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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 777, page id 1815201908:0834
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3C
61
1111I
EN P L A NY M. 1 C
Demonstratio.
Faatgudum HTEM ad GFEMEN rectangutum racionem habet composicam
ex HIF ad GFF, id est : FTK ad C R (quia C K. FTR, TR B prOPOrtiONALES TUNE) a L. DeprO
_E Ex FAEIOHO P. M ad MINT, id CA MIK adt NR (OB NR, MK. L R proporcionales) er
tar
Sedracio quoque rectanguli FIRM ad C KNV compolla t ex tallLL dd CR parabola
_E MK ad NR; igicur veTIIEM rectangulum clLdOm
TTKM ad GKN rectangulum; igiturve ex 4. huius colligitur, III ductum in L. N
2d G TI ductum in MNY, CAVE TIK ductum in RM ad C R ductum in R I. uod
etac demonecandum.
lnios
PROEOSITIOL.
AVper recta BB describanEuE ErOS
 parabola AB, CB, DB, qua-
rum diamerri per verricem sinccon-
rinux proportionales, e B B ordina-
rim ad eam sic polita.
DicoCBplanum ductum in (C X.
quari AB plano ducto in planu BD
ete
Demonstratio.
DVenneur quomis C A B D Paraltele ad
diamerros primo daras. Cum enim dia-
metri per verticem ponantur proportiona-
les, etiam diameeri AB, BC, BD cruNE
concinux: quare CB parabola ducta in
Ce aequalis AB parabola ductae in parabo.
lam BD. Duod tuic demonctrandum.
PROP OSIY1IO CXI.
DArabolam AB C cuius axis BD, e Ordinacim PBHICA ILC COIIHI S
L in B recta L. F. occurrens diametris AP, C F. in P. X F: dein per A de
B, irem B ∞ C parabola de(CribaNEUF QUAFUMI aXES LUINE A C, C F.
Dico CITluperticiem ductam in superticiem LK x quari FII plano
ducto in sc.
li LLLt 3
Demon-
1 1 . .   1   . . 1. . 1  . . t 1     te e t ta t t.  t    e ta       ate   e     u