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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 628, page id 1815201908:0685
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FL Y P F R, B, C
Porreat his policis altignare pun-
ctum M incerlectionis rectae AM
cum perimerro sectionis NCM.
Constructio es demonstratio.
CTaE Cx 28. huius rectA A MT parallela
OP, que concingat sectionem in O. de pro-
ducta verimque recta AM, vsque ad ay mpco.
10s, hac quadraro OP aequale rectangulum
RMO. Dico punccum M Core incerlecrio.
REM COIMLIHOM ECCEX AM cum lectio.
nC NCM. Quod paree ex 14 huiusy dc.
PROPOSITTOOLZZAMI
N omni cono sectiones hyperboli.
ex parallelae similes figuras exhibent.
Demonstratio.
PTE ABC criangulum per axem coni
aABD C, AEGuCF F C+ lectio bal aequi-
distans: ducta deinde A FI in plano crian-
guli per axem. quae circulorum diameeris
occurric in Iex HI, cum in eodem Anc
plano, erigatur ex FI recta FTOnormalis
ad BC, occurrens circuli perimetroin D.
ducacurgue D A, occurrec illa circuli
E F CPerimetro in P: iungacur aurem IF:
denique secundum HYD, EI lincas plana
ducantur parallela, qux cum AB linca
conveniane in R ∞ L, e A C in O) _R.
crunc isitur IFQ, RHIDa hyperbolX
quarum diametri ROF, L R FI ad quas
ordinacim polca (une IF, TID: quia vero
aequidistane F C, BC, bitem YF, ITD ve
AF ad FF, hC AHF eAt ad FTD: curlum
allumpeo in IO puncto quodam P, Pona-
EUF CX A PET P LInCA, OCCUITTENS L R qux
in eodem cum TK, Plano cM in O: po.
BANEUTAuEeM PMI, O N aequidistancestI.
FID: cum isitur IO, R IT aequidistent:
Ve OP adOL, sCRO cA ad RII; igi.
EAEKPO rectansulum est ad rectangu.
Ium RIO, VE LOR rectangulum est ad
rectagulum L HIR: ICdVE R PO adXIO.
Crtnius. Fectangulu C LHs Guauacu Ad quadraruM YF _E DE L. OR, rectangulum ad
cer Ar.
LHIR, lc OH quadracum ad quadratum L(D; quadracum isitur ON est ad HD,
ve PM quadracum ad quadracum Lf: de PM. EF lince proporcionalesrectis ON
HD: quia vero. Leeca suogue Propolrionales TunE RO, R HI: Agura
eM. OIE simileslunctiguris RONI, RFID: similes igicur d lunc lyperbola
redem.  NF, RN D. Quod ctt  .
altouins.
616. vndo.
mi
eROPOSITIO CLXXXV.
L LCC
    ue et   t te e te us e s  e  e  1  s e    e a    e e e te e   e e  et  e et i  e  e e   ate le  t    e  s e pi