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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 236, page id 1815201908:0293
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PROL E GOM E N A
Scholion.
Demonstratio.
N cono recto ABC incerse-
cent sese muruo in F puncto
quaevis balesF F G, IF R erian-
sulorumnon per axem FBC
IB R, _ CIFCA DF, inteF cen-
crum D ex F punctum incerie
ctum describe circulum DEI
LF: dico perpendiculares L
verrice B ductas ad FF. C,
TF K, incidere in peripheriam
DE B. jungancur enim BL.
BFT, DT, DTI. eric angulas
DE F in Cemicirculo rectus;
vnde rectae IP. X I. K a qua-
les crunt; est aurem recta B I ∞
qualis BK; igicur ctiam BI
normalis est ad rectam IK. A-
milirer ostendemus P normale
esse BHY ad F C. crgo omnia
triangula per F punctum et
verricem ducca normales luas
inveniene inperimetro circelII
DE F. quod oporruit demoi
Arare.
Vm intersectionis panclum E. aut intra basim dari possit, aur inperimerro basis, au extre
basim, fit vt hic triplex casus oriatur. primus, quo circellus D E. F totus base comprehen-
ditur. Secundus quo idem occurrit puncto perimetri AIC eundem contincendo: in quo casut
quarea est pars circuli, qui fungitur basis vice coni ABC: tertius vero quo extra basim dif-
fusus circulum baseos secat in duobus punctis; se d quia triplex hic casus diversitatem nec in ip (a
constructione, nec in demonstratione inducit, hinc silentio ram in propositione quam demon-
stratione suppressus est.
P ROPOSITIO XV.
cono recto exhibere criangulum quod per apicem coni ex pun-
ctum datum sive inera, sine exrra coni balim cranseat, HabCaE VerO
ad criangulum per axem dacam rationem.
Constructio es demonstratio.
esto AB C reccus, d per cius axem tacto erian suro B. C decur punctum
am D. OPOTTCAE verO per punccum D, de verricem coni contticuere
rsusum L BL quod ad criansulum per axem A B C racionem habeac I ad R
dacam. Inveniacur per duodecimam criangulum Y. BMI, quod habeat ad criangu.
TAMI AB C rationem I ad R. DeindC CX D pUNCEO dUCATUE DF F, SIC VE FF lB
equaS ipAI LM. per ca guxe de circulorum b proxrieracibus conscripsi: X secun
culis. dum P F _ B, agatur planum, hoc iplum exhibebit criangulum BostulacuM BP. P.
erie
  e i  i es  1 1e    e    . 1.    p oe e e  e        u  te t A    e ua u au    e