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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 212, page id 175905688X:0234
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=234
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 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.
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# After the first blank line: the recognised lines in reading order, one per line.

2 I2
FR AN OES CF, Q SCHOOY F N
Ouod iptum est; quod ab Apollonio est ostentum Theoremate
decimotertio primi libri Conicorum. UIbi docet, rectangulum
quodris, sub recta NF. Seur Sc inventa, de diametri segIEHEO F I
leux, quod inter ejus rerricem P de ordinatim adplicatam FI
incerjicitur, comprehensum, minus rectangulo NOP, quod sub
eodem diamerri LeGIENEO F P vel OP, de lined NO, ad quam
OP eandem rarionem habet, quam D F ad F N, ContinetUE,
quadraco ejuldem ordinacim adplicacae FI esse aequalc.
Eibi notandum lineam F. D, Sectionis diametrum, ab Apollo-
nio rocari Latus transverlum uc e Diametrum crantrer-
Camm EIlipliS, _ lineaI InVeNEa NTF. Latus rectum, vel
etiam Lineam, juxta quam poltunt, qua ad diametrum
ED ordinatim adplicantur. a Msydorgio aucem haec linea
NE Parametex appellatur. Oua porro linca, ue aute in Hy
perbola, poltquam linea FS ipli AC ducta est parallela, bre-
vius obcineri porest, si tancum ipsiS BM, M A, AS F quara-
cur quarta proportionalis: quandoquidem haec semper cadem
existic, qua ipsaNE, inventa, ue supra. Sicur luperius à nobis
in Fyperbola es occensuIm.
Fix his porro facile liquet, quam inter se racionem habeane
quadrata ordinatim adplicatarum ad diametrum in unaguaque
vide fou- harumerium sectionum. Fcenim liin Parabola linea P. D voce.
FaM 1.
Tur Z, ee ordinatim adplicata CD vocetur v, erit, uE Cupra,
ccdZ
 Dvv: ac proinde yy ad vr, hoc cA, HF I ad BG D, ut
ccdX
ab
1 cc42
2c
 sCux adZ, hoc est, EI ad F D. HOC eA, in PX
rabola quadrata ordinatim adplicatarum F L, C D inter se lunE,
Sicue linca FL, F. D, quae ab iplis ex diamretro L D ad verricem
E. ablcinduneur. Quodipsum est, quod docet Apollonius Propu
Eoma sibri ) mi COnICOrUI.
videlig. 2. Fodem modo in fIyperbola _ Flliph acceptd pro P. I alid
X 3
magnieudine quaii ante, ut puta Z. eric in Llyperbola vv D
de in EIlip(i vD ~ acq2 = a CZ2
a c92 = ac22
Unde ry ad vr
3
in typerbola Hic, uc ac qu. + ac u x 1d acq X. + ac 2 2
4 X -L X X ad 9
1
3b
hoc ett, ut
.Zi ac in EIipl, _t acq. ~- acH  9d
11
PIO
Gulos
taci
Parabe
admod
beria