 2f7 e
B. si X - Z sit 7 0.
statim habebitur intentum
ex - lX7 , 2xC -9 CC 1sr1 27 + f e. tam cum si jacius 
erit X X, 3 ZV droo
jam cum nmeri e, et X sint arbitrarii, poterimus eos assumere tates ut in se tucti
faciant quadratum quod quadratum sit - f + 2f g -g, seu negativum, et
fet aequatio - fg + gd  + 2XC= C  e, 2ef
+ e sive X E 2X C + CY
+ 2F
earf
modum quo extrahi queat radix ex utiaque aequationis parte, que ponamus e, esse quadneu
seue aquari
t, fier: = 2q
2
L f9
oa
+ 2s
(+ 92X) 1 (10 4)+ eg X hl 4+ t 1
Habetur ergo valor apsius X pure est rationaliter ad hunc effestum praestandum
= et eritque XV - c2
indo scilicet
LV
2c
4qu hi2
2C 1 9X + h, et X et est rCY-  hel
c+
- 2le ff- 5 el4
e+ 2F
Unde Na( - 2set B + he  - ca
et
e + 2f
c el sive _ eg +2792 et
set
hlG
hrcuius X Xe
8 Se t- ho t
ehl
(A = h2t
2gh.
+ h rc
sXk
4gte
Tartum ergo opus est inventione psius, C, qualis hu reprae
sentatur, quoniam in terminio alias includente se non reperitur, sed nec
h, in eo reperitur; quaerenda ergo tantum talis explicatio ipsarum h. et c
ut ipsarum irratio quadratum alterius alteratia non nisi pura extet
potestatibus destructis. ponetur 2 Chp m erit Cp  eoque valore
in ejus locum ubique substituto, fiet. 7
4ta
didisisque omnibus per h fiet: s l4 - 2∞ h B + h= (a
fingatur quadratum considerantum nos habere hic S1- n dcc
+92
m+
+ha 1 N l ht 2m mk
m+  nsme + meter)
elm)
4 1 sel m ponamus 4g, esse numerum
 negativum, fie - K, fret: a ( sel m - m
A 12 setr (2 hi2 (2
raton K
e vel +(, Xlm + m
Asen 1= 2tsto B + LCK
quadratus
ergo)
debet esse numerus rationalis erit ergo +2Sh (=h4 ( numerus
atrculis quadratus. ergo +2N ( t , erit numerus quadratus e- h + 2hg. 
eritque +2N F g + H. Cum ergo sit X 14, A(M + m= h +rgh -g, ponendo
pacena simnti se t at i aed ti voti daatum ys r. e at + H pronntar pur
pecudutu sim  e d  pna