# Leibniz Legible — https://leibnizlegible.com
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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 267, page id 175905688X:0289
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=289
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000289.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 51 lines, status machine
# Lines: 51 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.

NIND.
cip
Mapo
1n II
H
a1A
Cireu
a
U
O_ M LHT ALIE IN LTDRUNIL. 267
Duibus sic explicaris, ut ad propolicum redeamus, atque re-
etam, qua Trochoidem in dato punctotangae, ducamus: lcien-
dum elt, lineam rectam, transeuntem per punctum dictum, de
punctum, in quo rota balin, dum punctum in Trochoide datum
describitur, concinsit, secare sempertansentem qua litam ad an-
gulos rectos.
ETch inrenienda siclineare
eta, tangens in B curram (-
re Trochoidem ABC, de
Scriptam super Ba(in AD per
punctum aliquod circumte
TentIX FOEX DNC. Super ba
Ein AD circumrotutX: OpOF-
rec tancum per punctum B
rectam lineam ducere BN.
Parallelam balI AD; _ dein-
deobNV (ubiroca occurtse) ad D, (ubi rota balin tangit) rectam
ND; cumque eidem pataselam BO; ac denique huic perpen-
dicularem BL: Oux erit cans ens quaelica.
Cujus reibrerem acque simplicem demonstrationem aferL. UE
sequitur.
Si super rectam lineam circumrolratur polygonum aliquod
rectilineum, erit linea curra, quae per aliquod ejus punctum de-
Scribitur, compolica ex pluribus circulorum portionibus, quarum
cangentes ad linsula earum punctanormalicer secant lineas re-
etas, quae ab ipsis ad puncta, in quibus polysonum, unamquam-
que portionem describendo, balin contingit, ducuneur.
Exempligratiâ, si facia-
mus ut rolratur HlexasO-
num A B C D SuPCF sC-
Etam F F C D, delcribet
punctum ejus a, lincam
curvam E. FTIA, compoli
cam ex arcu LFI, qui de-
scribitur, dum Flexagonum
hoc concinsit balm in pun-
cto F (quod ejuldem arcus
baL (cuscto cenerum eAt punctum C1); ue
t 2
_ ex
eAECCHETUMI); ee ex