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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 187, page id 1815201908:0244
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=244
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R
C IR C V E VS.
LICOEODLLIO LLLL.
Z A ducta (ICPer CMMIM CITCUM BOF sectA AB, que AD ad
87
ABraciocademlalione , adC B.clcbla eleoMaC. F,
Dico At concingere circulum.
Demonstratio.
Penim nOn COnTInSAE, POnatuF PCF L
contingens FG OCCUTrCNS AD in
Ci eric ergo per praecedencem DG ad
ErB, Ve DC ad CB; sed exhypochesi
veest DC ad CB, ita cAD A ad AB,
Tgicur ve DG ad GB siC D A ad AB.
e dividendo ve DB ad B C se DB ad
D A: Guodherinon porest; cum puncta
A _ C supponantur diversa: quare
F C non est tangens: (cd AF. Ouod
crac demonstrandum.
IUnSREUE AF.
ROTOAITIO XXXII
VIc AB recunque divila in C, ee ex A ducta quaenis AL, extri-
bens angulum E. AB rectominorem: Oporceacin linea AF, pun-
AtaalIgnarE F. d F, a quibus ad C ee B rectae eductae, angulos AFB,
AEB bitariam sCcCME.
Constructio e demonstratio.
PRoducta AB in D, HaC vE
AC ad C B, ita AD 2d
DB: _ suPCF C D diamCErO
descripeus sic circulus CFD:
cuiuscenerum H: Cccabit au-
cem ille, vel concinger rectam
AD vel neuerum peaectabit:
Sececisicurprimo A F lincam
in F ec F punctis: Dico illa
ense, que deliderantur: crecta
enim BC. perpendicularicer
ad diamerrum C D, JUngANEUF
AO, FC, FB, FFT: CK, BF. HT E: quoniam ipituF VE AC ad CB, ita est AD 2d
DB; a normalis sIE B C, diametro CD: erir AC recta concingens: circulum. Lr hain
vnde _ AH, CTI, b B FI, continux sunc proporcionales. est aurem Fi FI, vel F. FI, b27. huius
medix CH, aequalis; ergoc anguli AFB, AF B, Per rectaS C F, C P. divisi lunc bi- c u. dopro
fariam.
presionibum.
Ouod si circulum C ED contingat AC, in C: iunganeur punct a G B, GC, GTF
quoniam AHI, CII, B FI. Cune in concinuata rarione; e C. II linca media CFL, 2.
qualis est, deric AGB angulus bifariam divilus per rectam CC:
Manitektum aurem ck A A F. F recta circulonon occurric, ccMarE MaCeTIat PEO;
POLCam.
1 2bia
Corolla