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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 149, page id 175905688X:0171
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=171
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000171.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 58 lines, status machine
# Lines: 58 recognised, mean confidence 0.81
# 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.

ut
2
exilli
visione.
Deiensd
lucando
boCcrult
atCm, AI.
iCataM.
QuaNEII
et C, tC
e
DecC, lB
t illim p
Ormdt
illolu.
cocte
natural
endent, 
e5 MMBaH
sunt 1
=bec
bABIsI
verunt
SOH MLL NZARTI EN LIBRUM L.
P R O B L E M A mum.
T49
Atam rectat lineam AB, uccunque sectam in C,
ita producere ad D, ut rectangulum lub AD, DB
Comprehenum, aeguetur quadrato rectae CD.
Conlidero rem relue jam La-
ctam, hoc est, suppono rectansu-
lum AD F F aequari quadrato
CDOHI, quod taciendum pro-
ponitur. Deinde, cum omnis
quaestio Geometrica eo reduci
Poltut, utnon nililonsitudo alicu-
jus vel aliquarum rectarum ex aliis
rectis sit quaerenda, e nemo non
videat, ad ejus constructionem tantummodo quaerendam esse li-
neam BD, omnemque difficultarem in ca invenienda esle sitam;
nomina impono lineis eam datis AC, C B, quam quaelica BD.
Proinde, prolinea A C pono quantitatem cognitam a; pro C B, b:
atpro BD quantitacem incognitam X, HCEquC AD a L b L N
CD autem b L x. Ouibus peractis, ut ad Aquationem perre-
niatur, de habeam rectangulum AD F F, duco AD, hoc ett,
aut b. f x in D F seu DB, hoc cA, x, quod proinde erit a x 1
bx. L x x. Similiter uc inreniatur quadratum CDGII, multi-
plico CD, hoc est, b. L x in sc, hetque bb F b x L ~ N. ITa UE
habeatur aequatio a x L b x + ∞ x ∞ bb - 2 b x L ∞ X. Ad quam
reducendam tollatur verinque b x ec x x, EIC ut ex una parte rema-
neacax, de ex altera bb. F bx; cum transtatob a ad alteram par -
tem sub contrario signo, etit requatio a x = b x ∞ bb. Cujus uera-
que parte dirisa pex a -- b, provenic x ∞ -,. F quibus paTCE,
lineam quae sitam B D inreniri per divitionem quadrari linex C B
perexcellum, quo linea A C luperat iplam CB, vel etiam per
hunc excessum, eanquam primam, ee lineam C B, tanquam (c
cundam, inveniendo certiam proportionalem BD.