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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 695, page id 1815201908:0752
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DC
ac
XMI.
DC
CUH
ecta
FUM.
hob
SD IR AL +8.
CAC A HI, ad IE A NY hOC CsVEG A ad K A. D WATE CHIM CK HY POTHCHOM
bilecta sic in K, circulus duplus ericellipseos, sed etiam lpiralis prima
dupla est sccunde. Frgo ve circulus ad elliplim ica spira prima ad securii
dam: ee permucan do ve circulus se habet ad spiram primam hoc est suam.
ica elliplis ad secundam hoc elteriam ad Tuam, ac proinde licur circulus
eriplus est lui spacii nempe spiralis spacii, sic e ellipss cripla eric spiralis
spacii lui A IFB. Nerird icaque dicecur spiralis elliprica. Quod crar de-
monstrandum.
PROPOSITIO XXIV
Dauslelosrammum rectansulum AF.
L hrabeac latetae, CE limilicer divila
in punctis B, d D, ductilque B O paral-
lelis ad AHI, ex A per puncti D delcri-
bancur rectae quae parallelis occurrane in
punccis C.
Dicopuncta C esse ad parabolam.
Demonstratio
Darallelarum vna BC produeaent donec oc
CUITEAC ipA AF in puncto F. AF CA ad F P
ve AB ad BC, scd AB est ad B C VE C D ait D F,
sunc enim AC, F F. Similicer secta ex hypochesi
ErgO AF est ad FF G ve CD ad DP; hoc est
(quemadmodum exelem. Facile demonstrabicur)
veBGadCF. Ergo paret ex 5. Archim. de qua-
dracura parab. punctum C esse ad parabolam. Si-
milicer ostendemus de quibuslibet punctis D. Parecigicur propolicionis reritas.
APPLICATIO SPIRALL
punces D, D, a B, B: Duccis aurem
exCEHErO A ad pUIHEtA D Fecris A, D
cenero A per lingula puncea B ducan-
eurarcus BC; ea ratione quain Rour
exhibec, occurrences linels AD
Puncris, C:
ir
DEripaeria primaculi eiulque ra-
dius AC Crmilirer sine diuita in
Dicopuncta C ad spiralem esse
emonotro.
ria ehimradius AC, dPeripheria cir.
culi similicer sinc diuilx in puinctis, B, B
s DD, crir ve AB, 2d BC, hoc cAvEAC
ad CD, ica arcus C Dad religuam periphe-
riam DDC. Ex quo parec punctum C5 ad
69
quis et punctis.
retiptie
spiralem esse. Similicer oltendemus de teli.
a  eo ca, score  pta pune Patis plcto A in parabola, radius A C; e
Cct 
  se t  es e e e te    t tes e  e ite ste us 1t. e t  e. i Ae  s. . .  .  1 11