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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1023, page id 1815201908:1080
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Y N CYL A P A HC ABOLIC A.
Demonstratio:
Vcatur recta PD, et sume in axC F B.
quoduis punctum I. a quo ducta ordinacim
TFT, que proindle parallela eric ad AF, CZ TI in
cxlindri superticie ponatur recta FIC, quam
quia axi FS aequidistat, pacec eriam recte AF
requidictare. Ouoniam isitur TFI, FTG aequidi-
REANE P A, AF, crunc plana 2 ITTG, F AF P2
rallela: quae quoniam sccat planum F. AD, C.
runcbcommunes sectiones AF, R C parallela.
sane aurem _ TII, AF parallelae. ergo criam
CiK. FTI parallele. Demde quoniam parallela
PlanA F AF, S,ITIOK secac planum BF SD.
erune communes sectiones TR, F. S Parallele:
led eciam FTG ad axem F S, est paralIela. eF
SOTR, ITO ParallelX. Ergo OFI, IK paralle.
logrammum est. erso HII, CR aequales. ITis dc
monstraris huncin modum concludemus pro-
Policu. ducatur in exlindri superticie recta BD
cric haec parallela axi F S, acproinde eriam ad
TK eric Parallela. Igieur F. D est ad RD, vE
FB, ad IB, hoc eA, cvE quadratum A F ad qua-
C d. parabi
deacum TTT, hoc est ve quadratum A P, ad quadeatum CR. ergo d AC.D parabo- dibid.
la est. Quod crac demonttrandum.
P R OP OSITIO LX X X V1
ixlindrus parabolicus rectus ABCD (cuius balIS ABD, e balCOS
LaxIs E B, ordinatim verO pOsITa A P. D) Secerur primo sectione per
AD exhribence parabolicam vngulam F AOCBD, e alcera sectione
GFMI qua aequidisterbaM ABD.
Dico rngulam eoram AOCBD ad
partem rescistam G F. C. M, quincuplica-
iam eius habere racionem quam habet
AD, ad C NI.
Demonstratio.
DTuidaMCML PIOBOTCIOHALIEEK FECLE AV.
CM in quibuluis punctis I e L, de cri-
Sancur diametri TK, L N) de sectiones hane (e.
cundum lincas EB, TK, XTIF, L N exhiben.
ces in superficie cylindrica rectas lineas BC,
KO, _ FC, NP. lunsantur denique P C, 1O
ex FTC, L P. Ouoniam plana TRO, F BC
parallela secar planum A C D, crune commu-
hesfectiones IO, F C parallela. pari argumen-
EOpaFaHIClX sunE FTC, L P; X similia exunE
criangula F BC, TKO _HIEC, L. NP cum
tam anguli BF C, RIO quam anguli FBC,
TKO. icem eam anguli FTTC, NLD quam
FIFC, LNP aequales sinc. Deinde quia re-
Etx AD, CM Smilicer ex Constr. sunc diuilx,
eric rectangulum AID ad rectangulu AF. D,
ida
13
b.
5. Vndoc
Au e  t ut pes e  e  te  e e     e ete e et e   u    te  e e t   t    ps e  s  t tt   s e  te  t 1 e e s  1   .