# Leibniz Legible — https://leibnizlegible.com
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# Permalink to this reading: https://leibnizlegible.com/page/175906937X:0209?run=74
# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 185, page id 175906937X:0209
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=209
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000209.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 68 lines, status machine
# Lines: 68 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.

luetr d
et qu.
dett, 12.
nibiden
a Calio
perbole
BlDe
C AIgm.
lllctu
HAB
Det vul
ad
M
ITTeNS
produc
UETINGI
Derooluto
Dicola
FBC
Ata HC
Isgimpu
HA
lUI Ls
BC6.
1
L I B. I. C A D. TI.
185
Alpeotorum alteruet parallela essec, aue, si rel huie vel illi
A(ynIPEOTO exCSICMI F A F OCCurrereE, ex puncto intra an
gulum X A eI ad verticem ei qui TErperbolam continet dueta
hanc relillam A(ymprocon lecaret; ideogue = CUEVR In UNOFAN- L per 2 (9 3
cum puneto non rero in duobus occurreret, ac producta candem Cor. 3 hujus.
Fecaret, non autem uerinque extra LIy perbolam caderet, contra
Id quod ponitur. Ac proinde constat propolitum.
I HI E O R E M A V.
Propossiio 5.
Allumpeis, vel in una cademque, vel in oppolicis
Eyperbolis, duobus urcunque punctis, ductisque. per
eadem lirc una rectâ sire duabus, sibi mutuo parallelis:
crunc rectangula sub ducta vel ductarum parcibus, IIy.
perbola e Asympoco uerinque interceptis, ibi invi-
cem xequalia.
Sine, vel in cadem, vel
in oppolicis Hyperbolis
BPCD, cujus AIrm-
PEOLI AE, AF, acum
pea uccunque bina pun-
Eta B e C3 aC Per Ca-
dem duetxe bina rectae
BD, C P sibi invicem
Parallelae Asympeoci-
GuC OCCurrenteS In Pun-
etis F, F, G, HI a: dico aquiurique
rectanoulum E B F rC- OCCUrTuS in
Etangulo GC II aequale casu primX
esse.
EDurae AE
intra angu-
Ductis enim per ca- lum E AF,
Per a hujus
dem puncta B e C rC- , per 16 sex
ctis, utrique A(ympEOtOti.
Parallelis alteraque A- = Per 3 Bc-
jus.
outa IBL _ AOHIS a gunta, ac L2 un A C, hoc CA3, utF B mi, e a
2
ad Sexti.
Crmptoro terminatis, BI, BL, CR, CM: eric, ProPter rectan- 3 per 29 pri