# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068049:0141
# Permalink to this reading: https://leibnizlegible.com/page/00068049:0141?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 71r, page id 00068049:0141
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 72v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068049&page=141
# Source image: https://digitale-sammlungen.gwlb.de/content/00068049/jpgs/default/00000141.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 112 lines, status machine
# Lines: 112 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.

28 Fel. 1691
in Hyperbola primoria est D y = aa: x e dy = - aadx: XX et dx + aus = dx a + X B. X
sid x -  +bB et X  a b =+ h3 + 46b a + 6hb n + 4 hb 3 = b  2
+qu+6dce 4+ a
= quadrato ab stgatma =se f + 2fgn + 2f m H
fiet. S: Sk ta e et m - b + a
et
+ gy n + 2gmN + n 
g- 4 2h +2aeC,: (h4 at  -  hbt ace,: t
2th +aC (b+ + 4h+ 8ha ce + 4ace: D a   6kb 6a c
quibus propribus aequationibus duabus solatis utcunque, problema est etiam in irrationalibus
habetur quaesitum, adsunt autem literae tres in effectu in determinatae
faciendo Dh2+ la Ce = o-gn fiet C = - h: 2C et b = (a ch: ac =) h: àc
40
ex 44
 it.
16 12 20
ax
224
40 1121224
e +364h: ac
+ah PK + h a K +   = gh + 9a  + 18a  23
x= h + bn et X+  = h + 4h Bn + 6FbAN + 4h bN + Pn (XX = vaet axdx- ava
ce t en
444 set dx = ava: 2 tra
ac44  ent6ac en +4aen + a en
et Xra aequand. quidut ab fupn - f 4+ + 2fsn + 25.  R + 29m N + m n av+ va = vr coco
sit f= h + a c
et m = N + q eF
42
12 18
et hb = + aC t b: a c8
18)
17,6
postremo 3h  + 3h
X: a
+9m
et C = - n b: at 6 posito g- d
+R 3sd.
ad seu R: C = a
seu 3h + 3 l  Th + h2 + h2 + f2 = 0
 faxco
quod non procedit Ergo non licet facere
fb=h + aC
120
1618
seu 6+2 K =0
M = ,b+ a. ~ 2h b + 2aC 2hb f2aC
6h = +ba 256m 10
quod sufficit ad solutionem
h + a 
b + at
quae duae resoloi possunt in numeris
rantur edy. Ergo dutu et xyix set ssa ex
lur Extdus
ergo datui et sxhya = SX a +X da monilsumesra
faciamus _da +x a: X = y habebitur syda ex datis sydx jam a txa = x y
fiet X = a: y- a et X = a  aVa. Y a. Tantum opus est ut ex
a possit extrchi radix quadnato quadratica
rydus = av alia et Y - a =  = l + 21 n B + 2l’ n v2
Sar a = 5). 5y - = 5 .V du: p sx +1
y-   t . (+ m B+ nV
PEAB+ v
con a ida pe ae sax iX
+ mt V + 2m n V + n vF
ao v. sit  penient ex - a p - ga V - 6a p v - 4a pv - a Y
aequani quto ab AF + EB =
 2aqV - a v
ar +4+ 8v +6YSV + 4rSV + st V
r5 = l. Znt m- a 
Pr = 2Vm: a - 44p,: 25:
Ss-a 24 mn - 4a p : 2 (n, ete
ergo 2l m - 4 aap. 2m n - 4a p = + 3, (n + m - a p (
ta -  pata et Wlat B 2Vm - a p a = 4 5 Pn + Dm - a p 1 - a p
Suk. a 10
et
F 2amn - 48 p = 4 5, (3n 7  m - a p an - at
Hae tres aequationes si solvantur a numeris rationalibus vel
ircationatibus habebitur quaesitum
X+a) = (X + a  2aX + 2X coa + 2 Co u co fiet X = + 22c0 - ac0
2aco 420
cov fiel
+2a2 = a c0 = 2C00V + 2acov usi datur quidem divulsio sed no ex hibet solutione
indetermnatam  Y-  B bm + Ca. et Xa=
dia ra 0- 3b+ DC sa Bnd a 1. 6 be  6 a p a anve fit nt i n-  na 0.a
M
a bm
y- a = v: a
se invile un
vr a
qaeato
a -da a
s  2ha h. aep
adct a5c6
S. Va+X x:X fut
lata dx:x-a tdo
qel avtra d
 con
a + v= co
quod non procet
p FV + V
debu quib
ebma
sit - a gytus
amb-e fiet
C = p = qui
ergo c-42
i quare gato eo
reduxcinus,
oportent
- naae quare
conto