# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068064:0022
# Permalink to this reading: https://leibnizlegible.com/page/00068064:0022?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 19
# Folio 11v, page id 00068064:0022
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 10r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068064&page=22
# Source image: https://digitale-sammlungen.gwlb.de/content/00068064/jpgs/default/00000022.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 110 lines, status machine
# Lines: 110 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.

t
summalis ver, curvam
 fiet O= h sdo s6b + net
2 Vcvrie 10B
 Quaeritur D (6)  F (∞x de
DI. fn fag m. B. av
v-
I+ncoci  sit coco = cvrea et du = cdv. Etex
(dco H
ve in
seu 0- hes do ter
drax
Abb + n cD
b iblac ecV -a VB
aaee +bbCV
fiet sit Xx = ag + imv et fiet  nar
(10)
nrpid
sit  ∞ D. fiet m = (4) C Ergo;  n = (+
+a- 2agmv nup
-aag9
C 151)
lag sed bb  24 (+ pag. seu b = 2ac + rag
rursque bb = pag - nea seu per. 13, bb = pag(+) pea. Ergo
sit p=
2 Vagtmr
spq Hmo
seu D =10 = fm (av S
agamv. Va-Eg aagg- ragmv-mnivr
(1277
14) 
2aC + bb=
metuus
e
ys c
(20)a
(+)2. postemo (22a eB () 2aa e9 aa e = a - aagg
fiet  ac +ad= laa
fe (+) Ag = saa. Ergo fit
per 16 et 21, b - 2a sed per 16 Ero b tra taa. sed
ex 21 fit 4)g = a
e
et Ex 19 et 13 fit n =
b2 a12 et
e2 
datum s
debet p esse affirmabiva ob tp. Ergo siet
(161
porro
per 19 fiet
=2 et (+) = et n -2   et m -c et etgus a
es debeti esse  ag+ mo quantitas affirimativa, seu ag - cv debet
posita  . XX
esse quantitas affirmabiva. 
 perro _quaeramus jam
Hyperbolam re punctum conicae respondens ad punctum
carva quadralidae.
 per 7 fit et 38 fit v +
VEag  = 1Xx. Ergo per C fit  co = taq = XX. id est per 29
+ ea
fit coco = aa - XX porro gy aco ut 
(34) H
porro yy 4= L r9 + C0C0 ergo rjus =  Ne + 19. 4 4 7XX
  Xaa
sit porro bb = rq.  94. 4 = 6 (per 23) auc 24a, seu 9  q a 2t2
N =
+V-4 seu per 25 et 3b --  Y urg. (9 = + rCD seu  r +9
seu per 2. r= + a212 Ergo ex 34 fit yy = C41 +arc, art 4 ; +g. XX
1 +.L, +9 aa
seu y- aa -xx Y quod est altudum. u Ergo est iimpossibilis est Hyperbola
summanda ddd0 = Dd0 -0d
de qua agitur. sed quarum curnam
2 et 13 = a pe carz. m. vit
x,  n: W =  a xx. a- X 1d = 2d+ dx G 10-
EF curari seu dW 2xa eax (X + X
a  1a- x
EF: toseu ar: : dW: dx d:: 22X,  s 
A9 = _ A Hg = n 2B=  X -, 5t
~x
H, fiet XX - 2X  +M F N-
BH _ BH: QH =  B a- x: 4 a’X. seu fiet
4a, Xx-2X2 F M + e e =. n p. 1) a X
unde differentiando fiet
44,  Fx- ixd + H + e + 4 a X. 2. X - s2 = - (n ( 3 X P a - x
seu 14a XX = _ 16XI + 4 a H + 4a H 4a n  = - 3n en X p2 a - x
x-1
ro d
dsaez - a3 = d (rg) ae Z - 4Z = d _ v = et   - + v
et 
se
seu Xadz
LLaZ. a7
seu fad
SaZ-a
adz - 3a37 dZ
21 aZ - a3
== 242 4
m...
3a - 222
2 1aZ: aa 22
2Vu.
= 2 adz. aa 7 - d az- aZ. ht a7- 2 e. fit 2a 4 
3.de Sa - t - d YaZ- a5
du
ade
1h. t - 5. sel g1 17
i aa 2
2 aZ
at. 
2