# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0469
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0469?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 412, page id 1815201908:0469
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=469
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000469.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.

perete
A R A B O L. L
Demonstrario.
BOnacur ordinatim linea B G: ee BD tortmalis ad con
encom P B. Ouoniam anguli F. BF, B P. F ex hypo
chesi xguales TUnE, CrINE e F B, F F linex quoque aequa-
les, vnde cum ex angulus F B D reCtUS LICS RICCHETOF, in-
ceruallo F R circulus describatur; cransibie ais per B et D.
Duare _ FF, LD lincg rquales; adeoque LA ae qualis
bquarexe parci laceris recti. Duod crac primum.
Rursum cum angulus F B D ponacur rectus, de B C ordi.
nacim applicaca ad axem A D, eric D C Equalis dimidio cla
cerisrecti, adcogue dupla AF: quare L A ad F C, VE AF
ad CI, d Coponendo ve F F ad FD) RC AF ad CD:
quare L. D CapIa es ipsIuS F F, d cirCuIUS CCHErO PinCer-
PEB incer se aequales. uoeat demonstrandum.
SCtaG A E x quali AD, aucatur ex D linea D C occurrens parabolae
in C; e ex C erigarur diaerer CF, Occurrens J. F. iqua normalis sic ad
Dico DC. F Olineas ce incer (c aquales.
Demonstratio.
Ciacurper C comtinsens C C. conueniens cum aire
in C; ad quem ordinacimm ponatur CFI. Guoniam
CC es contingens; rectx AC, A FL d aequales lunes
addicisigicurx qualibus AD, AR EOEX C:D, PII a.
quales sine; sed D C recta este xequalis CFD, igitur et
D C aequacurlincx HIF, id est C F. Quod erac de.
monstrandum.
1t 35
PROeOSITTO CZIZ
Darabolam ABC cuius axis AD produ-
crus exera sectionem, lic x qualis laceri re
loBE. A x qualis taFANSMIIS LBF.
BF F, L BF esscinter le alsales.
R SPOSTFIO CXBII.
DArabolam AB C cuins axis AD, contingacrecta quaeuis BL, ec angu-
Dico F A lineam aequalem ese quarea parti lateris recti; _x (I PACE
quarra pars lateris recti, dico lineas FB, FF) de consequenter angulos
penca
b116. ha-
c I2+. hM
11
valIo F F descripeus, cransibit per B ex D; cruncqs linex FB, F F X anguliF BF.
d17. huiuim
c. 117. ha.
aXCM AD) in F.
P R OPOSITTO CXVIIIdo
SeoA B C parabolx axis A B alsualis quarrae parei lateris recti: Fa-
C. lineaC C quae semicireuli concinsac in C.
DicoAC, C6 lineas elle Mut te aequales.
eto, contingat in Alinca AF, demissaq ex A sCCanTE AC, CriGAEUIF exC
diameter C F, occurrens AF contingentiin F, d DF quae parallela Ae
AE IN F, FaCEOGUC SIIDEF F F vE dTaLICILO, CemicirCUIOF GE, duCAEUF ex
Demor.
( us u e e sus        et   .   s  s p 1 .   1  ut           .    t .   1     1  1  1e  . 1  1 111