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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 175, page id 1815201908:0232
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E ve
ulum
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pelleca
BC0
ei AH
0
duobu
11 due
ec p.
XI
alupe
eA136
GIR C V L V S.
bali eriansus deleripei educaneur rectae occurrentes perimerris in D e F.
Dico puncta B, B, E, in directum constirura elle.
Demonstratio.
DRimo vertex crianguli ABC in perimetrO BE
circuli, qui super bali A C, delcribicur. iungan-
curque DB, P. B. OUONIAM E D, PEF CCNETA F_ C.
acta est, secabir bitariam, cum a recta A B, cum arcum
AD B. eadem quoque racione radius F FL, diuidec bi-
fariam cum BC rectam, cum B F C arcum. IgituE
Cu ADB, B F. C similia sinc sermenca anguli A BD
CBE. Cimilibus arcubus insistences, aequales (UnE:
quare ex angulus ABD equalis est angulo BC F,
qui2. F B arcus aqualis estareui P. C. est aurem an-
sulus ABC aquales angulo BR C ex hypocheli, igicur anguli ABD, ABC.
CBF. aequales sunerribus angulis crianguli B P C adeoque duobus rectis xquales.
quarelinea DB, BB b sunc in directum.
Sccundo B apex crianguli, Cuper bati ABC Crc-
cti, incra lesmenci AK C aream CadAF; PTOdUICANEUT
AB, CB, cadec illa in comunesc circulocum interse.
ctiones I_R. Duoniam L. C, F. II linca cenera coitin-
Bune circulor sele INECFICCANCIUM CTUHEAECUS AD I,
RF C in D ex F Bitariam adiuisi, vnde AB D, DBI
anguli, ITCm RBF, CBP sunc aequales, sed ec an-
suli ABI, C BR ad verricem oppolici quoque inter
sc aequantur, isitur _c angulus ABD, ipSI RBF 8
TBD, angulo F. B C est aequalis. quare in directum
IMED, B, E puncta. Quodexar demonstrandum.
PROPOSITIO XIV.
Vodsi super ABC criatsuH caletous lesmenca circulorum limi-
sdelcripca tuerint; a recta qua dant Le per  reulem acta:
circulorum AF B, DDC, perimetris occurrat in D, de F.
Dico lineas inter cauas circulOrUM A F. B, BDC peripherias e exti-
mam circuli ABC incerceptas, aquales elle.
Demonstratio.
ee L.DContinga Clculum ABC in B.
JUngancurque AE, C D: Ouoniam R B el
contingens, eric angulo R B A, aequalis can-
sulus ACB: eadem raciome angulus
C AB aequalis est angulo CB D: vnde cum
anguli B A C, BC R per BypOchCSIM SInE
requales, crunc quoque ansuli E B A; CBD
incer se aequales. sune aucem ee anguli AF B,
CDB, (0b AR B; CD B Scomenca Cimilia)
aquales, insuper ex AB, linca aequalis lince BC, a AE. B, Ctianeu-
SCCHHCO F D POnATUE COnCIIISCHS, Cllanoulo A B C existence Scaleno, dicL L
in B bitariam sccari. sic A B lacus, altero B C. maius, et P D contingeni, po-
naLUE
Ie primo criangutu Lelium ABC;
10 CBD SE F B lacus, laceri BD cAaequale
32. Verris
  i ea
e