# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068172:0023
# Permalink to this reading: https://leibnizlegible.com/page/00068172:0023?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 18
# Folio 12r, page id 00068172:0023
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068172&page=23
# Source image: https://digitale-sammlungen.gwlb.de/content/00068172/jpgs/default/00000023.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.87
# 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.

Ad Dn Ferdinandi Helfrici Licht scheid
WurulaAustriaa concionatoris
Cizensised considerationes de
velocitatibus pendulorum in diversis
circulis
quaeritur qualis sit in curva
(C) cujus talis sit proprietas
ut posita BE constanti a,
et AB vel AC, X, et EC, y
sit yy= 2ax - aa
sit Hoc ita investigabo:
(2)
sit AE 7 = dXX  yy
 seu  X = Z2+ yy
xaeq. 1. fiet yy=2a 1724yy-aa
5
seu y + 2aagy +a = 4aaZZ+4aayy
seu
416
y - 20a9y+ a = 4 a 4Z.
e
ac denique fyu Jaa = 2 aZ seu yynaa - 7242
 est aequatio in parabolam
lacet  quae Du Lichtscheid ingeniose exco-
DF
gitiavt cirea motus ad pondulorum tam per geometriam
quam per examinan expertmenta examinandos
Si sit y = a fiet Z= 0, et coincident (C) et A
ut sit y = 0 fiet yy = + 2aZ + aa = 0
adeoque Z=  + a: 2. si itaque id punctum curva
seu vertex sit V, fiet VA siu Z eo casu =  a
10)
e
sit ergo v = 2a +Z. seu Z= v- a fiet
11)
q. 8, et ex aeq. 8 fiat yg = + 207 +aa, (consi-
derando scit.  ut regulairter majorem quam af
(126)
cum scil. y est affirmativa) fiet yu= 2a0 -aa + aa seu
yy 2av
parabolae
itaque a est semilatus rectum
SSC 35 vot 10, Mr. 18