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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1031, page id 1815201908:1088
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V N GVL A P AR ABOLTCA.
Demonstratio.
DErBs. hurus LM D OTT. Parabola est,
diameerum habens AV. deinde
quia parallela plana IBFI, M F. C lc.
Cac planum parabolicum IMDOFI, c.
runc a sectiones IFI, MG paralIClX.
Ouare cum TFI sic ordinacim posca 2d
AD, CrIE X MC. ducacuriam recta
F F, cric haecb ParaIlela AB. crgoBD
ad F D, vE AD ad FD, scd AD est ad
FiD, in duplicata cius quam habcc I A
adMF. erzo ecratio BD ad FD, hoC
est rario 4 ad 1. duplicata est racionis
TA ad MF. ErgOLaTIO TA AdMIF, Ca-
dem estcum rarione dupla, ae inver-
tendo MF, est adTA, ve F 2d2. conci-
AmccurracioF, ad 2, per (ex terminosni-
mirum L. 2, 4, 8, 10, 32. Frit ergo racio L.
ad 32, quincuplicaca racionis F, ad 2, b0c
estracionis M Fad IA. Acqui raciovu-
Sule NDO adrigulam IDFI, quin-
cuplicata c est racionis MIF, adIA. EF.
soongula MIDC cst ad rngula TD FI
vc 1, ad32. Ouoderacdemonstrandum.
PROPOSTTIO XCVI
Ngula parabolici exlindrirectisit
divita sectione DEB, Per axem
parabolae AF C extribence in cylindri
superticic rectam E B, iunetisque AF.
C E HanEplanA PET A F B _C F. B, OC.
currencia bali vngulari ABC. secun-
dum lincas AB, B C; deinde per has
rectaS AB, BC plana ponantur divi-
dencia lineas NO, KI decerminatas in
92. huiusbitariam, Formacia in cylindri
superticie lineas curuas AOB, BFC.
Dico vngulam EOTaM AF BC ma-
iorem esse prramide inclula AE BC,
una cu lesmeto cylindrico C FBIHIC.
magnicudinibus qua superticicbus
comprehenduntur AGB, ANIB; e
CFB, CLB.
Demonstratio.
37
D
Scensum elt a leomencum Cnnauum
OBa(COSCR F. et alcirudinis R lbitariam
dinisum esse plano BF C. quod ducirux per punctum F in quo bilecarur recta KI. C.
mulicer
d Coroll. 2-
D2 huins.
o e t ptet s t  e ae at ett Ae e   . es   ate se te te st  e e pt      oue      ee  t ts   s    s  s  1e. 1e e 1  1  1 e 1. 1) 1 1 1 1