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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1060, page id 1815201908:1117
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1060
GONOTDES P AR ABOETCVH.
De planis parallelis quae conoides parabolleum intersecant.
eR OPOSITTO CXLIN.
Celtoles patallele in conoide parabolico similes Aguras exhib ent qua
Demonstratio.
aequidistane bale sectiones, circuli sune, et
concequenter Agurae similes. Si cum baM
CONCUFFuNE, crunE elliples. octendendum ai-
cem est illas esse limiles. AaC plaMUM A C F peF
axem conoideos rectum ad plana parallela
ABC, D E FsCrUNErCCtR A C D Faxessectio.
nUm ABC, DF. F: divilis icaque AC, DF li-
neis proporcionalicer in FI e O, crectisque
HI B, C P normalicer ad planum A C F, secun-
dum illas rectas FIB, CF. plana ponancur b al
conoideos parallela, ac proinde recta ad planu
C AC: nempe plana IBR, L F M. quare de
per detin. 3. Vndec. eruncBFI, FC normales
ad rectas KD, AC, ML, DF. rectangulum
cAFTC est ad D C F rectangulu re CAtLFLK
ad L. CM rectagulum, hoc est quoniam BFB
P Cnormales Suncad diameeros DR, LMI, vE
quadracum AB ad OP. sune isicur ABC.
DE F elliples smiles iuxea definicionem et
Larum per axem conoidis rectum
ad quamlibet aliam sectionem, il-
lius sectionis axem exhribebie.
Demonstratio.
Vplex hic est calus: alter quo sectio ad quà
arium per axem est rectum, axi xquidi-
Aat; alcer quo axi conoidis occurrie.
Ponacur primum lectio C: C F, ad quam pla-
num Peraxem K AY rectum est, aquidictare
axi. per axem ponatur planci L ATI, parallelum
plano CCB, CruncerSO AB, C D communes
sectiones plani R AI cum planis F A FI, OCF
dparalLelE. Ouare cum AB, veporc axis rectus
Hc planO R FL, cric c e C D recta cidem pla-
nO. ergo CD normalicer (CCAE F C,, que est
communis leco planorum OCF, K F I. Inlu-
Pauns  C. L, Cidem paraltelum, plane
Lu ett. est aurem ex planum R AL
rectum
aALBCCUTTUIHE.
137. hA -
B140. hu-
E Por 138.
viis.
lixscon similium.
PR OPOSITIO CXLV.
per planum F A FT, F rectum cA planO RPI.
d16. undbs.