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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 466, page id 1815201908:0523
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P AR A BOF
3
l.
Conslio e demonstratio. erclitoaen
DE ABC seomencum datim: duet aque diatiecto AD
ponatur ordinauum C D, agatur que per A ipR CD.
aequidistans A F, ocCurrens crectae ex C diametro in B:
cum F C dinila in F VE F C quaEEA ParS SIE F C, duca-
EUIFEK A Pet F linea RGOCCurrenS CD in C. dico
EA C trianoulum xquale eNe daco seomonto AB C.
Duoniam AEs C O linex aequidistane, vE C F ad1 FP.
sc OC est ad F A: Sed C F cerria pats eAt F R; ipieur
 CC, cerria pars est P A hoc est CD. OuarE _
CAC triangulum certia pars est crianguli C AD: est
aurem ABC scomencum aequalecerriea parci crianguli
CAD. iBIC d  A C crianigulo est aquale: datoisi.
1
praxi solui problema quo pecteu cu parabola, criansulum xquale extuberi–
R O P OS+ L+ O sCCX F 10C 5i. 
11
d et Et 
Darabolae terminaix cam
incer se Portiuneur ratio
nem quam criangula maxima
illis inseripea. El A R cns:
Demonstratio. 
Ine ABC, FFC parabolis teF-
minacis criangula maxima interi-
Dea ABC, F. FC. dico parabolaS
illam incer se habere racionem qua
criangula ivaxima. Triangulum
b AB C est ad AB C, pacabolam
verria ad quaruor: triangulu quo-
que P F G est ad parabolam F. PC,
vecria ad quatuor; igicuE VE ABC
criangulum ad parabolam ABC.
siC F. F Ccriangulum ad parabolam
EDC, _ permurando vE AB C crianeium ad criangulum L. FC, sIC AB C paca.
eROPOSLTIO COKZXIZ.
Ato scgmenco pataBocoansulum xquale exhibere. ss
lscest i
aitis
ecesic
10. (1 25. _d Ed 3 AB H t
1
1s ede ll
EX Coroit
tuino
cur scomeneo parabolico aequale criangulum exhibuimus; quod eracimperacum.
232. bu-
Corollarium.
Tinc pacecrriangulum C A D aequale esse parabolX ABCB; adeoque eadem
bola ad parabolam F. F C. Quod crac demonttrandum.
Cdblarium.
alticuamesi d  alticuaeStUCKIME d quales, erun incerle rebuleS.
Inc B dux parabolae habeane candem vet aequalem subrenlam, eruncilla incex
o      s u s s so tt s  c u  s  oos  u pa ssemoiso