# Leibniz Legible — https://leibnizlegible.com
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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 193, page id 175906937X:0217
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=217
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000217.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 71 lines, status machine
# Lines: 71 recognised, mean confidence 0.84
# 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.

quoque
deunque
apuneto
n ducta
sperbola
C AP,
Hyper
Ierlam
camque,
S Term
COnt
que H
ermine
ipli per
VH, sC
aE VerB
ccunda
rectu
dieme
Oppot
dam dia
IuSaCalui
L X B. l. C A P. II.
193
oncarum Fyperbolarum IC, LIF..
quarum AEymptori BC, DF, diameter eran verlauccunque al-
minum P ducta recta FP. O poralle
la ip(i BD, qua Curram IN ver-
tice C contingie, ita VEHXC AE-
que illa Asymprotis occurrantin
punctis B, D d P, C: dico prX-
dictam quoque F F. C, oppol
cam FIyperbolam continsere in
E; ec li per centrum A ducatuF
secunda dinmeter AK, diame-
ero C L conjugata, ordinatim
ad eandem A HE applicatas ip(i
CF diametro aequidiltare.
Ouoniam eniin eAt= FaIM AF. 1 per 29 pri-
ad F C, ut AC ad C B, quam mi. e 4
A F ad F F, UE A C ad C D; et Sexri.
LUINEEAI AF, A C = quam CB, 2 per 1C0-
CD3 aequales, erit quoque + rol. 5 hujus.
3 per Ghu-
ta E C ipEC B, quam L F ipCI jus.
C D, dc proinde _ LC ip(I F F. + per Y 8
quinti.
aqualis. Unde s recta F (7 Op- 5 per 6 tou-
policam leperorum lLCominset in puncto F. Quod primo jus.
loco propolitum suit. Porro li per C de D ducatur recta GD, sC-
cans secundam diamerrum AK in K, oppolitisque Hyperbolis
occurrens in HI d I, cum aequales ee parallelae lint L (7, C, D,
erunt ec quae iplas conjungunt GD, C F parallelae  aequales. 6 per 33 pri-
Ideoque cum secunda diameter A R contingencibus BD, FC, id mi.
7per 3COr. 6
eA 7, ordinatim ad diametrum C. P applicatis xquidistans sIE, UE- Bugus.
Poce ex Fypochesi ips C P conjusata: crunt quoque  rectae  per 34 pri-
OK, EA, ut _ RD; AC, ideoque_ GR, H D aequales.
mi
9 per ICOr. 5
Quibus si addantur aequales o O FI, DI: crun similiter rectx bujus.
Z HI, II libi inricem aequales. Ouocirca cum 2r ad Cecundam 10 per 2Cor.
hujus.
diametrum AHC applicata sic recta LII, CtIaI CXTCTA OMHCS ad i1 per 6COr.
eandem applicatx  eidem FIIac proinde et diamerro C F. X = s hujus.
quidittabune. Quod secundo loco propolicum erat.
22 pen 5146
Cor. StWiuS.
dit Fyperbola svel0
Cumpea C F, Petesle ejus
P.