# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:1180
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:1180?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1123, page id 1815201908:1180
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=1180
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00001180.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 recognised, mean confidence 0.91
# 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 ADR A TVR A
CIRCVLI
in a cories concincat rationem pacallelepipedorum ex I in NV, _R in 9, 2d paral-
selexipeda qua Hunc ex L. in P, e Min O, quoriestaec ipsa racio continec rationem
parallelexipedorum ex A in H, et B in F, ad paralle lepipeda orca ex ductu plani C in
C, e D In FI. Duod Fuic demonstrandum.
Corollarium.
TEmalciplicentur MoroIX demonstrationes, propolitionem pexesentem exrendi
voluntus ad casusoes qui alcicudines horum parallelexipedorum bifariam, vel
quadritariam, vel lecundum quamcunque rationem in parces ae quales diuiderenc, ad
mulciplicanda rectangula gua in aduerlae fgurx rectangula ducta mulciplicareHE
quemcunque numerum parallelepipedorum: nam discurlus demonstrationis vnus de
idem semper occurric, reiproposicione 8. huius est demonstracum.
P R OP OS I FIO XL
Dico rarichrem Colidi ex ductu plani parabolici R S in planum pa-
rabolicum X Z, ae losidum orcum ex duccu plani parabolici concaui Y V
in concaltumr Patavolicum Z e, cories concinererationem Colidi quod
nascitur ex duccu rrapezii I IE in crapezium NO, ad Colidum quod Ac ex
craperio L. M ducto in craperium PO, quories haec ipla ratio continet
rationem corporis ex duccu varabolx convexx AB, in F. F parabola con-
veram, ad corpus orcum ex dueru C. D parabolici convexi in CH con-
vexum parabolicum.
Demonstratio.
Stentum est proposicione praecedenci ex Corollario quodrario mediecaris hou-
raruminseripearu cerrio lchemaci ad alceram medierarem Agurarum inlcripea-
rum, tories corimeac racionem mediecaris figurarum se cundo (chemari inscripearum
ad alteram suam medietarem, quoties hec ipla racio concineerationem medictatis A-
surarum primo schemati in Ccriprarum ad reliduam medierarem, e quia hoc iplum
Temper heri porestiioicur cum cerminis iltius progrestionis qui in schemace vniuerlali
sune clZ _ DKZ rectansula, conneniat eadem propriecas. e racio rectanguli
FTa adrarionem n K C acories contincat racionem rectanguli P L a ad dR V, quo -, vet
ries haec ipsa rario continecrationem rectanguli F IB ad dK FI, per propolicionem huius.
universalem libri de ductibus quadragesimam sextam, eriam ratio solidi ex R S para-
bolico in ZY parabolicum, ad Colidum ex parabolico coneauo T V in Z _, tories co-
rinecrationem Colidi ex crapezio TK in NO, crapexium ad Colidum ex erap CZIO
TM in PO, quories haec eadlem rario continebicrarionem solidi ex ductu parabo-
lici conuexi AB in P. F, ad solidum ex ductu paraboliei C D in convexum parabo-
licum OdI. Quodtuir demonstrandum.
VlirisCIII.
A   e            1         e            u     u  e