# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068102:0021
# Permalink to this reading: https://leibnizlegible.com/page/00068102:0021?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 7
# Folio 33r, page id 00068102:0021
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068102&page=21
# Source image: https://digitale-sammlungen.gwlb.de/content/00068102/jpgs/default/00000021.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 62 lines, status machine
# Lines: 62 recognised, mean confidence 0.83
# 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.

11 octotz. 1690
invenire aequationem
 infinitarum
lineam
linearum Ad culveum
curcurum secundum certam
legem descriptilium tangentem communem
seu ub duarum quarum libet ex infinitis
lineis curvis inassignabiliter vicinarum intersectione
corcuatam
 linea
a  sit curva LL quam
linea
tangunt curvi BB, quaelibet. Datum
sinea
aequalio ad curvas BB nam
AF extistente X et FL, y, sit
aequalio y.
mntam x + mb
aa
+aall
quo casu linea BB sunt rectae.
quoritur quae sit relatio inter X et F
pro linea LL. pono autem ipsas lineas BB
variari pro variata linea, qua paraneto
parametro m. Aequationis quaeratur
pro linea 1BB sit aequ. l. fiet, pro linia BB inde.
s
finire vicina: y unq 2mam tam ramtactu mb 
aa
at
et aequationum + et 2. ope in venietur inter sectio communi
sed opottet dari am seu progressio ipsius m. sed si duo
.
psi
seu jam inalite pate 1B, et 2B2B sint sibi indefinite relinae, fiet:
B
tunc aequationes iet 2 conjungendo idem prodit, ac si
q
1
differentialis sed ita ab sola in litera consideretur
ut cdiversificata, quia in princa ilaque si
lineo.  ut
quaeramus aequationis I differentialem, variata solum in
me Et siet G 2m + a x + B = 0. tmjus seu m= -b- ax 2
quem valorem substituendo in aeq. I. fiet:
eme
() b + 2bax taaxX D - 2Xb R - 2axx A +4a X - 2bXaa - 2aXY
J
u 4aaX
uae est aequatio ad curvam
LL
ub notandum quod si abfuisset b. seu si b0.
fieret m cart it rerpro aeqsint r agta
sed inderum quae aquatio  ad rectam. vel 0 vel
2m + a 20 utroque ado sit 6. Nam si X2O
it y aa (per aeq. 1. si absit 6) sin nmtamemtano seque
Hic quaeritur quid mfi
quin dividas
pontietur
oye
si etil