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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1024, page id 1815201908:1081
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1024
247. parab.
erma
parab.
NGVLA PAR ABOLTCA
VEFECLAHBCH GF MI ad rectanoulum OFTM.
c80a _ tR eHt ad B B, VE L N ad HIF. DC.
inde ob errangulorum similicudinem, OK es
a C B, DIK ad E, B, hiOC CAVEINadHIF
hoc est ve NP ad F C. Igicur rngula A BCD
ad ongulam GF CM, rationem habet com
posicam en racione baleos ABD adt balim
FM, ded alcicudine B C ad alcicudinem
quoatones parces baleos ABD al
omnes pallesbaleos CFM, hoc eA pars balis
ART ad G HL, veI TRBF ad L NFHI
caroen tationem habene quam cota parabo-
la ABD ad parabolam G F M ec alcicudines
DeSVa ABCD ad alcicudines rnou-
ECM, VEBC ad FC, vel RO ad NP.
Scat Lac baleos b ABD ad balIM G F M.
tic
A OBR, est criplicata racionis AD 2d
e ratio BC ad FC, hoc cA. F B ad
HE, hoc eAt SB, duplicaca c CA eius, Quam
habet AD adO R. Igirur quoniam raciorri.
plicata AD ad OR, ducta in duplicatam
eiuldem producic quincuplicacam, manifestu
est racionem ongulae ABCD ad ongulam
CFCM, quincuplicatam eAc eius quam ha-
becrecta AB ad K, HBCCM AB ad TIC, Sine AD ad CM. Ouod crac demon-
Arandum.
abus, polirisq conhschdus Hei Ce ponancur ordinarim BC &
FI, _ crectis FC, BHI que aequidistenc axibus; mixcilinex superticies
AEBHI _ C DFO, ducancur in leiplaS.
Dicocorpora producta ex ductu illo habere incer se quincuplicatam
rationem eius quam habet BC linea ad lineam FI.
Demonstratio.
Lutcate ploporrionalicer AFI, C CInR e
MI, X COnSICLANEUE R E L, M D N parallela
diamectis. cric islea lectangulum FL P ad FNP
hoc cst BCO ad BLO, relinca sIC ad ND
hoc ete C A ad L H. ergO vE A C, hoC CA R I ad
L, HBC Cst MN, HaCrIC F. L ad DN, vel RF
a M D. Lgitur AB ductum in (c ad CCF.
in Ce cdel, habecracionem compoticam ex (u-
pertele LLA F B de luperticiem GCDF, X Cx
alcdine HIB ad CFi alcicudinem secundum
cenorem discursus lacti praecedenci propolicione
sed balis AF BHL act BalIm C D F C, criplicacam
fersterem AE B sI ad CD I C. eandem racio.
nem habere quam parabola, ABOad parabolam
FC P:) ex ratio HB au CF, hoc eAt A C ad C li
du-
E RO POSITTO LLLAVIT
Abeant parabole ABC, CDP aequale lacus rectum inscruiens axi-
habec racionem eius quam habec linea AHI ad
CO, hoc est CB ad TF, (ostendimus enim su-
1
du