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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 361, page id 1815201908:0418
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P A R A BC
Demonstratio.
DOEra per L punctum? LM paralleta
AC ducacur secundum LM; planum
LKM aequidistans plano baleos ASC:
circulus ioiEmE a CA L RNI, _ TTK, FC
communes incerlectiones b parallela. e
quia FF C ex hypochelinormalis ad dia-
merrum A C, ab eadem in R bitariam est
dinila, TTK quoquecnormalis est ad L. M,
_ d in Ibitariam divila. Ouod erac. dc.
monstrandum.
Corollarium.
JX hac proposrione paret, in parabola, si
diamecer rectam quandam bitariam se-
cec, omnes quoque eidem bislecta aquidi-
Cances bitariam secari. pater, cum P. D dia-
mecer scquae cunque, _ TIIK queuisaequi.
dictancum recte FO in P. bitariam divilae.
PROPOSITIO I
Acalinca, parabolam in duobus punctis secanie illius exhibere dia-
mecrum.
Constructio es demonstratio.
Tuicae A C bifariam in D POnaEuT F F xqui-
distans, qua limilirer bissecta in Cn duCaTUE PEF
C _ D, linca BC D: dico illam diamerrum esse
quaestam: SinOn, SE L D diameter, quae produ-
Eta sCCeE E F in NI: quoniam igieur L D diameTEF
Bitariam secar AC, bissecabic C quoque in M, F F.
ips AC xequidistancem, sed F P. bissecta ponitur in
D: cric igitur in D et M, bissecta linca FF. Ouod
fierinon pocest. non igitur LD diamerer est sed
BD. exhibuimusisicur, ecc. Ouod cxar Faciendum.
PRO P OSITIO IV.
Daco in perimetro parabola puncto, ad da-
LAcam diumerrum ordinacim ponere.
Constructio es demonstrario.
cin Pechaelto patabola AB C. datum punctum A, d
diamecer data sic BP. D ad quam ex A ordinatim 0.
Porterponere lineam ARC, iuneta AB producarur in
F, vE A B, BF aequales linc, d ex F demissa F C Paral.
leta BF, occurrac parabolae in C. iungacurque A C:
PATCE AC Fin P bitariam esse divilam, cum AF, bis-
secta sic in B, _c FC, BP aequidistenes a dacoigicur in pe-
rimetro parabole puncto, et c. Quod erac Faciendum.
b1b. Vnde-
C EX clemet
Xer.
Pro-
Corol.