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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 411, page id 1815201908:0468
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c
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10
ARS TF, R TI A
Sectionis socum eo muluas parabolarum intersectiones
Geometrice desienat.
PROPOSITTO CXIV
Arabolam ABC cujus axis AD, contingat in B quXuIS BL, OC.
Lcurrens axi in E: poliraque ordinatim BD, ponatur B F normalis ad
B.F, occurrensaxi in F.
Dico DF lineam aquari dimidio laceris recti
quod axiinsernie.
Demonstratio.
Vmacur A C aequalis laceri recto. quoniam BD ordina-
eim ponicur adaxem, quadracum BD aequale est rectan-
sulo D AC: quia vero angulus, B B F rectus est, eric ee qu2-
deaco BD aequalea rectangulum E D F. iBicUE E D F. DAC
rectansula luneinter le xequalia, ex Ve F. D ad AB, sC A C+ est
ad D F: eAt aurem E D dupla bipsius AD, cum F B, SccOn.
ringens; igitur _ AC dupla eAt rectae D F: ad coque DF a-
qualis dimidio lateris recti. Ouoderar demonstrandum.
PROPOSITIO CXV.
Adem maence Routa: SIE A C latus rectum et
sillius dimidio eguerur DF: ponatur aurem or-
dinacim DB, ex B F. contingens, iungancurque BF.
Dico angulum E. B F rectum esc.
Demonstratio.
AVm E B sic Continsens, ex B D ordinarim pOSiT2, erie CR DaUPIA recte AD: _ C Ibid.
quia A C dupla ponitur D F, cric D AC rectangulu daquale rectangulo F. D fi: a10. out.
sed D AC rectangulo cquale est quadracum BD, isitur _ quadrarum D B aequale
EX ele-
ckrectangulo F DE, unde cum D B normalis POHAEUTipGE F, paret c angulu F. B F monis.
eerectum. Duoderac demonsteandum.
PROP03111D CAV1.
DArabolam AB C cuius axis AD, contingat linea
BE, conveniens cum axe in F: policaq3 BD ad F. B
rectam normalicer, dividatur ED bitariam in f.
DicoF A quartam parrem esse laceris recti.
Demonstratio.
riam Sicdluila, _ F. C+ in A (ob F B contingenLEM) VEF. D
ad BF, (IC P. C: eA ad P A, vnde ex residuum AF ad residuum
GD, VEcocum P. D est ad dimidium sui F F: AF igicur dimi-
dium est C D: hoc est quarra pars lateris rectii cum CD late.
risrectidimidium (Ic. Ouod etar demonctrandum.
FFF
C
DOnacur B Gordinacim ad axem; cuim ixitur E D in P Bita-
relo