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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 185, page id 1815201908:0242
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O2
males
31
am B
InEcIII
CHI
AB
octet
2d
deli
B noI
Det
trabe
ircult
C
mb
nales
3, seb
ACi
CIR. C V V Y S.
Demonstratio.
Gacur reCtA BR peF GS OCCUEreNS AD in F
x perimecris in Ide K, cum rectangula AL. TI.
EF B,xqualialinc, rei ex rectangulaIL B, AT. Iis
_ RPB, ALD; cruncraciones blacerum recipro.
ca: hoc ett, eric AP ad L B, vE OP ad FTL, e
AL. ad F B, VEIF, ad L. I, vel KL adt L D: qua-
re cciam ve GT. ad I. FI, cita IG ad TTF, _ LR
ad F D, sivc LR ad F D. rursim cum sIE VE A C+ ad
G B, ita IC ad F G vel KC ad CC (Ob AGF.
CGB, Icem KGB, AG C. rectangulorum aequali
cacem) erit IG ad G L, VE RIad F C. QuaEC CX X
quo F. C ad F D ve Ci F ad FIF. Ouod fuir de-
monstrandum.
PR O POSIFIO XXVY
Puncto P exrra circulum posito, ducta ad cenerum ejuldem H
Linea AD dinila licineres continuo proportionales. quarum media
Sc lemidiameter BD, terria C D: crectaque ex C perpendiculari CF,
IUnGRnEUE AF.
Dico A F contingencem eNe _E COHETA.
Demonstratio.
DOnatuE DF. Ouoniam DC, DB id
eAt DF, D A, circum angulum Com-
munem ADF proportionales (WHE,
CrunE FCD, AFB criangula similia:
unde angulus AFD aequalis est anou-
10 FCD per hypochesim recto: quare
AF circulu corinoit. Ouod erat primu.
Tam vero sic AF contingens _
FC normalicer ad AD diametrum po-
Sira. Dico AD, BD. CD in concinua
cleanalogia: Cum enim AF siE Concingens et FD diameter, erie angulus A L D
rectus adeogue aequalis angulo F CD, est aurem angulus AD F communis crian-
sulis AF. D. FCD, igitur eriangula illa sumilia sune, et AD ad D F, id cst D B, VEDF
id DC. Ouod crac demonstrandum.
Est bac apollonus L. prim. propo s. 35. alicer demonistrata,
PROPOSITI LAVIIL
TOntingat AB linea circulum BC D: ductaque AD Per cen-
serum ponatur ad illam orchosonalis BF, quam in C. secet quxedam
AF, occurrens circulo in II, F:
Dico quadrarum AB, aequari rectangulo F C HI, rna cum quadra:
id GA.
35. Lerri
Demon.