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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 83, page id 175905688X:0105
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=105
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
# Lines: 39 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.
# 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.

DOr
ell
+0c.
X, lat
2n
5DO
6∞0.
1,0
L C6.
Proble
Opo
duca
ad LL 2 L. B LLaSi
versis B, sic aequalis ipsi NB. DOCCE PappUS, quod, rum reclas-
poltquam primum lacus BD productum est ulque in 7, sionum.
ItAUED Caquetur DN, circulusque descriptus ett, cu-
jus diameter B C, producendum deinde cantum (ICla-
cuS AC, donec circumterentix hujus circuli OCCurraE
in puncto F, quod requirebatur. Oux lane constructio
inreltigatuiis, quoslateret, difficilis latis Foret: Pcc-
nim quaerendo illam persmechodum hic proxolitam,
nunquam certe cogitarent allumendam esse D CF pro
quantitate incoonita, sed porius CF vel FD vel CP:
cumhae tales sine, qua facillime omnium nos ad Aqua
cionem perducanti se dad Equationem quae non ica ta-
eile absque regula, quam jam expolui, explicari postet.
Duipreponendo a pro BDvet CD, cproBF, _xprO
DE, HEC F ∞ a= X; ECuECFseua =X CA ad FP (CUC,
SICFD Seux est 2d BF, qux proinde exit-
. Deinde
propcer criangulum rectangulum BDF, cujus unum
lacus estx, _ alterum a, quadeata iplorum, UEPOLC X X
=aa aequalia sune quadrato balis, quod est
CC X X
Vnde multiplicando EOEUII PEF X X - 2 AX. 1 a a, in-
remeTUE AE QuaTIO Xt -  a ∞3 L a a X X -  a3 X-+ a+
D C6 X X, Vel X+  a X3 F 2a a
C0 N N  a X  at ∞ O.
V