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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 186, page id 175906937X:0210
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=210
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000210.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.87
# 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.

186
E L F M. C U R Y A R U M
+per 16 sex ad G C, ita C M ad BL, id est, ita C HI ad B F. ac proinde re
Etangula EBF _ CC EI aequalia lunc. Ouod demonstran-
dum Crat.
Fodem modo ostendetur, s per bina puncta, ut B e
D, una recta ducatur BD, qua utrique AImpEotOOC-
currat in punctis E de Fa, rectangula E B F, F.DE. libi
invicem aequalia cAc.
Corollarium +.
In oppors LPeTDONS, Si parallelarum altera per centrum
transeat, ut C P in rertia figura, eadem demonltratione compro-
bacum erie, rectangula sub partibus quarumlibet rectarum, quae
Per AlymptotoS ad utramque curram ducuntur, Singula xqua
lia esse quadrato aequidistantis a centro ad EIyperbolam ductae.
Duare cum ex dictis appareat, si. ducta per centrum rectâ ut-
cunque reluri C C P in cadem tigura; eidem ubiris alia rectax-
quidistans ducatur BD, gux secet ACymprotosin P _ P, rectan-
culum E B F vel FD P. quadrato C C itemque _ C P quadrato
aequale esse: sequitur, iplas quoque GC, G P esse libi invicem
aequales, hoc est, quamlibet rectam ad oppolitas IIyperbolas
per centrum ductam, in eodem centro bitariam secari.
Corollarium 2.
Conseuc queque cusunvet rectae, sire per unam candemque,
sire per oppolicas Fyperbolas ducta, parces Hyperbola _ A-
sympeoris incerceptas libi inricem esse xquales.
Ducta enim uccunque BD, guxe ACympEotIS OCCUEraL In F e
I, cum ex ancedictis,F hic ad D F, uE D F ad B F: erit quoque
diridendo 5, vel, in ponus Firperbolis, componendo 7, BD
per 17 ad DF, ut eadem BD ad D L, ideoque DF, B L 3, ac proinde e
5 per 5 Bu-
sus 910
ean.
Duinti.
et 18
duinii.
d
Duinti.
BF, D E sibi inricem xe quales crunt.
Lidt ouat iit 3.
Unde Pallletcontat, eccala, qula relantus ejuldemque, vel
ollatua L Dclbolalatu. Bin FunelaconsumetC, AHIID a110