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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 844, page id 1815201908:0901
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84+
OVCFVS PL AN
Demonstratio.
 Ectx FO aGuaes uma ICcus XC, quadima stur LO aequalia lune
aas. huius.  Quadraris AC id est rectangulis (iF. V. planumisitur T9 a ductum in sc x
quatur L. C plano auetora LV.
PROPOSTTIO CCXIX.
NIrCUH ADBC diamerrum AB, SCCCE OrFIIOS MalIter recta quaenis
cur, quem in L lecene quoruisrectx DL. F occurrenres circulo AEB in I
punctis, per quae normales ad AB ponancur FC. Franc deinde D P. lineis,
aquales L. K, ica polica ve a diamerro AB bisecentur in C. Rectis aurem
DF, aquales AanEKN d L. I.
Dico lBNpuncta, irem C IE L. D, ad veras esse parabolas.
LCD: cenerogs B, intervallo BC, Sine B D circulus C E D delcriba-
Demonstratio.
YcanTUrreAtx B D, D A, A F. OuoniaM Au BUIUS DD A LCCUS CA, vrpote in se
Mirculo constitutus, estque B D. Semidiamerer circuli C L.B, C D Alatis et
ve BF ad bt, ellam C L C dd 6L, BC BX ad BF3 adtebde quadratum C 1, 4d
quadra.
c Perele
menta.
b92. ccrriy. circulu C F. D, in D. Ouare anguli inMetes arcubus D F, aquantur B angulis A D F
arcusisicur D P limiles luntatetos AL. LGOTBCCnIX DLIOCCHS A L, abCB9
ec quadeaca D F quadractses proporcenaa unc: sed quadeacum AI cst ad qua
dracum AF ve crectangulum B A C ad B A C id est ve recta AC ad reclam 
Ergo quadratum D F est ad quadracum D R, hoc est ex hypochen quaaacu AL
ad K L, hocest R C est ad quadratum R G, ve A G ad A G; puncta igieut L au r.
tam sunc parabolam. Idem eodem discursu ostendemus de punctis L.
Ouod adem puncta II, N NY eciam ad veram sint parabolam, Ec demonstro. SupCr
BD descripiolemicirculo se canre BF in FI, iunsantur B FI. Ouoniam anguli BHD
Poliri in semicirculo lunt recti, criant A DIIL ICCLI crunE, adcoque aequales.
lunc aurem d angm mconemLaccmemo aguaes. crgocriansula BFHI
Similia (UnC; CroO DF 2d B L, VE HIF ad FII. Deinde, quoniam recte B FTCx Cen-
ero B circuli E B, hornatesm ad DF, (aneum ehim B FTD sunc in Cemicirculo)
CrUNE DF. BiscClG M FT. OuarC cum CtIam RL Cx HyP. BHCClE MC in C, lincquo
ae qualesips DF, crunt D HIxquales P. C. Aequi ex liyp. EOEX D F aequantur coris
T. I. ergo reliquae FIF Tenss C Lauas. Guta Ieteur sanoendi ese FTF ad HIF,
eorott