# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068195:0140
# Permalink to this reading: https://leibnizlegible.com/page/00068195:0140?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 70v, page id 00068195:0140
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 71r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=140
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000140.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 126 lines, status machine
# Lines: 126 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.

a 6- 4 = X+ 16 -48
5= a +C
ateta
 3  Eogo
ca+ ac puso
quod
Quadratis omnibus fiet: 
v bre
fe
+i re2feb s
f+   + 2fe b + bfd a + b
fic - 6e a = 25 e bs a - bf d s
14ct a bd-264fe∞ 2bd
carars a
ba - 2bax + saxarsa
beq 4 ppx.
beraeq
pa
siterum
esindratisque omnilus, fiet:
 qua
22 2
b 
sa
pvapup 1a
lane
.
Xsab
14a
s
5
Atque ita habemus aequationem, qua terminus X, qui solus desideratur, haud dubie dabitur
Xcujus reductio, ut fiat facilior, et ut multitudine terminorum nos expediamus, substituatur rursus ipsi
fiet b aX f. valor sug, c + d. et quoniam traque pro arbitrio assumtae sunt, ponatur e d= a, erit etiam
a X
AbCSb sax  ob naturam prrabolae, etiam e = a. et f = c + a et aequatio inventa
1B., ax
ita enuntiabitur: ca + a +b sax = + sV + ba BbCs +ba sa +b
c + a + hux 
= b sax + Y.
dicsat (et et a + nca = b  + b + bV 2 cra + 2S BC san + 6 sax.
a 26 1ba x 1aX+ acX 164Cat C2b  Ca bxt Acab e
++
+ 2ab + 2C ab44cab
X + X9+ g rg + 
N462 8. dant
s
et
Jam 3
18
a(94, s = 1. Equ = s
X G  7 erpo item quia
XA 3
gn  d
A2
= 1.
2. radicer esse ipsum 4
b5 a
Ao Eumjus rad quadr. P 6
fuit () Sa p) E=
feuet 27 16 = 929. que
= f+ a +X.
red = 2 bes a
ax=
ab = 2y2
= 2ab x + 2C a bx + 4ca b x
= 26522x
X+ b a = y +C+ 2yc
ax +ba +x F pb + 2xb, L
Sax +X + exb
El F +  - +y + pyc
inventa
L al = ax+baC yc 7 = lf. (.
aec autem aequatio se se + bes =. 4
a =  bfra +b (= H A Styc
d et. a X= Y    px ibu, a trer ergo l Y +7
ideo
ut fiat simplicior assumenda ex e vel d, quoniam alterutia earum pro arbitrio qu s
sume potest, eligantur tates, ut quales natura figurae ad hunc scopum aptissimas a
ostendet, ut hoc loco si d = a. ponatur, erit etiam d = e ob natioram parubolae,
ideoque se mutuo destruent, fietque aequatio: f+ bsa  sbfs  + bi
ee pox
+b.
x
= b
partem aequationis
et aliaq termino quadrata= F +)2 
6X b
fa
fl
2bX
s’a
ax
na
anferatum atrolique X semel, nota O, d etf anseratuer adhuc smel nota  Jum vero se
ab) 16
a =X
ax
+ 262Y
= velique aequatum, fieteu aditone as - Xs a + 2b a X = f 2+ bX
divisisque ommibus sive a = X + 2bX
af
axfx.
( - 2x + b 
sa
Quae aydatio reduci quidem poterit, sed praestat tamen aliam addmere conditionis
tertiae implendae rationem, quae facilius ad aconum duere videtur praesertum quia
Tangentium inquisitionem, quae nihilominus caeteris absolutes restaret, jam tum praevertit
Nimirum etiam intervalla sperpendicularium; ab ordinatis in axe sumta sunt
ex conditione 3. inter se ut ordinatae, seu AB ad GH ut BZ ad GZ. Cum autem in
parabola intervallum tangentis dictum, sit dimidiam latus rectum,
ergo GZ. erit data. a. cui si addatur AC = c. data, et CG= X erit a+ C+ X = ba
dimidio later recto. sive posito 2 + c = g.  2gH + 2X= sba  omnibus per X
 fiet: a. 8 4+ Ox + X = b vaX, sive oX + x + 29X = b ax, a proinde
vel 5H = g 92. qubd estalsudi 92
E9X g X +  2Xg + 29x = b a
bf X2, + b
a+ 3ac +3eatc
a+ 3ac + 3e at chac
+
26
s
esto enim
fax 197
anx 
i