# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:1270
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:1270?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1213, page id 1815201908:1270
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=1270
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00001270.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.88
# 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.

QV AD R ATV HA H Y PF RBOL H.
PR OP OSIT. 1,OCA XAFII.
Tonsruantur aaocemata, unum quod circulari eplindro Tubseruiae
arcerum; quod cylindro hyperbolico. Consructionoro veriulque
hocpacto Aac. lrio alx aequales parabola constiruanvur ubalcerne po
sice ad communeutaxem, in alcero vero loco parabolarum lubalcerne po-
licarum anr pacabolx parallela incer se licur libro de parabola dictum
cA. Cincq; illa palabolx in veroque secmace ABC, DF F, quarum axis
communis M HD. Deindearibus aequidistances ponaneur CG, III, guX
ab axibus distene ae quali inreruallo. RANEPEXTerCa GSI, R II ordinarim ad
AXEM AD _e duCanEUE A C, D T constituences xquales angulos cumaxe
AD. Denique construancur parabolae D NS, AL. C quarum verrices sInE
AeD; e contingant axem in ijldeni punctis.
Dicorectangula L. MIN, OM P; IEM HI essc in concinua proportione
in veroque scemate.
Demonstratio.
DScenTum enimA L NE, ONE RN, itEM MPY, ML P, ME esse proporrionales li- numm
ness. lssicur per demonstrata libro de prosressionibus propolcione s8. eciam re-
ctangula L. M N, OMP, RMFI proportionalia lUNE.
PROPOSITIO CXXXIV.
TIdemmanentibus:
Dicorectangula OMIP, BM O, KMHI esse proporcionalia.
Demonstratio.
DEmonucuimus proxositione 29. de quadracura circuli hanc iplam proposicio-
22.
nemsled praecedeneous suoue immediatis b ostenlum eAt linCaSOM, BNI, R NI, b123. Bu-
a ME, MO. M ET proportionales elle in scemacchyperbolico. Igitur per ca guxe si- ius
bro de progressionibus lune demonsteacac etiam rectangula OM P, BMO, RMFY CProp. 58.
proporcionalia lunE.
eROPOSITIO CXZAV
IIdem denuo manencibus:
esse inccLeproporrionaa, veretiam Cune parallelepipeda, super rectan-
gulis  e L, M, L, dM, RI. Tub eadem alcicudine rectae MR.
Demonstrata.
Dicoparallelepipeda cua lapet oisclato LIr, l3, M,
R T _ KMI, RI conttruuncur habentia communem alcicudinem MR,
roniam demonstrarum iam dest L. MI, OA RMI, de rectaS R S, R F, R F PTO- APCTILI.
ex L H InRS, OM in RI ec RM, in RI. lunc aucem parallelepipedacommu-
Lporrionales esse. Poitur eriam rectangula proportionalia Cune quae constrnuncur huius.
nem habencia alcicudinem inter le rebales. Quare cum bales perhibeantur propor:
cionales, etiam parallelepipeda proporoan , Suotum illa bales lunc. Lodem
modooltendicur parallelepipeaadea alestectanguaMil L,DM, LER. d
 RL a Comm   R proporcionalia esse, constac iraque veri-
hasplopdacionis.
Sa    t       p   e  1.  e . e t  1  t p e   p .         tu t t t t i