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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 759, page id 1815201908:0816
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HIIIHII
IN PL A N Y M
PROPOSITIO LXX. YI.
DOlicis iiidem circulis e se-
smentis velupra, ductile
C.C, DD parabolis, sIC AF
mulciplicarum in F. B aequale
CE in FD.
Dico C A ductum in E. D
corpus proterre aequale illi
quod orieur ex AF ducto in
DB.
Dem
LA E in E. D, vna cum AF in DB aqUabIEE C A in F D, vna cum AF. in
F. D; ablaco igitur communi AF in F. D remanebit C A in F D ductum, aqua
lc AF duco in D P, quod fuic demonstrandum. Vera Guee est propolicio s DD
ParabOla COnEINGAEFeCtAIM F. F.
P R O P O StT1O
TIrculum CF, cuius diamerer A A continsac linca D Da Guantans
ec aqualis diaerro AA, ponaeur aucem d AB Patabola cransiens
per D punctum contactus. Ducancurq intinica D C. B A F, normales ad
Dieo planum Db duetum in AB planum masnirudinem extibere
xqualem illi quae emersir ex C B ducto in BF.
Demonstratio.
InCX D A, C A, BA MMIIIC L PEC
Voniam cOrpUS exductu A F. in F. B Pax illi pOnituE quOdOTICLIEEx CE IN L. L,
il5
XXV II
deaco AB. sed A C guadratum a-
quale est quadraco AB vna cum re-
ctangulo CBF; igicur CBF, rC- B
ccangulum vnâ cum quadesco AB
aQUaTUE A B D rectangulo vna cum
quadraco AB; dempro isirur com
muniquadraro AB, MANCE DBL
rectangulo aequale rectansulum
CBF; acque ita omnia rectangula
CBF aqualia lune rectangulis om
nibus DB A. unde cum alcitudo A A
sc communis, D B ductum in AB. D
aequale est CB ducto in BP. Quod
tuie demonstrandum.
ron Ga MaeCtO AA, circulu nON concuS  C
Ldemlecce, aucremocior a circulo ponatur, ponaneur aurem tres proporcionales
D A, C A, B A, eadem manebic corporum aequacio, crieque A B ad parabolam, vri
lib. de parabola octendimus. Quodverboindicaste (uHicier.
dddd
porrionales; igirur A C. quadra
cum aquale cltectansulo LABI
eA DB A rectangulo vna cum qu
Corollariui