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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1026, page id 1815201908:1083
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1026
d20. vaaee.
VNGV. L A P A K A BOLLC A:
Demonstratio.
lcca AB in L, dUCCAqUCL P. AL; Perre:
CEAS L MI, MO C dueacur planum taciens
in plano FK C: communem leccione RIC1,
ee in plano AC BIECTIODCM L. K C, in super-
Acic aucem chlindrica rectam PIC. Quo-
niam AM ex construccione parobolam AP. B
concingit in A, erBOAL B, PM aequales lune
linex. cum ergo planum FK C aquidistet
AM B, erit quoque O K D aequidistans L M.
ergo ec R I aequalis IHI, cum criangulum
T. MC, Similc AE KC C criansulo e L B ad
EM, VE RI ad IC, quare ceriam GF PAra-
bolam FKY concingic in F. Quod deimon-
Arandum Fuit.
PROPOSITTO XC.
DOnatur cylindrus parabolicus re
Ctus ABCD sectus quacunque
sectione perrectam DF in plano D AF
policam, extribente secrionem FOD.
DicoFGD esse parabolam.
Demonstratio.
iuita bitariam A D in E, sIEEB diame.
cer parabola ABD, per quam ponacur
planum parallelum ad AF, exhibens commu-
nes incerlectiones FHI. HIC, BC. Deinde Aa-
CUAEUE PK aequidistans L A, eric IK ordina-
eim posica ad diamerrum E. B. secundum LK:
tiac sectio aequidistans AF, occurrens plavo
ECD secundum rectam MNV, qux proinde
Parallela erir rectE DF per 16. II. exhribens
precerea communes incerlectiones cum cylin-
dri superticie KM, ON Pacallelas incer (C; Po-
licaigitur ex N recta NP, qux xequidistetOK
Crit OR P paralletogrammum, ideoque PN,
aequalis est K O, d quia bitariam dinila cAO R
in I, diuidetur quoque PN, bitariam in O per
TE, communem incersectionem planorum
EBC, _ ORM qua IE aequidiltAE RM: 20
proindecciam MN bifariam dinila est in L,
eA vero d FD bilecta in II.
Deinde quoniam cplindeus ex hypoc. rectus
eA, CrunEangULi F AD, MK O hOC CA MPN.
recti rurlum quia A F, F D aquidistane PM,
M N, d anguli A F D, P MI N ParES CrUNE crIan.
Sul2 ergOD AF, N P M aeguiangula lunE. FrgO
DE AD ad PN, siC FD ad M N. ergoquades-
cum AD es ad quadracum PN, hoc CARO.
DE quadrarum FD, ad quadEAEUI MN. sed
quadra.