# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:1139
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:1139?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1082, page id 1815201908:1139
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=1139
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00001139.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
# Lines: 50 recognised, mean confidence 0.89
# 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.

1082
a1B. hyib draris L HI, N M, _ reCSS L E_L AS sumpeis, hoc esta rectangulis PLO H
deaca PM aequalia sunc rectangulis PL 9, LNV una cum quadraris NM. ablacis
icur communibus PP 9, rectangulis ec NM quadracis, remanent rectangila
PNMbis Cumpea aequalia L NV. Cediildem rectangulis L NV aequalia lune quadea-
ca NR, quodNR lincrectae ad diamerros circulares LV. Igitur N R quadeaca x
qualra lunt rectangulis PN M bis sumpris. Quare rerectangulum PNMad PNNI.
hoc est VE LInCa NMTad NTM, hoc est vE N B ad N B, ita est quadracuM N R ad N R
quadtarum. quare BR P, sectio parabola est. Ouod erar demonstrandum.
ROPOSILIO CLXKXI
IE ABC conoides conolD DE F, alymprorico inclulum, Fact a de
indelectione D F. F per comistunem axem coni d conoideos, hat al-
cera CtIl atimpiore Gulde C. L a quidictans lednormalis ad planum
Diectas palarab ete palaltelas seu saudere communilacerere ct0.
Demonstratio.
laE SECTIO LM N paralIela BaH exhIBCHS I
conoe conoide circulos LM N, OP O _
producens in plano GFTL communem inter-
lectionem R MI, que, quia est communis seccio
duorum planorum LMN, GFII rectoruM
plano DEF, eric r9. vndecimi recta plano
D F F, ac proinde defin. 3. vndeciminormalis
ad lineam N OOL, reccansula igituIF NRL
ORO RGUanEUE quadEATIS RMI, RP. pari aF-
Sumento reccansula FHID, CH A xquantur
quadeatis HII, HIR. Ouare cum reccangula
NOL. FCD sinc differencie brectangulorum
NRL, ORO AE FHID, CHIA, crunc quo-
que cadem rectangula NOL, FCD, differen-
FIX QUAdEATOTUM RMI, R P d HTI, TIR. AEqui
rectangula NOL, FCD exegualia sunc. Igi-
cur excectus quo quadracum R M superatqua
dracum R P aequalis es excessui quo HII qua
dracum excedie FTK quadrarum. Punc igieur
per ca qux lib. de parabola diximus s parabolx
BIIR e OHII parallela, saudentes eodem
lacere recro ad communem azem. Ouod Fuic
demonstrandum.
EONOTDES HYPERBOLLCVH.
comtingenti, hoc eA BZ, hoc estrectis 19, erirgue quadeacum P MI xquale qua-
ut cum qua icaris NM, _rua cum rectangulis P NM bis sumpeis. led criam qua
D E F exhibens parabolas BFTK, GIII.
PROPOSITIO CLXXZI
I conus rectus asymproricus AB C lectus plano per arem exhibens
criangulum ABC, de Pau O PTaHADLF, CHIL hormalilet
comnuca dd planum se qualu communes incersectiones FD, II6
cumcriansulo AbC agaae laleliDe.
Dicopalabolata DLFMPlGEC
ab alymproco BC.
mor