# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068200:0322
# Permalink to this reading: https://leibnizlegible.com/page/00068200:0322?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 160v, page id 00068200:0322
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 159r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068200&page=322
# Source image: https://digitale-sammlungen.gwlb.de/content/00068200/jpgs/default/00000322.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 113 lines, status machine
# Lines: 113 recognised, mean confidence 0.80
# 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.

2a X + a X = Hγ,
et + yX
+  X
+ β3 V. + ad
Ellattipicems posteriorem per arbitratian quandam sive indeterminatam,
 +ea
 ec
VX + de X + B V + de H 0. Eteq B)
Quonam autem in Eaequatione altera est YX,  nec, quantum invenio tolli faite potest, ideo efficiende est
publema servatis iisdem incognitis, quod vellem brevitatis causa; ad circulum et sectionem Conicam datam
constini non potest, nisi ordinatis adhibitis obliquis. Quentam om aequatio(A) mutanda est
i aliam ad ordinatas obliquas; prorsus ut paulo ante fecimus, popendo tantum Z in locum X
et contra d et Vin locum Y et contra. Ordinacalautum sectionis conica intelligenda est in
paralam tangentem verticis Vide fir. 31, pay fp. pure scilice G N B et
AN1 GL By e por sibret cum sit GL B X et LH, X erit
GN et ANNZ.  posita Jam X, HL  erit X aZ.: et
LN eutyd
sive LN  ZSia eritque GL sioi 3. ( B LN, sive
XH,  y r v + Z Si Repertis ergo ipsarum X, et V valoribus in a
tequ (cH) substitutis, fiet
29Z +a3Z
nequatione (B), proditit A En 
tequatio (ED) ejusudi:
naq
in + b
V 2m VG.
un, +. (ACq.
+d in X X
dam re 1 a.
- ∞ V. + 2at 110
Productu ecioidarutio
42e 6i.
e sugaitutis
BB V. de I r 0
Bmces logiae causa faciem inposterum: H0
 e
sive xper   fiet aequatio:
+4. id 2vsa ..
1n  nn
100
Producta Aequatio G dcarebit qud termino D.
de
Dividatur per cognitam Termerni a
Nesumta Aegratio E divictatur
per + a d + ac  1, sini ( axodo  cos per Y t poneno D 1 1 4 aC At vero
habemus jam tum Aequationem quod in hoc problemate feliciter ad calculum contrahendum evenit,
habemus gam tum Aequationem nempe D, quae caret  termino y
4 -1 + atd
Eam erga
(+a 09 - 1 + a  + a  8
qeu sive per
voc es A ud o)co, pe V C 1 4 a 
9es ger) e
quoda anteqam
fiet faramus
Quod antequam faciamus, morbimus tartum ind eaedem aequatine G, teminum cogntar
 ipsis DZ  nempe A- 2S
s partes ejus ad communem
2
(2a 4) Aque ita Aequation G.
commutabitur in Aequationem H
quae sit talis:
Aequatio
A0: ad (IY-
Culum
Quae ut contrahatur quantum
ossibile est, ideo faciemu
r  Quod
curnque ab ipsa D
maeterminao s est pro mognita hhaberi
neio quatis, e f.  A
 ua e1. 
idere pgnnere 
 nos talem ites
emim fieret 
sper at
denominatorem fet C s (16 5)
Reducemus ergo et ecognitam ipsius 7, ad num parbium denominatorem, a
+ma ( racosite
+ sud 00
lae 
equationes ergo sunt
Aodutuo aquato (C)
multiplicata prius per aubitrariam
AG Aeq. (C)
Ab nac dieqs (F) anfratur Aeq (C) fer:
+ fet
Quoniam autem in hoc problemate feliciter
ad calculum contrahendum, evendit, ut
jam habeamus aequationem, nempeD
in qua sola ex incognitis V ascendat
ad quadratum ideo dus divisam.
cognitam ipsius v nempe  addemus
aequationi (H).
id quid addemus ipsi  serit tale:
utique faite est notis cum  prrarbitrio assunta sit, nel alibi, in tota aequatione producta reperiatur faver cgo 
summa praedicta erit L, ac proinde in aequatione producta plane omitti poterit, cum unitas
conferatur e gantae quatio a palitum fuducta cum asia aequatione ad cprculum comperta, facti  ati,
collatione teminarum cognitarum iptius VZ Fe aequatio haec:
a e S.., vel a 
+ba. 10.
estant Aequationes collatitiae
B Vm ef nttoliq d
vel pi e - 1. Ex cognitis ipsiusZ pro sini sulestituento ejus valorem inventum 
ergo in promubitrio, habetur e, vel contra; et his habitis 9 et habita o etiam
tyHo et sun
peretis auterduo locu 
10. et lilgulus non obliquus sed rectus. Et tame
pax +qpy
 quoii ersi
unc saim d. et f nihul ad rem pertinerent hrsi villem id ploncere posse a prict er ale so. vid. plag.
statim habetur 
e et qui