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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 123v, page id 00068124:0248
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=248
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 112 lines, status machine
# Lines: 112 recognised, mean confidence 0.79
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

s
(L Hincatiud notabile. si et) sit curva, intervalla
4
tangentium ab ordinatis in axe BF
applicentur axi in BL, (B) (L). et in punct
L, (L) ipsae BC, ipsis BL norinaliter
applicentur, in LM, (2 (M). erit curva
spatium LM(M) (L) L spatii C7
iplum
ABX BC+ y H a EA AE, YAB. EF BBC
erit C
ergu XF Z. et EF
aesi
g. 
nempe
ABCD.
+Y
quadrilineo CE Mc duplicato unde VCBE+
per puncta B. C. F disranseunt rectae Lndefinitae, BL, CM. FC
l
e
s
 DGK, transferatur
FA ad X9. erit spatium DGKgDO duplum spatii
BL ad DO, CM ad GD.
casus, quo BCF, est lince recta est illo qui tat therrema quod antea consideraveram
BDGK 1 FC B.. Cujus Vheorematis
Alter casus fingipotes, simplicessimus quo fingitur DGK linea recta qualis RS.
D, ubi cuurva BCF cum langentes BD, CG
DGK repraesertanti in punctis DGX. et transtatis
gratium ODKGD
ralii BLK
et
X
sit in eon rem
X occurunt rectae RS curvam
BL, in DO, CM in GP, parallelismo servato
CB duplum. nec refert quem angulam adeas faciatrecta
Rs. em Nec refert sitne curon con BCF concava an convexa, vide figs.
ide plura
2au octobi
1
Hsperbola memorabile quadrilineuum CBN MC. aequam hic
sit alia curva DGK, cu in punctis DG,K cin in punctis D. GX langenses prioris
tam
ut DL, CpM, KN sint lungentes curvae D
alia figura
ert
Ep 2X
2a unde illud ruifin
revrema illud intum memorabile, jam video non nisi Casum esse uncum aa simplicissimum generalioris, insprcefiguram 
 sit curva _ BCFI, cujus laterm infivite parda BC, CF, Li S
ECFG, HFIK occurrant
. ubi et
illudamolatur, si ordigatae acuva BCF, ad recto RS ut FY quae sunt
scitficet aud angulos, applicebitur ei dem ad angulos
langentes currae B
in
W. erit spatim 
t
ABB KFCB duplui
a.
et
ubi
sH jt
rectos, sed ibi ubt curma
RSVW
ipsius 
.Quae mita alis thcorempla f sunt et
primm in figs. 4. Cujon BCd. longentes BDCH, B
APE K9
spatium
qavallelae et aequales DoB
ODKQ PO duplum spatii K.
C1
et Do
LB, MC, FN. er cura
FK I
BCF
sit vigs. ABCF quadrens circuli cujus centrum R. N
erit DLD ad LB, ut LB ad AX. sive LD+ a prti NL erit NDd
ubu
et La
D y+xr
que
a
q2
x
= X  v.
NB tonstutae ad LH sunt ad Hypertotum
simplicissim) et ex stocharnctercistito longentes insistentes arcubus, aequantur portioni iuperbolicie seu sectralibus
675 C ad axci. sed hoc obler. jam et perum
arl
XB.
et. DOH Sae-ad
Commensurabailis sive. a+
patia angulisivumo genea sunt
s
si =b, transferitur ad D0, eum sit  a  et ZHNd a ent
s
a TI a5Z- a, et currucum aequatio: 72C
L r
alaco H 2 sive h
Sa co
e
st
2y2
4.
taZ -a, euit harculo
7. perdet ex inculi quadrotura et et illa ipsa cujus
2 videl elissil 24. octobe
.