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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 796, page id 1815201908:0853
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=853
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000853.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
# Lines: 54 recognised, mean confidence 0.83
# 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.

796
V C FYS BL A HL
PR OPOSITIO CZLVII
parallela ponatur diamerrus DP, lancaeque A C. quaenis TK aequidi
Aer, occurrens D Mmex in HI: hanicque CII, C F linea proportiona-
x
les lincis CD, C L: deindeper AI. P puncta parabola M M describacur
Dico NO superticiem ductam
in planum PX, corpus proterre
aequale illi quod oricur ex ductu
MN in alcicudinem OP.
Demonstratio.
TCANEUF quoECUnque reCtRMNO
PZ, Parallela ad L. F. ve CTI ac
GF, AcDC cst ad G L per hypoche-
Em diurdendoigicur vrCFPadHIF, AIC
GD eAt ad DL. ergo LDOHI rC-
ctansulum equalerectagulo DGH Fs
gulis NOt A. Pla si et adctum b ini OP vel in alcirudinem C LI X.
1. (111I
et1 1
PR OPOSTTTO CXLMIII
Nirculo E DCinccripcum sr rectangulum DTK L pohtaq F. C dia-
LAmCrrO qua DI, LK lacera ad angulos secetrectOS, POnaEUFPer C
COnCInGenS C A, OCCUTreNS DL, TK lineisin A e B: deinde per IF. D
puncta parabola delcribatur D N F. L habENSAXCM F C.
Dico POsuperticiem ductam inplanum OR corpus proterre ae qua-
Deilli quod oricur ex M N ducto m alcieudinem FC.
Demonstratio.
VCANEHE vE PriuS quOTCUngne ReCtX M. N
OPOR parallela 2d F C. VE FF CR
ad NTO, SCCD F T rectangulum est ad rectanou-
um DOI; Scd vE F F ad NO, SC F F C rectan
gulum quoque ad rectangulum NOR, veigicue
DFI rectangulum ad rectangulum DOI, Sc
P FC reccansulum est adrcctangulum NOR:
ex PermUTandO VE P FC ad D FiI recrangulum
screcrangulum NOR ad DOF rectangulum.
aequantur aurem recrangula R F C, D F I, Fecran
SulaisITHE NVOR, D OIquoque x qualia CunE, de
quia. DOI reccanonlisd aequalia lune reccangula
MOO recrangula MO Q. NO R aequalia sune.
quare MD estad Na, VE GR ad OG: ec COn
CAs. huius. FC, cE quale est plano M O, id est PQ ducro in planum CR. Quod erac demon.
Arandum.
Irculum AB C dux seceneae quidistances et requales A B, F. C; quibus
cuius axis (IELC.
colliciur quia veto AL E parabOta EA, rECtan BliIa a GUIOqUC M NOP aequalia sunc rectan.
is.tmine. quale ost plario NYO dct0 in P. A. 11715.
vercendo OM est ad NTM ve O R ad O R: recrangula igitur M NO R equalia
sune receanoulis MO O R. ergo MN planum ducrum in alcicudinem RO GuC
d LX C
10bldpto.
ek0.