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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 693, page id 1815201908:0750
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d
SPYR A L 15.
PROPOSITIO XXII.
lact pentets qdae saperiori propolicione,
Bcobb, it, ll esse proportionales.
Demonstratio.
TAnc propolicionemcos or ex meis lucubrationibus
demonstrare, eo quod Archimedis non Cc: illius de-
monctracionem reperies propolicione cencelima lepeua-
sesima libri nostri de parabola.
AILLIBALVR BETRAL
a
Dico semperarCuS DPC, COD, HOL
ese in continua analogia.
IIdem quoque poliris in spirali,
Demonstratio
Aecus DPC eAt ad arcum GOD, vearcus
et
13 c11).
Di lib. +. VE A C dd C G HvC AD ad DC. CII-
licer arcus FTOL eA ad arcum L S TT, DE aECIIS
CTN adarcum, CNhOCCAVE AL adLN, (-
HC AHI ad HI C. ergoinverrendo arcuS LS FI
est ad arcum L. Q H: ve C HI ad FI A, hoc CR
DE AD ad DC, (cum ex hypoch. CFI, AD, SinC
aquales) hoc est, sicuc iam olcendimus ve aecus
DPC ad arcum GOD: Scd aECuS FTS L PCF
prxced. aequalis est arcui COD; ergocciam ar-
cus GOD elt ad arcum FTOL. VEAECUS DPC
ad arcum GOD. TunE igItUE EreS AECUS D P C
GOD, HIO I inconcinua analosia. MModerat
demonstrandum.
Similicudo in eo polica quodarcus D P C extra
spiram, rectam DC extra parabolam; arcus
DOC incra spiram rectam C F intra parabolam; arcus denique FTO L iterum
exera spiram, rectah III. rursum quoque exera paTaBOLAM REPTA(ENCENE.
Cdrollarium.
11
LLCB Tadarcum BINYC hoc es peF 13. PaP-
X poluis licet interre eriam spacium spirali linea de circuli perimeiro D B C, Cet-
Minacum aequari spacio spiraL C ec arcu LII clauso: X in hoc symbolizacio
verseueral, Hatu ACrL, L. BK parabolica spacia inter se lunc aequalia.
kDEOSITIO, XXII
lepatabola ACB, qua bea B. Beau Mane C.D.
quas bilccainpunetis F.
eo Puticta Li aet tat ab atal lla il crtuiteta Etd.
Ddemon.