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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 419, page id 1815201908:0476
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PA R A BOL.
Constractio ex demonstrario.
A ABC parabolae atis BD, e in eo pun-
ctum dacum D, oporcec cenero D circu-
lum describere, qui parabolam incerius con-
cingac in duobus punctis: Oporret aurem BD
lincam maiorem esse dimidiolaceris recti. Aac
DE aequalis dimidio laceris rectii ex per Frc
eta agacur F AC, ordinacim ad axem: iun-
gancurque puncta D, A: Tum CenEEOD incer
vallo D A circulus describatur. dico illum
concingere incerius parabolam in duobus
Dunctis. agacur enim per A ContinsEnS AF
conveniens cum axc in P. Ouoniam linca
A F Parabolam concingir in A, _ F D aqua
tis est dimidio laceris recti, angulus a F AI
rectus est; est aucem ex hypoches BD maior
dimidio laceris recti; ergo per pracedencem
circulus cenero D, incerualIo D A deseripeus
parabolam concingecinterius in duobus pun-
Etis: a daco igirur in axe puncto D circulum
descripsimus, Xc. Ouod crar faciendum.
PROPOSITIO CXXXIII.
DArabolam ABC cuius axis AD continsac interius in duobus pun-
cis B ee C circulus HIB C. actaq per B contingence parabolam in B,
quae axi occurrarin F, ducatur exF, linea FHI, Secans circulum in G e
HI, dein per C e FI, normales ducantur IEOI, N EI L. OCCurrentes pa-
rabolae in K ee N, axi veco in l e l.
Dico eseve HL ad 61, sic NL. ad H1.
Demonstratio.
Ccinsic in B e C, d lB MnCa Pet B ducta p2
taboram in B concingit, eadem B F circulum quo-
que concingic in B; ipitur ve HIF ad FO, ACDTIP
onde L A ad AI duplicaca habectacionem L A ad
AI. duplicaca esiationis FLN adRI, igiturNI
est ad K I, ve L D ad. DI, id cA LHT ad C: I. Ou0d
cras demonstrandum.
Voniam circulus B G C parabolam irteus con-
eR ad PC: eE VE T E ad F L, SC L D ad DI; Ced ve
F. F ad FI, siC F HI ad TO, igitur L D eAt ad D I.
veTHI ad TC. quia vero I. F in D ec B exrrema
ex media rarione proporcionali divila est, d FF
cbissecta in A, proportionaleS TunEA AI, AD, AL.
D e idCACLD ad DTVICaSATO quoque L A ad
PROPOSITIO CXXXIV
ISdemposiris:
to tectad Lut Ci lentit t eemlerte aqllaled
852
630. D
circatu
omibu
Demon.