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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1025, page id 1815201908:1082
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=1082
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 51 lines, status machine
# Lines: 51 recognised, mean confidence 0.89
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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IN GVLA PAR ABOLFCA.
2025
dupieata est rations Gua HaDCE ATT ad C G, hoc est CB ad IF, igitur cum
eriplicacaracio BC ad F I, ducta in rarionem duplicacam eiuldem B C ad F L, PrO-
dueac quincuplicacam rationem FT A ad CC, pacecrationem corporum ex ductu
AEBHI _ CDFC, in scipla esse quincuplicatam eius quam haber linca AFI ad
CC. Duodtuir demonstrandum.
EROLOSLLIOLKLAVIII
VInE ABC, DEF Patabola similes de aquales quarum verrices A X
A D, _ axeS AF, D C. Similicer parabOIX G FTI _E KL M, Similes in-
cer le d aequales quarum axes GIE, M I: sic aucem Olinea lacus rectum
quod omnibushis parabolis ad axesinleruiat.
Dico ABC D ductum in AD F. F ad GTTIMI, ductum in GML. K,
quincuplicacam habereracionem eius quam haber AD ad G. M.
Demonstratio.
ais Pe N, _ Polcis rectis BPF _
TTNL, quae aequidistene axibus descri-
bancur parabolae per AB D, EFTM ha-
bencesaxes BP, HINI. critigitur ABCD
ductum in ADPF, xquale a parabola
ABD ductae in sc, e similicer CTTIM
ductum in NLKC, aequale parabolX
C HIM in CC duetc. habene aucem parabo-
lE ABI, C FTM equale lacus rectum ad
aXes quod sc ostendo. DUCANEUT BS, S A
ip(S P A, PB paraHelX ve AS ad SB. RC
SB ad O, lacus rectum, b scd B P, P A ip-
sS B5, S A Cunca qualeS. ergOVE BF ad
ita NC adO, quonam ex constructione
parabola ABC; C FI L commune habene
latus rectum O. sed criam lincae BP, P A
communes uncparabolX A B D _ rectX
TTNI. NC communes quoque parabolx
GFTM. Poicur commune habene eriam
lacus rectum O. FIoc posico; demonstra-
cum estc ABD, ductum in sC 2d F FTN
in se duccum quineuplicacam haberera-
tionem AD ad ETVI. Ioicur eriam ABCD
duerum in A D RF ad GFTTM. duccum
in CM E. K, haber quincuplicaam racionem eius quam haber linea AD ad C. HI.
Duod uic demonstrandum.
luidancur AD, CM bitariam in Pun-
Pa, ica fk 2d0, a teses aue
PROPOSITIO LXXXIZ.
NI ABC D cylineas PacaCU,  IECHO AFCD, HGUTaIII PAIL
aes delicam preltucens, cuctilq: continsencibus parabolam A MI, BNI.
demictalus lecta MC, in qua alsumpro quonis puncto C, perilludHaE
Eectio FC K Patarieta plano ABM.
Dico FC concinsere parabolam FK l lectione per C. taAt 2 productam.
Demon-
e        e e e e   e e e Be e  a a s u   t  1 1 B ee e  e p e 1te B e t  t 1 e  e  te este e te t t e e e e es  e  ste t e e  e e 1t 1