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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1186, page id 1815201908:1243
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 recognised, mean confidence 0.83
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2106
QV ADR A FY R A CIR CYL I.
am
 ile den
A
t
L
R A TVR
LOFOSIIIOCIIL
 Ic AB axis parabolae C AD, cui xquidister recta M N diuila
 c
per parabolam inC, cumprilq; aequalibus CG, C F; irem CO,
ou de puncta C, F, ita O, S ordinacim ad axem re-
Dicorectangula  GL, L. L. D tore dgltallas irem rectangula POO.
2ST.
Demonstratio.
Eilacenim C. R media incer CF.
GI; _ OX media inter OP,
O9. icem FP, S V medixincer
P F, FD, _ RS, SF. ostensum
aest CK X, ireM CL V esse pa-
tabolas, X quidem CL. V aequa
lem plane bparabole C AD. Con-
curracicaque parabota C I. V cu
aXC AB in Z. manifectum cAt.
R ex Z ordinarim ducatur Z. V
ad axem CNV, aequalem eam F0.
reordinarim ducta ex C ad axem
AB, (cilicet aequalem CB; quare
CIIMI CF Z, CAD paraBOIX CX-
dem sinc, manifectum est aXCS
AB, CN agnales esse. Manite.
cum eA eriam ex construction.
Darabolam CKZ CTanCIEC PeF
A: naM EX A, duCaeUE A HL paralleta G K, eansCE c Ca parabolam C AD, itaque
deer +4. de cum drectanoulom FTGT sic ad quadeacum A.MI velinea C C ad CMI, etiam qua-
dracum C K ad M A quadracum crie vE CG ad CMI. PaTCE ItaqUC CR X parab0-
Ia ExANSIrC per A, ex quidem A MI vei _ C R ordinacim cric posica ad axem parab0-
Ix CR A cum sincad angulos rectos ductx ad axem AB, AC PFOPTerCA A NI ~qualis
erit BC, _ MC aequalis AB, hoc eAt CN. aqualesicaque rurlus sune parabolx
CRA, CF Z, quare e quadratum G K quadeaTO F P, X quadracum O X quadra-
co SV, aequale cric. manifectum igicur eAt eriam rectangula HIGL, DFD, icem
POO, SRT esse aequalia. Ouod erac demonstrandum.
PR OPOSITIO CIV.
Darabole C AD axis SIE A B, quevis aurem diameter C C F parabolam
secerin C; Factis deinde C G, C F incer se aequalibus, vrei e GO, FS,
irem OK, SL. _ (ic deinceps, per puncta C, O, P, 5, acc. ponantur ordi-
narim ad arem OG. 6 h, L. D, R M, et C. lecanres parabolam in R, C., tl. P.
icem
Por 339
BPOFY5L
e cylind
Bodoid. e
C PerYS.
arab.
parab.
 AC GI, F. D; OO, R T